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mw-list-item"><a href="/wiki/File:SquareWaveFourierArrows.gif" title="View the file page [c]" accesskey="c"><span>File</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=File_talk:SquareWaveFourierArrows.gif&action=edit&redlink=1" rel="discussion" class="new" title="Discuss improvements to the content page (page does not exist) [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span 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Information from its <b><a href="https://commons.wikimedia.org/wiki/File:SquareWaveFourierArrows.gif" class="extiw" title="commons:File:SquareWaveFourierArrows.gif">description page there</a></b> is shown below.<br /><span style="font-size: smaller;">Commons is a freely licensed media file repository. <a href="https://commons.wikimedia.org/wiki/Commons:Welcome" class="extiw" title="commons:Commons:Welcome">You can help</a>.</span></td></tr></tbody></table> </div> </div> <div id="shared-image-desc"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="mw-heading mw-heading2"><h2 id="Summary">Summary</h2></div> <div class="hproduct commons-file-information-table"> <table class="fileinfotpl-type-information vevent" dir="ltr"> <tbody><tr> <td id="fileinfotpl_desc" class="fileinfo-paramfield" lang="en">Description<span class="summary fn" style="display:none">SquareWaveFourierArrows.gif</span></td> <td class="description"> <div class="description en" dir="ltr" lang="en"><span class="language en" title="English"><b>English: </b></span> The six arrows represent the first six terms of the Fourier series of a square wave. The two circles at the bottom represent the exact square wave (blue) and its Fourier-series approximation (purple).</div></td> </tr> <tr> <td id="fileinfotpl_date" class="fileinfo-paramfield" lang="en">Date</td> <td lang="en"> <time class="dtstart" datetime="2014-03-06 20:54:27" lang="en" dir="ltr" style="white-space:nowrap">6 March 2014, 20:54:27</time></td> </tr> <tr> <td id="fileinfotpl_src" class="fileinfo-paramfield" lang="en">Source</td> <td> <span class="int-own-work" lang="en">Own work</span></td> </tr> <tr> <td id="fileinfotpl_aut" class="fileinfo-paramfield" lang="en">Author</td> <td> <a href="//commons.wikimedia.org/wiki/User:Sbyrnes321" title="User:Sbyrnes321">Sbyrnes321</a></td> </tr> <tr> <td id="fileinfotpl_ver" class="fileinfo-paramfield" lang="en">Other versions</td> <td> <a href="//commons.wikimedia.org/wiki/File:SquareWaveFourierArrows,rotated.gif" title="File:SquareWaveFourierArrows,rotated.gif">File:SquareWaveFourierArrows,rotated.gif</a></td> </tr> </tbody></table> </div> <div class="mw-heading mw-heading2"><h2 id="Licensing">Licensing</h2></div> <div style="clear:both; margin:0.5em auto; background-color:var(--background-color-interactive,#eaecf0); color:inherit; border:2px solid var(--border-color-subtle,#c8ccd1); padding:8px; direction:ltr;" class="licensetpl_wrapper"><div class="center" style="font-weight:bold;"><div lang="en" dir="ltr" class="description en" style="display:inline;">I, the copyright holder of this work, hereby publish it under the following license:</div></div> <table style="width:100%; clear:both; text-align:center; margin:0.5em auto; background-color:var(--background-color-neutral-subtle, #f8f9fa); border:var(--border-subtle, 2px solid #c8ccd1); padding: 0; border-spacing: 8px; color:var(--color-base, #202122);" dir="ltr" class="layouttemplate licensetpl" lang="en"> <tbody><tr> <td style="width:90px;" rowspan="2"><span class="skin-invert" typeof="mw:File"><span title="Creative Commons"><img alt="Creative Commons" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cc.logo.circle.svg/28px-Cc.logo.circle.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cc.logo.circle.svg/42px-Cc.logo.circle.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cc.logo.circle.svg/56px-Cc.logo.circle.svg.png 2x" data-file-width="64" data-file-height="64"></span></span> <span class="skin-invert" typeof="mw:File"><span title="CC-Zero"><img alt="CC-Zero" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Cc-zero.svg/28px-Cc-zero.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Cc-zero.svg/42px-Cc-zero.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Cc-zero.svg/56px-Cc-zero.svg.png 2x" data-file-width="64" data-file-height="64"></span></span> </td> <td>This file is made available under the <a href="https://en.wikipedia.org/wiki/en:Creative_Commons" class="extiw" title="w:en:Creative Commons">Creative Commons</a> <a href="https://creativecommons.org/publicdomain/zero/1.0/deed.en" class="extiw" title="ccorg:publicdomain/zero/1.0/deed.en">CC0 1.0 Universal Public Domain Dedication</a>. </td></tr> <tr style="text-align:left;"> <td>The person who associated a work with this deed has dedicated the work to the <a href="https://en.wikipedia.org/wiki/en:public_domain" class="extiw" title="w:en:public domain">public domain</a> by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. <p><span class="licensetpl_link" style="display:none;">http://creativecommons.org/publicdomain/zero/1.0/deed.en</span><span class="licensetpl_short" style="display:none;">CC0</span><span class="licensetpl_long" style="display:none;">Creative Commons Zero, Public Domain Dedication</span><span class="licensetpl_link_req" style="display:none;">false</span><span class="licensetpl_attr_req" style="display:none;">false</span> </p> </td></tr></tbody></table></div> <div class="mw-heading mw-heading2"><h2 id="Source_code">Source code</h2></div> <div class="mw-highlight mw-highlight-lang-python mw-content-ltr" dir="ltr"><pre><span></span><span class="sd">"""</span> <span class="sd">(C) Steven Byrnes, 2014. This code is released under the MIT license</span> <span class="sd">http://opensource.org/licenses/MIT</span> <span class="sd">This code should work in Python 2.7 or 3.3. It requires imagemagick to be</span> <span class="sd">installed; that's how it assembles images into animated GIFs.</span> <span class="sd">"""</span> <span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span> <span class="kn">import</span> <span class="nn">pygame</span> <span class="k">as</span> <span class="nn">pg</span> <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">pi</span> <span class="kn">from</span> <span class="nn">cmath</span> <span class="kn">import</span> <span class="n">exp</span> <span class="kn">import</span> <span class="nn">subprocess</span><span class="o">,</span> <span class="nn">os</span> <span class="n">directory_now</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">dirname</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">realpath</span><span class="p">(</span><span class="vm">__file__</span><span class="p">))</span> <span class="n">frames_in_anim</span> <span class="o">=</span> <span class="mi">200</span> <span class="n">animation_loop_seconds</span> <span class="o">=</span> <span class="mi">5</span> <span class="c1">#time in seconds for animation to loop one cycle</span> <span class="n">bgcolor</span> <span class="o">=</span> <span class="p">(</span><span class="mi">255</span><span class="p">,</span><span class="mi">255</span><span class="p">,</span><span class="mi">255</span><span class="p">)</span> <span class="c1">#white</span> <span class="n">circle_radius</span> <span class="o">=</span> <span class="mi">12</span> <span class="n">img_height</span> <span class="o">=</span> <span class="mi">300</span> <span class="n">img_width</span> <span class="o">=</span> <span class="mi">1000</span> <span class="c1"># pygame draws pixel-art, not smoothed. Therefore I am drawing it</span> <span class="c1"># bigger, then smoothly shrinking it down</span> <span class="n">final_width</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="mf">0.3</span> <span class="o">*</span> <span class="n">img_width</span><span class="p">))</span> <span class="n">final_height</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="mf">0.3</span> <span class="o">*</span> <span class="n">img_height</span><span class="p">))</span> <span class="c1"># Constants and function for calculating electron motion</span> <span class="k">def</span> <span class="nf">coef</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="w"> </span><span class="sd">""" f(t) = sum of Re[coef(n) * e^(int)] """</span> <span class="k">return</span> <span class="mi">0</span> <span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">/</span> <span class="n">n</span> <span class="k">def</span> <span class="nf">exact</span><span class="p">(</span><span class="n">phase</span><span class="p">):</span> <span class="w"> </span><span class="sd">""" exact square wave function """</span> <span class="k">if</span> <span class="n">phase</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">phase</span> <span class="o">==</span> <span class="n">pi</span><span class="p">:</span> <span class="k">return</span> <span class="mi">0</span> <span class="k">if</span> <span class="p">(</span><span class="n">phase</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">))</span> <span class="o"><</span> <span class="n">pi</span><span class="p">:</span> <span class="k">return</span> <span class="n">pi</span><span class="o">/</span><span class="mi">4</span> <span class="k">return</span> <span class="o">-</span><span class="n">pi</span><span class="o">/</span><span class="mi">4</span> <span class="n">center_x</span> <span class="o">=</span> <span class="mi">500</span> <span class="n">scale</span> <span class="o">=</span> <span class="mi">450</span> <span class="c1"># scale multiplies all horizontal distances</span> <span class="k">def</span> <span class="nf">draw_arrow</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="n">tail_xy</span><span class="p">,</span> <span class="n">head_xy</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">)):</span> <span class="w"> </span><span class="sd">"""</span> <span class="sd"> draw a horizontal arrow</span> <span class="sd"> """</span> <span class="c1"># tail_xy and head_xy are 2-tuples. Unpack them first</span> <span class="n">tail_x</span><span class="p">,</span> <span class="n">tail_y</span> <span class="o">=</span> <span class="n">tail_xy</span> <span class="n">head_x</span><span class="p">,</span> <span class="n">head_y</span> <span class="o">=</span> <span class="n">head_xy</span> <span class="k">assert</span> <span class="n">head_y</span> <span class="o">==</span> <span class="n">tail_y</span> <span class="n">h</span> <span class="o">=</span> <span class="mi">16</span> <span class="c1"># arrowhead height</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">18</span> <span class="c1"># arrowhead half-base</span> <span class="k">if</span> <span class="n">tail_x</span> <span class="o"><</span> <span class="n">head_x</span><span class="p">:</span> <span class="c1"># rightward arrow</span> <span class="n">triangle</span> <span class="o">=</span> <span class="p">[(</span><span class="n">head_x</span><span class="p">,</span> <span class="n">head_y</span><span class="p">),</span> <span class="p">(</span><span class="n">head_x</span> <span class="o">-</span> <span class="n">h</span><span class="p">,</span> <span class="n">head_y</span> <span class="o">-</span> <span class="n">b</span><span class="p">),</span> <span class="p">(</span><span class="n">head_x</span> <span class="o">-</span> <span class="n">h</span><span class="p">,</span> <span class="n">head_y</span> <span class="o">+</span> <span class="n">b</span><span class="p">)]</span> <span class="k">else</span><span class="p">:</span> <span class="c1"># leftward arrow</span> <span class="n">triangle</span> <span class="o">=</span> <span class="p">[(</span><span class="n">head_x</span><span class="p">,</span> <span class="n">head_y</span><span class="p">),</span> <span class="p">(</span><span class="n">head_x</span> <span class="o">+</span> <span class="n">h</span><span class="p">,</span> <span class="n">head_y</span> <span class="o">-</span> <span class="n">b</span><span class="p">),</span> <span class="p">(</span><span class="n">head_x</span> <span class="o">+</span> <span class="n">h</span><span class="p">,</span> <span class="n">head_y</span> <span class="o">+</span> <span class="n">b</span><span class="p">)]</span> <span class="n">pg</span><span class="o">.</span><span class="n">draw</span><span class="o">.</span><span class="n">line</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="p">(</span><span class="n">tail_x</span><span class="p">,</span> <span class="n">tail_y</span><span class="p">),</span> <span class="p">(</span><span class="n">head_x</span><span class="p">,</span> <span class="n">head_y</span><span class="p">),</span> <span class="n">width</span><span class="p">)</span> <span class="n">pg</span><span class="o">.</span><span class="n">draw</span><span class="o">.</span><span class="n">polygon</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">triangle</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="k">def</span> <span class="nf">main</span><span class="p">():</span> <span class="w"> </span><span class="sd">""" function for creating the animated GIF """</span> <span class="c1"># Make and save a drawing for each frame</span> <span class="n">filename_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">directory_now</span><span class="p">,</span> <span class="s1">'temp'</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'.png'</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">frames_in_anim</span><span class="p">)]</span> <span class="k">for</span> <span class="n">frame</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">frames_in_anim</span><span class="p">):</span> <span class="n">phase</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="n">frame</span> <span class="o">/</span> <span class="n">frames_in_anim</span> <span class="c1"># initialize surface</span> <span class="n">surf</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">Surface</span><span class="p">((</span><span class="n">img_width</span><span class="p">,</span><span class="n">img_height</span><span class="p">))</span> <span class="n">surf</span><span class="o">.</span><span class="n">fill</span><span class="p">(</span><span class="n">bgcolor</span><span class="p">)</span> <span class="c1"># draw all the arrows</span> <span class="n">x_now</span> <span class="o">=</span> <span class="n">center_x</span> <span class="n">y_now</span> <span class="o">=</span> <span class="mi">30</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">13</span><span class="p">,</span><span class="mi">2</span><span class="p">):</span> <span class="n">new_term</span> <span class="o">=</span> <span class="p">(</span><span class="n">scale</span> <span class="o">*</span> <span class="n">coef</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">phase</span><span class="p">))</span><span class="o">.</span><span class="n">real</span> <span class="n">draw_arrow</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="p">(</span><span class="n">x_now</span><span class="p">,</span> <span class="n">y_now</span><span class="p">),</span> <span class="p">(</span><span class="n">x_now</span> <span class="o">+</span> <span class="n">new_term</span><span class="p">,</span> <span class="n">y_now</span><span class="p">),</span> <span class="n">width</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span> <span class="n">x_now</span> <span class="o">+=</span> <span class="n">new_term</span> <span class="n">y_now</span> <span class="o">+=</span> <span class="mi">30</span> <span class="c1"># draw the two circles</span> <span class="n">pg</span><span class="o">.</span><span class="n">draw</span><span class="o">.</span><span class="n">circle</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="p">(</span><span class="mi">100</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">100</span><span class="p">),</span> <span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">x_now</span><span class="p">)),</span><span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">y_now</span> <span class="o">+</span> <span class="mi">10</span><span class="p">))),</span> <span class="n">circle_radius</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="n">pg</span><span class="o">.</span><span class="n">draw</span><span class="o">.</span><span class="n">circle</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="p">(</span><span class="mi">50</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="mi">150</span><span class="p">),</span> <span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">center_x</span> <span class="o">+</span> <span class="n">scale</span> <span class="o">*</span> <span class="n">exact</span><span class="p">(</span><span class="n">phase</span><span class="p">))),</span> <span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">y_now</span> <span class="o">+</span> <span class="mi">40</span><span class="p">))),</span> <span class="n">circle_radius</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># scale down then save the surface</span> <span class="n">shrunk_surface</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">transform</span><span class="o">.</span><span class="n">smoothscale</span><span class="p">(</span><span class="n">surf</span><span class="p">,</span> <span class="p">(</span><span class="n">final_width</span><span class="p">,</span> <span class="n">final_height</span><span class="p">))</span> <span class="n">pg</span><span class="o">.</span><span class="n">image</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">shrunk_surface</span><span class="p">,</span> <span class="n">filename_list</span><span class="p">[</span><span class="n">frame</span><span class="p">])</span> <span class="n">seconds_per_frame</span> <span class="o">=</span> <span class="n">animation_loop_seconds</span> <span class="o">/</span> <span class="n">frames_in_anim</span> <span class="n">frame_delay</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">seconds_per_frame</span> <span class="o">*</span> <span class="mi">100</span><span class="p">))</span> <span class="n">command_list</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'convert'</span><span class="p">,</span> <span class="s1">'-delay'</span><span class="p">,</span> <span class="n">frame_delay</span><span class="p">,</span> <span class="s1">'-loop'</span><span class="p">,</span> <span class="s1">'0'</span><span class="p">]</span> <span class="o">+</span> <span class="n">filename_list</span> <span class="o">+</span> <span class="p">[</span><span class="s1">'anim.gif'</span><span class="p">]</span> <span class="c1"># Use the "convert" command (part of ImageMagick) to build the animation</span> <span class="n">subprocess</span><span class="o">.</span><span class="n">call</span><span class="p">(</span><span class="n">command_list</span><span class="p">,</span> <span class="n">cwd</span><span class="o">=</span><span class="n">directory_now</span><span class="p">)</span> <span class="c1"># Earlier, we saved an image file for each frame of the animation. Now</span> <span class="c1"># that the animation is assembled, we can (optionally) delete those files</span> <span class="k">if</span> <span class="kc">True</span><span class="p">:</span> <span class="k">for</span> <span class="n">filename</span> <span class="ow">in</span> <span class="n">filename_list</span><span class="p">:</span> <span class="n">os</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">filename</span><span class="p">)</span> <span class="k">return</span> <span class="n">main</span><span class="p">()</span> </pre></div><h1 class="mw-slot-header"><mediainfoslotheader></mediainfoslotheader></h1><mediainfoview style="display: none"><mediainfoviewcaptions><div class="wbmi-entityview-captionsPanel oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><h3 class="wbmi-entityview-captions-header">Captions</h3><div class="wbmi-entityview-caption oo-ui-layout oo-ui-horizontalLayout"><label class="wbmi-language-label oo-ui-widget oo-ui-widget-enabled oo-ui-labelElement-label oo-ui-labelElement oo-ui-labelWidget">English</label><div lang="en" dir="ltr" class="wbmi-caption-value wbmi-entityview-emptyCaption">Add a one-line explanation of what this file represents</div></div></div></mediainfoviewcaptions><mediainfoviewstatements><div id="P180" data-property="P180" data-statements="[]" data-formatvalue="[]" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P180 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h3 class="wbmi-statements-title">Items portrayed in this file</h3><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P180" href="https://www.wikidata.org/wiki/Special:EntityPage/P180">depicts</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"></div></div></div><div id="P170" data-property="P170" data-statements="[{"mainsnak":{"snaktype":"somevalue","property":"P170","hash":"d3550e860f988c6675fff913440993f58f5c40c5"},"type":"statement","qualifiers":{"P2093":[{"snaktype":"value","property":"P2093","hash":"3b7828cd2048167823771a7b6858c9abfe55e694","datavalue":{"value":"Sbyrnes321","type":"string"}}],"P4174":[{"snaktype":"value","property":"P4174","hash":"5266c34d0be5600a07f74af9963345785eae0b69","datavalue":{"value":"Sbyrnes321","type":"string"}}],"P2699":[{"snaktype":"value","property":"P2699","hash":"8efa1f9257b226f81a70703843ccdaf89113ea48","datavalue":{"value":"http:\/\/commons.wikimedia.org\/wiki\/User:Sbyrnes321","type":"string"}}]},"qualifiers-order":["P2093","P4174","P2699"],"id":"M31481995$57A1BCB1-372D-41B9-BBAF-420E88048108","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":170,\"id\":\"P170\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P170\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P170\">creator<\/a>"}},"text\/plain":{"en":{"":"creator"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P2093\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P2093\">author name string<\/a>"}},"text\/plain":{"en":{"":"author name string"}}},"{\"value\":\"Sbyrnes321\",\"type\":\"string\"}":{"text\/html":{"en":{"P2093":"Sbyrnes321","P4174":"<a target=\"_blank\" class=\"wb-external-id external\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:CentralAuth?target=Sbyrnes321\" rel=\"nofollow\">Sbyrnes321<\/a>"}},"text\/plain":{"en":{"P2093":"Sbyrnes321","P4174":"Sbyrnes321"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P4174\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P4174\">Wikimedia username<\/a>"}},"text\/plain":{"en":{"":"Wikimedia username"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2699,\"id\":\"P2699\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P2699\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P2699\">URL<\/a>"}},"text\/plain":{"en":{"":"URL"}}},"{\"value\":\"http:\\\/\\\/commons.wikimedia.org\\\/wiki\\\/User:Sbyrnes321\",\"type\":\"string\"}":{"text\/html":{"en":{"P2699":"<a target=\"_blank\" rel=\"nofollow\" class=\"external free\" href=\"http:\/\/commons.wikimedia.org\/wiki\/User:Sbyrnes321\">http:\/\/commons.wikimedia.org\/wiki\/User:Sbyrnes321<\/a>"}},"text\/plain":{"en":{"P2699":"http:\/\/commons.wikimedia.org\/wiki\/User:Sbyrnes321"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P170 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P170" href="https://www.wikidata.org/wiki/Special:EntityPage/P170">creator</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M31481995$57A1BCB1-372D-41B9-BBAF-420E88048108" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi>some value</bdi></h4></div></div></div><div class="wbmi-item-qualifiers"><div class="wbmi-snaklist-container"><div class="wbmi-snaklist-content"><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P2093" href="https://www.wikidata.org/wiki/Special:EntityPage/P2093">author name string</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value">Sbyrnes321</span></div></div><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P4174" href="https://www.wikidata.org/wiki/Special:EntityPage/P4174">Wikimedia username</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value"><a target="_blank" class="wb-external-id external" href="https://www.wikidata.org/wiki/Special:CentralAuth?target=Sbyrnes321" rel="nofollow">Sbyrnes321</a></span></div></div><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P2699" href="https://www.wikidata.org/wiki/Special:EntityPage/P2699">URL</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value"><a target="_blank" rel="nofollow" class="external free" href="http://commons.wikimedia.org/wiki/User:Sbyrnes321">http://commons.wikimedia.org/wiki/User:Sbyrnes321</a></span></div></div></div></div></div></div></div></div></div></div><div id="P6216" data-property="P6216" data-statements="[{"mainsnak":{"snaktype":"value","property":"P6216","hash":"f88a8b9472789ca66067ed50ce20dc2650af5744","datavalue":{"value":{"entity-type":"item","numeric-id":88088423,"id":"Q88088423"},"type":"wikibase-entityid"}},"type":"statement","id":"M31481995$8433AFBE-6009-498B-888D-FED6FB2A9D11","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":6216,\"id\":\"P6216\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P6216\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P6216\">copyright status<\/a>"}},"text\/plain":{"en":{"":"copyright 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license</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M31481995$808D4988-476B-4C1E-9F0E-76259498C018" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q6938433" href="https://www.wikidata.org/wiki/Special:EntityPage/Q6938433">Creative Commons CC0 License</a></bdi></h4></div></div></div></div></div></div></div></div><div id="P571" data-property="P571" data-statements="[{"mainsnak":{"snaktype":"value","property":"P571","hash":"ffdfc892dbc7d3a12387958d723a1e16141af5ac","datavalue":{"value":{"time":"+2014-03-06T00:00:00Z","timezone":0,"before":0,"after":0,"precision":11,"calendarmodel":"http:\/\/www.wikidata.org\/entity\/Q1985727"},"type":"time"}},"type":"statement","id":"M31481995$7A55A14D-F9A7-44D8-8E65-B1137447300F","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":571,\"id\":\"P571\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P571\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P571\">inception<\/a>"}},"text\/plain":{"en":{"":"inception"}}},"{\"value\":{\"time\":\"+2014-03-06T00:00:00Z\",\"timezone\":0,\"before\":0,\"after\":0,\"precision\":11,\"calendarmodel\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q1985727\"},\"type\":\"time\"}":{"text\/html":{"en":{"P571":"6 March 2014"}},"text\/plain":{"en":{"P571":"6 March 2014"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P571 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P571" href="https://www.wikidata.org/wiki/Special:EntityPage/P571">inception</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M31481995$7A55A14D-F9A7-44D8-8E65-B1137447300F" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi>6 March 2014</bdi></h4></div></div></div></div></div></div></div></div><div id="P7482" data-property="P7482" data-statements="[{"mainsnak":{"snaktype":"value","property":"P7482","hash":"83568a288a8b8b4714a68e7239d8406833762864","datavalue":{"value":{"entity-type":"item","numeric-id":66458942,"id":"Q66458942"},"type":"wikibase-entityid"}},"type":"statement","id":"M31481995$4A26706C-3A0D-4DED-B1E5-9EC6D49EF90B","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":7482,\"id\":\"P7482\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"<a 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<tr><td>current</td><td class="filehistory-selected" style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/6/6b/SquareWaveFourierArrows.gif">01:59, 7 March 2014</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/6/6b/SquareWaveFourierArrows.gif"><img alt="Thumbnail for version as of 01:59, 7 March 2014" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/SquareWaveFourierArrows.gif/120px-SquareWaveFourierArrows.gif" decoding="async" loading="lazy" width="120" height="36" data-file-width="300" data-file-height="90" /></a></td><td>300 × 90 <span style="white-space: nowrap;">(214 KB)</span></td><td><a href="/wiki/User:Sbyrnes321" class="mw-userlink" title="User:Sbyrnes321"><bdi>Sbyrnes321</bdi></a></td><td dir="ltr">User created page with UploadWizard</td></tr> </table> </div> <h2 id="filelinks">File usage</h2> <div id='mw-imagepage-section-linkstoimage'> <p>The following 4 pages use this file: </p><ul class="mw-imagepage-linkstoimage"> <li 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