CINXE.COM

(PDF) Percolation on Fractal Networks: A Survey | Alexander Balankin - Academia.edu

<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="KVlAi39TYfSzkp2xuHCG8K4yyoYBZyjypbKs0pHLIrgWvKqEMlXuqE+WUvyOWhtB2O9//PQcVpc8XHBDQdGcYw==" /> <meta name="citation_title" content="Percolation on Fractal Networks: A Survey" /> <meta name="citation_publication_date" content="2023/03/05" /> <meta name="citation_journal_title" content="Fractal and fractional" /> <meta name="citation_author" content="Alexander Balankin" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey" /> <meta name="twitter:title" content="Percolation on Fractal Networks: A Survey" /> <meta name="twitter:description" content="Academia.edu is a platform for academics to share research papers." /> <meta name="twitter:image" content="https://0.academia-photos.com/31879133/53408813/41535800/s200_alexander.balankin.gif" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey" /> <meta property="og:title" content="Percolation on Fractal Networks: A Survey" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Percolation on Fractal Networks: A Survey" /> <meta property="article:author" content="https://independent.academia.edu/AlexanderBalankin" /> <meta name="description" content="Percolation on Fractal Networks: A Survey" /> <title>(PDF) Percolation on Fractal Networks: A Survey | Alexander Balankin - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '1bbbda12a33dda6b7b03832db85b3e64a22beabd'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732757133000); window.Aedu.timeDifference = new Date().getTime() - 1732757133000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"The purpose of this survey is twofold. First, we survey the studies of percolation on fractal networks. The objective is to assess the current state of the art on this topic, emphasizing the main findings, ideas and gaps in our understanding. Secondly, we try to offer guidelines for future research. In particular, we focus on effects of fractal attributes on the percolation in self-similar networks. Some challenging questions are outlined.","author":[{"@context":"https://schema.org","@type":"Person","name":"Alexander Balankin"}],"contributor":[],"dateCreated":"2023-12-31","dateModified":"2024-01-22","datePublished":"2023-03-05","headline":"Percolation on Fractal Networks: A Survey","inLanguage":"en","keywords":["Statistical Physics","Fractal"],"locationCreated":null,"publication":"Fractal and fractional","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Multidisciplinary Digital Publishing Institute"},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-102fa537001ba4d8dcd921ad9bd56c474abc201906ea4843e7e7efe9dfbf561d.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-8d679e925718b5e8e4b18e9a4fab37f7eaa99e43386459376559080ac8f2856a.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-3cea6e0ad4715ed965c49bfb15dedfc632787b32ff6d8c3a474182b231146ab7.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/text_button-73590134e40cdb49f9abdc8e796cc00dc362693f3f0f6137d6cf9bb78c318ce7.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&amp;family=Gupter:wght@400;500;700&amp;family=IBM+Plex+Mono:wght@300;400&amp;family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&amp;display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-10fa40af19d25203774df2d4a03b9b5771b45109c2304968038e88a81d1215c5.css" /> </head> <body> <div id='react-modal'></div> <div class="js-upgrade-ie-banner" style="display: none; text-align: center; padding: 8px 0; background-color: #ebe480;"><p style="color: #000; font-size: 12px; margin: 0 0 4px;">Academia.edu no longer supports Internet Explorer.</p><p style="color: #000; font-size: 12px; margin: 0;">To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to&nbsp;<a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.querySelector('.js-upgrade-ie-banner').style.display = 'block'; }</script> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span &nbsp;&nbsp;="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "1352427c417282277c0c94f1e481228e741ce3beafa725eadb48d59be0978e1c", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="&#x2713;" autocomplete="off" /><input type="hidden" name="authenticity_token" value="nxhGtqv9f7aZqBbKhLQA1K+u3pbMBpfkeQhekiJPdwCg/ay55vvw6mWs2Yeynp1l2XNr7Dl96YHg5oID8lXJ2w==" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="&#x2713;" autocomplete="off" /><input type="hidden" name="authenticity_token" value="H/eUtX4ksTbKVtGohS2FpvR2CFPAmpdXh4Xz3tjrIwAgEn66MyI+ajZSHuWzBxgXgqu9KTXh6TIeay9PCPGd2w==" autocomplete="off" /><p>Enter the email address you signed up with and we&#39;ll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><input class="btn btn-primary btn-block g-recaptcha js-password-reset-submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" type="submit" value="Email me a link" /></form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account?&nbsp;<a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script> <div class="header--container" id="main-header-container"><div class="header--inner-container header--inner-container-ds2"><div class="header-ds2--left-wrapper"><div class="header-ds2--left-wrapper-inner"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="hide-on-desktop-redesign" style="height: 24px; width: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hide-on-mobile-redesign" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a><div class="header--search-container header--search-container-ds2"><form class="js-SiteSearch-form select2-no-default-pills" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><input name="utf8" type="hidden" value="&#x2713;" autocomplete="off" /><svg style="width: 14px; height: 14px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="search" class="header--search-icon svg-inline--fa fa-search fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M505 442.7L405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9 0 208 0S0 93.1 0 208s93.1 208 208 208c48.3 0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9 0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7 0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7 0 128 57.2 128 128 0 70.7-57.2 128-128 128z"></path></svg><input class="header--search-input header--search-input-ds2 js-SiteSearch-form-input" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" /></form></div></div></div><nav class="header--nav-buttons header--nav-buttons-ds2 js-main-nav"><a class="ds2-5-button ds2-5-button--secondary js-header-login-url header-button-ds2 header-login-ds2 hide-on-mobile-redesign" href="https://www.academia.edu/login" rel="nofollow">Log In</a><a class="ds2-5-button ds2-5-button--secondary header-button-ds2 hide-on-mobile-redesign" href="https://www.academia.edu/signup" rel="nofollow">Sign Up</a><button class="header--hamburger-button header--hamburger-button-ds2 hide-on-desktop-redesign js-header-hamburger-button"><div class="icon-bar"></div><div class="icon-bar" style="margin-top: 4px;"></div><div class="icon-bar" style="margin-top: 4px;"></div></button></nav></div><ul class="header--dropdown-container js-header-dropdown"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/login" rel="nofollow">Log In</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/signup" rel="nofollow">Sign Up</a></li><li class="header--dropdown-row js-header-dropdown-expand-button"><button class="header--dropdown-button">more<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-down" class="header--dropdown-button-icon svg-inline--fa fa-caret-down fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z"></path></svg></button></li><li><ul class="header--expanded-dropdown-container"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/about">About</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/press">Press</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://medium.com/@academia">Blog</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/documents">Papers</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/terms">Terms</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/privacy">Privacy</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/copyright">Copyright</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/hiring"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="header--dropdown-row-icon svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg>We&#39;re Hiring!</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://support.academia.edu/"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="header--dropdown-row-icon svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg>Help Center</a></li><li class="header--dropdown-row js-header-dropdown-collapse-button"><button class="header--dropdown-button">less<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-up" class="header--dropdown-button-icon svg-inline--fa fa-caret-up fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z"></path></svg></button></li></ul></li></ul></div> <script src="//a.academia-assets.com/assets/webpack_bundles/fast_loswp-bundle-71e03f93a0fba43adc4297a781256a72e56b0d578ac299a0d81b09f4c7bc6f70.js" defer="defer"></script><script>window.loswp = {}; window.loswp.author = 31879133; window.loswp.bulkDownloadFilterCounts = {}; window.loswp.hasDownloadableAttachment = true; window.loswp.hasViewableAttachments = true; // TODO: just use routes for this window.loswp.loginUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F112693132%2FPercolation_on_Fractal_Networks_A_Survey%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F112693132%2FPercolation_on_Fractal_Networks_A_Survey%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":109843759,"identifier":"Attachment_109843759","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":112693132,"created_at":"2023-12-31T15:42:18.980-08:00","from_world_paper_id":247215481,"updated_at":"2024-07-26T07:07:01.724-07:00","_data":{"publisher":"Multidisciplinary Digital Publishing Institute","publication_date":"2023,3,5","publication_name":"Fractal and fractional"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Percolation on Fractal Networks: A Survey","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [31879133]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;swp-splash-paper-cover&quot;,&quot;attachmentId&quot;:109843759,&quot;attachmentType&quot;:&quot;pdf&quot;}"><img alt="First page of “Percolation on Fractal Networks: A Survey”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/109843759/mini_magick20231231-1-y3b799.png?1704066202" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Percolation on Fractal Networks: A Survey</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="31879133" href="https://independent.academia.edu/AlexanderBalankin"><img alt="Profile image of Alexander Balankin" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/31879133/53408813/41535800/s65_alexander.balankin.gif" />Alexander Balankin</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2023, Fractal and fractional</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">21 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 112693132; const worksViewsPath = "/v0/works/views?subdomain_param=api&amp;work_ids%5B%5D=112693132"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { const viewCountNumber = Number(viewCount); if (!viewCountNumber) { throw new Error('Failed to parse view count'); } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (viewCountBody) { viewCountBody.textContent = `${commaizedViewCount} views`; } else { throw new Error('Failed to find work views element'); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;continue-reading-button--work-card&quot;,&quot;attachmentId&quot;:109843759,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey&quot;}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;download-pdf-button--work-card&quot;,&quot;attachmentId&quot;:109843759,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey&quot;}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="109843759" data-landing_url="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="8100594" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8100594/Percolation_on_a_multifractal">Percolation on a multifractal</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15699231" href="https://ucu.academia.edu/EliasdeFreitas">Elias de Freitas</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We investigate percolation phenomena in multifractal objects that are built in a simple way. In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability. Depending on a parameter characterizing the multifractal and the lattice size, the histogram can have two peaks. We observe that the percolation threshold for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Percolation on a multifractal&quot;,&quot;attachmentId&quot;:48214723,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/8100594/Percolation_on_a_multifractal&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8100594/Percolation_on_a_multifractal"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="88751162" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks">Percolation on infinitely ramified fractal networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="241020478" href="https://independent.academia.edu/OrlandoSusarreyHuerta">Orlando Susarrey Huerta</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters A, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Percolation on infinitely ramified fractal networks&quot;,&quot;attachmentId&quot;:92667243,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="61395145" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models">Universal Behavior of Connectivity Properties in Fractal Percolation Models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52848710" href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Electronic Journal of Probability, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Universal Behavior of Connectivity Properties in Fractal Percolation Models&quot;,&quot;attachmentId&quot;:74438601,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="118703795" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/118703795/The_geometry_of_fractal_percolation">The geometry of fractal percolation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="132755638" href="https://bme.academia.edu/KarolySimon">Karoly Simon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;The geometry of fractal percolation&quot;,&quot;attachmentId&quot;:114268428,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/118703795/The_geometry_of_fractal_percolation&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/118703795/The_geometry_of_fractal_percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="19958827" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/19958827/Percolation_as_a_fractal_growth_problem">Percolation as a fractal growth problem</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="41222335" href="https://independent.academia.edu/AStella1">A. Stella</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="40828295" href="https://independent.academia.edu/LPietronero">L. Pietronero</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1990</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Percolation as a fractal growth problem&quot;,&quot;attachmentId&quot;:41239891,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/19958827/Percolation_as_a_fractal_growth_problem&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/19958827/Percolation_as_a_fractal_growth_problem"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="100796622" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/100796622/Fractals_meet_fractals_self_avoiding_random_walks_on_percolation_clusters">Fractals meet fractals: self-avoiding random walks on percolation clusters</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67950298" href="https://independent.academia.edu/ViktoriaBlavatska">Viktoria Blavatska</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Procedia, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Fractals meet fractals: self-avoiding random walks on percolation clusters&quot;,&quot;attachmentId&quot;:101516306,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/100796622/Fractals_meet_fractals_self_avoiding_random_walks_on_percolation_clusters&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/100796622/Fractals_meet_fractals_self_avoiding_random_walks_on_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="5447810" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation">The Fractal Dimension of the Minimum Path in Two- and Three-Dimensional Percolation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;The Fractal Dimension of the Minimum Path in Two- and Three-Dimensional Percolation&quot;,&quot;attachmentId&quot;:32571072,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="27521595" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d">New percolating structures in random fractals in 2d and 3d</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51612869" href="https://independent.academia.edu/MichelPerreau">Michel Perreau</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;New percolating structures in random fractals in 2d and 3d&quot;,&quot;attachmentId&quot;:47776883,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="113685008" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/113685008/A_probabilistic_approach_to_the_site_percolation_problems_using_fractal_tree">A probabilistic approach to the site percolation problems using fractal tree</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="226595100" href="https://independent.academia.edu/JulioG%C3%BC%C3%A9mez">Julio Güémez</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chaos, Solitons &amp;amp; Fractals, 2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A probabilistic approach to the site percolation problems using fractal tree&quot;,&quot;attachmentId&quot;:110582645,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/113685008/A_probabilistic_approach_to_the_site_percolation_problems_using_fractal_tree&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/113685008/A_probabilistic_approach_to_the_site_percolation_problems_using_fractal_tree"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="69177732" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation">Fat fractal percolation and k-fractal percolation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52848710" href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Latin American journal of probability and mathematical statistics</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider two variations on the Mandelbrot fractal percolation model. In the k-fractal percolation model, the d-dimensional unit cube is divided in N^d equal subcubes, k of which are retained while the others are discarded. The procedure is then iterated inside the retained cubes at all smaller scales. We show that the (properly rescaled) percolation critical value of this model converges to the critical value of ordinary site percolation on a particular d-dimensional lattice as N tends to infinity. This is analogous to the result of Falconer and Grimmett that the critical value for Mandelbrot fractal percolation converges to the critical value of site percolation on the same d-dimensional lattice. In the fat fractal percolation model, subcubes are retained with probability p_n at step n of the construction, where (p_n) is a non-decreasing sequence with \prod p_n &amp;gt; 0. The Lebesgue measure of the limit set is positive a.s. given non-extinction. We prove that either the set of co...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Fat fractal percolation and k-fractal percolation&quot;,&quot;attachmentId&quot;:79372658,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;continue-reading-button--sticky-ctas&quot;,&quot;attachmentId&quot;:109843759,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;download-pdf-button--sticky-ctas&quot;,&quot;attachmentId&quot;:109843759,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_109843759" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="21034819" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/21034819/Dynamics_of_swollen_fractal_networks">Dynamics of swollen fractal networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="10054032" href="https://ufv.academia.edu/AlvaroTeixeira">Alvaro Teixeira</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Europhysics Letters (EPL), 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Dynamics of swollen fractal networks&quot;,&quot;attachmentId&quot;:41681620,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/21034819/Dynamics_of_swollen_fractal_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/21034819/Dynamics_of_swollen_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="95789232" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/95789232/Towards_a_Better_Understanding_of_the_Characteristics_of_Fractal_Networks">Towards a Better Understanding of the Characteristics of Fractal Networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67779154" href="https://independent.academia.edu/MarcellNagy1">Marcell Nagy</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cornell University - arXiv, 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Towards a Better Understanding of the Characteristics of Fractal Networks&quot;,&quot;attachmentId&quot;:97873366,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/95789232/Towards_a_Better_Understanding_of_the_Characteristics_of_Fractal_Networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/95789232/Towards_a_Better_Understanding_of_the_Characteristics_of_Fractal_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="112693131" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks">Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31879133" href="https://independent.academia.edu/AlexanderBalankin">Alexander Balankin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters, 2019</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks&quot;,&quot;attachmentId&quot;:109843796,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="5447256" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447256/Fractal_Behavior_of_the_Shortest_Path_Between_Two_Lines_in_Percolation_Systems">Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems&quot;,&quot;attachmentId&quot;:32570516,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/5447256/Fractal_Behavior_of_the_Shortest_Path_Between_Two_Lines_in_Percolation_Systems&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5447256/Fractal_Behavior_of_the_Shortest_Path_Between_Two_Lines_in_Percolation_Systems"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="100796699" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/100796699/Walking_on_fractals_diffusion_and_self_avoiding_walks_on_percolation_clusters">Walking on fractals: diffusion and self-avoiding walks on percolation clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67950298" href="https://independent.academia.edu/ViktoriaBlavatska">Viktoria Blavatska</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and Theoretical, 2008</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Walking on fractals: diffusion and self-avoiding walks on percolation clusters&quot;,&quot;attachmentId&quot;:101516378,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/100796699/Walking_on_fractals_diffusion_and_self_avoiding_walks_on_percolation_clusters&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/100796699/Walking_on_fractals_diffusion_and_self_avoiding_walks_on_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="48351108" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions">Shortest-path fractal dimension for percolation in two and three dimensions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="282899" href="https://umich.academia.edu/RobertZiff">Robert Ziff</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Shortest-path fractal dimension for percolation in two and three dimensions&quot;,&quot;attachmentId&quot;:67009732,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="89896103" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters">Physical Properties of a New Fractal Model of Percolation Clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31313596" href="https://independent.academia.edu/AAharony">A. Aharony</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Physical Properties of a New Fractal Model of Percolation Clusters&quot;,&quot;attachmentId&quot;:93609890,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="7" data-entity-id="74007298" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74007298/Diffusion_and_fracton_dimensionality_on_fractals_and_on_percolation_clusters">Diffusion and fracton dimensionality on fractals and on percolation clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="36407694" href="https://biu.academia.edu/SHavlin">S. Havlin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Diffusion and fracton dimensionality on fractals and on percolation clusters&quot;,&quot;attachmentId&quot;:82317053,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/74007298/Diffusion_and_fracton_dimensionality_on_fractals_and_on_percolation_clusters&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/74007298/Diffusion_and_fracton_dimensionality_on_fractals_and_on_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="4467161" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks">Thermodynamics of fractal networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3723086" href="https://cnr-it.academia.edu/francescacolaiori">Francesca Colaiori</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Thermodynamics of fractal networks&quot;,&quot;attachmentId&quot;:31875273,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="26525698" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26525698/II_Territory_covered_by_N_random_walkers_on_stochastic_fractals_The_percolation_aggregate">II. Territory covered by N random walkers on stochastic fractals. The percolation aggregate</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50493670" href="https://upv-es.academia.edu/LuisAcedo">Luis Acedo</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;II. Territory covered by N random walkers on stochastic fractals. The percolation aggregate&quot;,&quot;attachmentId&quot;:46821742,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/26525698/II_Territory_covered_by_N_random_walkers_on_stochastic_fractals_The_percolation_aggregate&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/26525698/II_Territory_covered_by_N_random_walkers_on_stochastic_fractals_The_percolation_aggregate"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="10" data-entity-id="67877508" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/67877508/A_box_covering_algorithm_for_fractal_scaling_in_scale_free_networks">A box-covering algorithm for fractal scaling in scale-free networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="44051251" href="https://snu-kr.academia.edu/DoochulKim">Doochul Kim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A box-covering algorithm for fractal scaling in scale-free networks&quot;,&quot;attachmentId&quot;:78560144,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/67877508/A_box_covering_algorithm_for_fractal_scaling_in_scale_free_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/67877508/A_box_covering_algorithm_for_fractal_scaling_in_scale_free_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="11" data-entity-id="95789239" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/95789239/Investigating_the_Origins_of_Fractality_Based_on_Two_Novel_Fractal_Network_Models">Investigating the Origins of Fractality Based on Two Novel Fractal Network Models</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67779154" href="https://independent.academia.edu/MarcellNagy1">Marcell Nagy</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cornell University - arXiv, 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Investigating the Origins of Fractality Based on Two Novel Fractal Network Models&quot;,&quot;attachmentId&quot;:97873370,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/95789239/Investigating_the_Origins_of_Fractality_Based_on_Two_Novel_Fractal_Network_Models&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/95789239/Investigating_the_Origins_of_Fractality_Based_on_Two_Novel_Fractal_Network_Models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="12" data-entity-id="81783435" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters">On intrinsic properties of fractal lattices and percolation clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48874348" href="https://independent.academia.edu/JVannimenus">J. Vannimenus</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal de Physique Lettres, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;On intrinsic properties of fractal lattices and percolation clusters&quot;,&quot;attachmentId&quot;:87708010,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="13" data-entity-id="26525695" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26525695/Territory_covered_by_N_random_walkers_on_fractal_media_The_Sierpinski_gasket_and_the_percolation_aggregate">Territory covered by N random walkers on fractal media: The Sierpinski gasket and the percolation aggregate</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50493670" href="https://upv-es.academia.edu/LuisAcedo">Luis Acedo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Territory covered by N random walkers on fractal media: The Sierpinski gasket and the percolation aggregate&quot;,&quot;attachmentId&quot;:46821735,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/26525695/Territory_covered_by_N_random_walkers_on_fractal_media_The_Sierpinski_gasket_and_the_percolation_aggregate&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/26525695/Territory_covered_by_N_random_walkers_on_fractal_media_The_Sierpinski_gasket_and_the_percolation_aggregate"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="14" data-entity-id="120805367" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/120805367/Projections_of_fractal_percolations">Projections of fractal percolations</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="132755638" href="https://bme.academia.edu/KarolySimon">Karoly Simon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Projections of fractal percolations&quot;,&quot;attachmentId&quot;:115839671,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/120805367/Projections_of_fractal_percolations&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/120805367/Projections_of_fractal_percolations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="15" data-entity-id="49182700" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals">Percolation on infinitely ramified fractals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="136645528" href="https://independent.academia.edu/DavidMovshovitz">David Movshovitz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Percolation on infinitely ramified fractals&quot;,&quot;attachmentId&quot;:67567229,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="18237064" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory">On the Fractal dimension and correlations in percolation theory</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38221071" href="https://bgu.academia.edu/AmnonAharony">Amnon Aharony</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;On the Fractal dimension and correlations in percolation theory&quot;,&quot;attachmentId&quot;:39948825,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="17" data-entity-id="54413735" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54413735/Biased_diffusion_in_percolation_systems_indication_of_multifractal_behaviour">Biased diffusion in percolation systems: indication of multifractal behaviour</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="101630805" href="https://independent.academia.edu/EduardoRoman28">Eduardo Roman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and General, 1987</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Biased diffusion in percolation systems: indication of multifractal behaviour&quot;,&quot;attachmentId&quot;:70788564,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/54413735/Biased_diffusion_in_percolation_systems_indication_of_multifractal_behaviour&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54413735/Biased_diffusion_in_percolation_systems_indication_of_multifractal_behaviour"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="18" data-entity-id="17420214" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17420214/Conductivity_measurement_on_percolation_fractal">Conductivity measurement on percolation fractal</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37146797" href="https://independent.academia.edu/AlexanderPalevski">Alexander Palevski</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Conductivity measurement on percolation fractal&quot;,&quot;attachmentId&quot;:42261347,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/17420214/Conductivity_measurement_on_percolation_fractal&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/17420214/Conductivity_measurement_on_percolation_fractal"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="19" data-entity-id="5557037" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5557037/A_Note_on_Fractal_Channel_Networks">A Note on Fractal Channel Networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7892475" href="https://blogspot.academia.edu/RiccardoRigon">Riccardo Rigon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1991</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A Note on Fractal Channel Networks&quot;,&quot;attachmentId&quot;:49243972,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/5557037/A_Note_on_Fractal_Channel_Networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5557037/A_Note_on_Fractal_Channel_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="20" data-entity-id="124959132" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/124959132/Emergency_of_Tsallis_statistics_in_fractal_networks">Emergency of Tsallis statistics in fractal networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="130089763" href="https://independent.academia.edu/AirtonDeppman">Airton Deppman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">PLOS ONE, 2021</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Emergency of Tsallis statistics in fractal networks&quot;,&quot;attachmentId&quot;:119087974,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/124959132/Emergency_of_Tsallis_statistics_in_fractal_networks&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/124959132/Emergency_of_Tsallis_statistics_in_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="21" data-entity-id="32428505" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class">Percolation on a multifractal scale-free planar stochastic lattice and its universality class</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62710135" href="https://independent.academia.edu/kamrulHossain8">Kamrul Hassan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Percolation on a multifractal scale-free planar stochastic lattice and its universality class&quot;,&quot;attachmentId&quot;:52622835,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related topics</h2><div class="ds-research-interests--pills-container"><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="16460" href="https://www.academia.edu/Documents/in/Statistical_Physics">Statistical Physics</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="172625" href="https://www.academia.edu/Documents/in/Fractal">Fractal</a></div></div></div></div></div><div class="footer--content"><ul class="footer--main-links hide-on-mobile"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a rel="nofollow" href="https://medium.com/academia">Blog</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg>&nbsp;<strong>We&#39;re Hiring!</strong></a></li><li><a href="https://support.academia.edu/"><svg style="width: 12px; height: 12px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg>&nbsp;<strong>Help Center</strong></a></li></ul><ul class="footer--research-interests"><li>Find new research papers in:</li><li><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul><ul class="footer--legal-links hide-on-mobile"><li><a href="https://www.academia.edu/terms">Terms</a></li><li><a href="https://www.academia.edu/privacy">Privacy</a></li><li><a href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia &copy;2024</li></ul></div> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10