<p>A view of the <a href="https://en.wikipedia.org/wiki/Burning_Ship_fractal" class="extiw" title="w:Burning Ship fractal">Burning Ship fractal</a>. This is a fractal generated by iterating the following equation for each point with coordinates <i>c</i> in the complex plane:
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<dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{n+1}=\left(|\Re \left({Z_{n}}\right)|-i|\Im \left({Z_{n}}\right)|\right)^{2}+c,\quad Z_{0}=0}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msup><mrow><mo>(</mo><mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi mathvariant="normal">ℜ<!-- ℜ --></mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mo>−<!-- − --></mo><mi>i</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi mathvariant="normal">ℑ<!-- ℑ --></mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>,</mo><mspace width="1em"></mspace><msub><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle Z_{n+1}=\left(|\Re \left({Z_{n}}\right)|-i|\Im \left({Z_{n}}\right)|\right)^{2}+c,\quad Z_{0}=0}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0bf7f6e2ac92390f7e3948dbcff537d2f894436" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:45.196ex; height:3.343ex;" alt="{\displaystyle Z_{n+1}=\left(|\Re \left({Z_{n}}\right)|-i|\Im \left({Z_{n}}\right)|\right)^{2}+c,\quad Z_{0}=0}"></span></dd></dl></dd></dl><p>This image is in the complex plane with lower left corner (-1.8, -0.02i) and upper right corner (-1.7, 0.055i). Some descriptions of this fractal give the equation with an addition rather than a subtraction. This produces a reflection in the real-axis, which means that it is hard to see the "burning ship".
</p><p>If the iteration "escapes" to large numbers, it is coloured according to how long it took to reach a cutoff point (here, 40). If it does not escape after 100 iteration, the point is coloured black.
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This image was made in Ultrafractal 4.
<a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a>
02/11/07
<span class="int-own-work" lang="en">Own work</span>