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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="120805367" 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/120805367/Projections_of_fractal_percolations">Projections of fractal percolations</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" 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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 &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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fat fractal percolation and k-fractal percolation","attachmentId":79372658,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation","alternativeTracking":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 class="ds-related-work--container 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This is in stark contrast to the other commonly studied notions of dimension like the Hausdorff or packing dimension.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Assouad dimension of randomly generated fractals","attachmentId":117687664,"attachmentType":"pdf","work_url":"https://www.academia.edu/123197106/The_Assouad_dimension_of_randomly_generated_fractals","alternativeTracking":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/123197106/The_Assouad_dimension_of_randomly_generated_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-wsj-grid-card" data-collection-position="5" data-entity-id="101765057" 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/101765057/On_Hausdorff_Dimension_of_Random_Fractals">On Hausdorff Dimension of Random Fractals</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="254785096" href="https://independent.academia.edu/ATempelman">Arkady Tempelman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><p class="ds-related-work--abstract ds2-5-body-sm">We study random recursive constructions with finite &quot;memory&quot; in complete metric spaces and the Hausdorff dimension of the generated random fractals. With each such construction and any positive number β we associate a linear operator V (β) in a finite dimensional space. 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href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Electronic Journal of Probability, 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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Large-$N$ Limit of Crossing Probabilities, Discontinuity, and Asymptotic Behavior of Threshold Values in Mandelbrot's Fractal Percolation Process","attachmentId":79372642,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177704/Large_N_Limit_of_Crossing_Probabilities_Discontinuity_and_Asymptotic_Behavior_of_Threshold_Values_in_Mandelbrots_Fractal_Percolation_Process","alternativeTracking":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 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