Animated <a href="https://en.wikipedia.org/wiki/newton_fractal" class="extiw" title="wikipedia:newton fractal">newton fractal</a>.
<p><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}:=z_{n}-{\frac {p(z_{n})}{p'(z_{n})}}}"><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><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo>−<!-- − --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>p</mi><mo stretchy="false">(</mo><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><msup><mi>p</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle z_{n+1}:=z_{n}-{\frac {p(z_{n})}{p'(z_{n})}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e7b76ca2da8a0f2d24f9e33e8283815833ccca5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:20.085ex; height:6.509ex;" alt="{\displaystyle z_{n+1}:=z_{n}-{\frac {p(z_{n})}{p'(z_{n})}}}"></span>
</p><p><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 p(z)=z^{\alpha }-1}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>p</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>α<!-- α --></mi></mrow></msup><mo>−<!-- − --></mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle p(z)=z^{\alpha }-1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ad8bb36e7c5408f3084eca4f886ece056b3a67e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:13.632ex; height:2.843ex;" alt="{\displaystyle p(z)=z^{\alpha }-1}"></span>
</p>
The animation iterates over <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 \alpha }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>α<!-- α --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="\alpha "></span>: from 1 to 6.
<a href="//commons.wikimedia.org/wiki/User:Arichnad" title="User:Arichnad">User:arichnad</a>
CC BY-SA 4.0
<span class="int-own-work" lang="en">Own work</span>