@prachwal/mandelbrot-generator
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Professional Mandelbrot fractal generator with TypeScript support, interactive web interface, and multiple output formats
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<html class="default" lang="en" data-base="../"><head><meta charset="utf-8"/><meta http-equiv="x-ua-compatible" content="IE=edge"/><title>mandelbrotIteration | @prachwal/mandelbrot-generator - v1.1.1</title><meta name="description" content="Documentation for @prachwal/mandelbrot-generator"/><meta name="viewport" content="width=device-width, initial-scale=1"/><link rel="stylesheet" href="../assets/style.css"/><link rel="stylesheet" href="../assets/highlight.css"/><script defer src="../assets/main.js"></script><script async src="../assets/icons.js" id="tsd-icons-script"></script><script async src="../assets/search.js" id="tsd-search-script"></script><script async src="../assets/navigation.js" id="tsd-nav-script"></script><script async src="../assets/hierarchy.js" id="tsd-hierarchy-script"></script></head><body><script>document.documentElement.dataset.theme = localStorage.getItem("tsd-theme") || "os";document.body.style.display="none";setTimeout(() => window.app?app.showPage():document.body.style.removeProperty("display"),500)</script><header class="tsd-page-toolbar"><div class="tsd-toolbar-contents container"><a href="../index.html" class="title">@prachwal/mandelbrot-generator - v1.1.1</a><div id="tsd-toolbar-links"></div><button id="tsd-search-trigger" class="tsd-widget" aria-label="Search"><svg width="16" height="16" viewBox="0 0 16 16" fill="none" aria-hidden="true"><use href="../assets/icons.svg#icon-search"></use></svg></button><dialog id="tsd-search" aria-label="Search"><input role="combobox" id="tsd-search-input" aria-controls="tsd-search-results" aria-autocomplete="list" aria-expanded="true" autocapitalize="off" autocomplete="off" placeholder="Search the docs" maxLength="100"/><ul role="listbox" id="tsd-search-results"></ul><div id="tsd-search-status" aria-live="polite" aria-atomic="true"><div>Preparing search index...</div></div></dialog><a href="#" class="tsd-widget menu" id="tsd-toolbar-menu-trigger" data-toggle="menu" aria-label="Menu"><svg width="16" height="16" viewBox="0 0 16 16" fill="none" aria-hidden="true"><use href="../assets/icons.svg#icon-menu"></use></svg></a></div></header><div class="container container-main"><div class="col-content"><div class="tsd-page-title"><ul class="tsd-breadcrumb" aria-label="Breadcrumb"><li><a href="" aria-current="page">mandelbrotIteration</a></li></ul><h1>Function mandelbrotIteration</h1></div><section class="tsd-panel"><ul class="tsd-signatures"><li class=""><div class="tsd-signature tsd-anchor-link" id="mandelbrotiteration"><span class="tsd-kind-call-signature">mandelbrotIteration</span><span class="tsd-signature-symbol">(</span><br/> <span class="tsd-kind-parameter">cx</span><span class="tsd-signature-symbol">:</span> <span class="tsd-signature-type">number</span><span class="tsd-signature-symbol">,</span><br/> <span class="tsd-kind-parameter">cy</span><span class="tsd-signature-symbol">:</span> <span class="tsd-signature-type">number</span><span class="tsd-signature-symbol">,</span><br/> <span class="tsd-kind-parameter">maxIterations</span><span class="tsd-signature-symbol">:</span> <span class="tsd-signature-type">number</span><span class="tsd-signature-symbol">,</span><br/> <span class="tsd-kind-parameter">escapeRadius</span><span class="tsd-signature-symbol">?:</span> <span class="tsd-signature-type">number</span><span class="tsd-signature-symbol">,</span><br/><span class="tsd-signature-symbol">)</span><span class="tsd-signature-symbol">:</span> <span class="tsd-signature-type">number</span><a href="#mandelbrotiteration" aria-label="Permalink" class="tsd-anchor-icon"><svg viewBox="0 0 24 24" aria-hidden="true"><use href="../assets/icons.svg#icon-anchor"></use></svg></a></div><div class="tsd-description"><div class="tsd-comment tsd-typography"><p>Computes the number of iterations for a point in the complex plane to escape the Mandelbrot set</p>
<p>Uses the standard iterative formula: z_{n+1} = z_n^2 + c, where z_0 = 0 and c = cx + i*cy
The function returns when either the maximum iterations are reached (point likely in set)
or when |z| exceeds the escape radius (point definitely not in set).</p>
</div><div class="tsd-parameters"><h4 class="tsd-parameters-title">Parameters</h4><ul class="tsd-parameter-list"><li><span><span class="tsd-kind-parameter">cx</span>: <span class="tsd-signature-type">number</span></span><div class="tsd-comment tsd-typography"><p>Real part of the complex number c</p>
</div><div class="tsd-comment tsd-typography"></div></li><li><span><span class="tsd-kind-parameter">cy</span>: <span class="tsd-signature-type">number</span></span><div class="tsd-comment tsd-typography"><p>Imaginary part of the complex number c</p>
</div><div class="tsd-comment tsd-typography"></div></li><li><span><span class="tsd-kind-parameter">maxIterations</span>: <span class="tsd-signature-type">number</span></span><div class="tsd-comment tsd-typography"><p>Maximum number of iterations to perform</p>
</div><div class="tsd-comment tsd-typography"></div></li><li><span><span class="tsd-kind-parameter">escapeRadius</span>: <span class="tsd-signature-type">number</span><span class="tsd-signature-symbol"> = 2</span></span><div class="tsd-comment tsd-typography"><p>Threshold radius for considering a point as escaped (default: 2)</p>
</div><div class="tsd-comment tsd-typography"></div></li></ul></div><h4 class="tsd-returns-title">Returns <span class="tsd-signature-type">number</span></h4><p>Number of iterations before escape, or maxIterations if point doesn't escape</p>
<div class="tsd-comment tsd-typography"><div class="tsd-tag-example"><h4 class="tsd-anchor-link" id="example">Example<a href="#example" aria-label="Permalink" class="tsd-anchor-icon"><svg viewBox="0 0 24 24" aria-hidden="true"><use href="../assets/icons.svg#icon-anchor"></use></svg></a></h4><pre><code class="typescript"><span class="hl-0">// Check if origin is in Mandelbrot set (it is)</span><br/><span class="hl-4">const</span><span class="hl-2"> </span><span class="hl-8">originIterations</span><span class="hl-2"> = </span><span class="hl-1">mandelbrotIteration</span><span class="hl-2">(</span><span class="hl-5">0</span><span class="hl-2">, </span><span class="hl-5">0</span><span class="hl-2">, </span><span class="hl-5">100</span><span class="hl-2">); </span><span class="hl-0">// Returns 100</span><br/><br/><span class="hl-0">// Check a point outside the set</span><br/><span class="hl-4">const</span><span class="hl-2"> </span><span class="hl-8">outsideIterations</span><span class="hl-2"> = </span><span class="hl-1">mandelbrotIteration</span><span class="hl-2">(</span><span class="hl-5">2</span><span class="hl-2">, </span><span class="hl-5">2</span><span class="hl-2">, </span><span class="hl-5">100</span><span class="hl-2">); </span><span class="hl-0">// Returns 1</span><br/><br/><span class="hl-0">// Check an interesting boundary point</span><br/><span class="hl-4">const</span><span class="hl-2"> </span><span class="hl-8">boundaryIterations</span><span class="hl-2"> = </span><span class="hl-1">mandelbrotIteration</span><span class="hl-2">(-</span><span class="hl-5">0.7269</span><span class="hl-2">, </span><span class="hl-5">0.1889</span><span class="hl-2">, </span><span class="hl-5">1000</span><span class="hl-2">);</span>
</code><button type="button">Copy</button></pre>
</div><div class="tsd-tag-complexity"><h4 class="tsd-anchor-link" id="complexity">Complexity<a href="#complexity" aria-label="Permalink" class="tsd-anchor-icon"><svg viewBox="0 0 24 24" aria-hidden="true"><use href="../assets/icons.svg#icon-anchor"></use></svg></a></h4><p>O(maxIterations) in worst case</p>
</div><div class="tsd-tag-see"><h4 class="tsd-anchor-link" id="see">See<a href="#see" aria-label="Permalink" class="tsd-anchor-icon"><svg viewBox="0 0 24 24" aria-hidden="true"><use href="../assets/icons.svg#icon-anchor"></use></svg></a></h4><p><a href="https://en.wikipedia.org/wiki/Mandelbrot_set">https://en.wikipedia.org/wiki/Mandelbrot_set</a> for mathematical background</p>
</div></div><aside class="tsd-sources"><ul><li>Defined in <a href="https://github.com/prachwal/mandelbrot-generator/blob/da157e1b866785501d38ccb7552859d4482dd1a8/src/mandelbrot.ts#L61">mandelbrot.ts:61</a></li></ul></aside></div></li></ul></section></div><div class="col-sidebar"><div class="page-menu"><div class="tsd-navigation settings"><details class="tsd-accordion"><summary class="tsd-accordion-summary"><svg width="20" height="20" viewBox="0 0 24 24" fill="none" aria-hidden="true"><use href="../assets/icons.svg#icon-chevronDown"></use></svg><h3>Settings</h3></summary><div class="tsd-accordion-details"><div class="tsd-filter-visibility"><span class="settings-label">Member Visibility</span><ul id="tsd-filter-options"><li class="tsd-filter-item"><label class="tsd-filter-input"><input type="checkbox" id="tsd-filter-inherited" name="inherited" checked/><svg width="32" height="32" viewBox="0 0 32 32" aria-hidden="true"><rect class="tsd-checkbox-background" width="30" height="30" x="1" y="1" rx="6" fill="none"></rect><path class="tsd-checkbox-checkmark" d="M8.35422 16.8214L13.2143 21.75L24.6458 10.25" stroke="none" stroke-width="3.5" stroke-linejoin="round" fill="none"></path></svg><span>Inherited</span></label></li><li class="tsd-filter-item"><label class="tsd-filter-input"><input type="checkbox" id="tsd-filter-external" name="external"/><svg width="32" height="32" viewBox="0 0 32 32" aria-hidden="true"><rect class="tsd-checkbox-background" width="30" height="30" x="1" y="1" rx="6" fill="none"></rect><path class="tsd-checkbox-checkmark" d="M8.35422 16.8214L13.2143 21.75L24.6458 10.25" stroke="none" stroke-width="3.5" stroke-linejoin="round" fill="none"></path></svg><span>External</span></label></li></ul></div><div class="tsd-theme-toggle"><label class="settings-label" for="tsd-theme">Theme</label><select id="tsd-theme"><option value="os">OS</option><option value="light">Light</option><option value="dark">Dark</option></select></div></div></details></div></div><div class="site-menu"><nav class="tsd-navigation"><a href="../modules.html">@prachwal/mandelbrot-generator - v1.1.1</a><ul class="tsd-small-nested-navigation" id="tsd-nav-container"><li>Loading...</li></ul></nav></div></div></div><footer><p class="tsd-generator">Generated using <a href="https://typedoc.org/" target="_blank">TypeDoc</a></p></footer><div class="overlay"></div></body></html>