Microfractal<p><a href="https://mathstodon.xyz/tags/mathartmarch" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathartmarch</span></a> II: On a square grid</p><p>A third degree Newton fractal zoom in.</p><p>Domain coloring technique adapted from this beauty: <a href="https://www.shadertoy.com/view/wld3zl" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="">shadertoy.com/view/wld3zl</span><span class="invisible"></span></a><br>Sorry for the not-so-high quality, I'm too lazy to export it to a direct video at the moment.</p><p><a href="https://mathstodon.xyz/tags/grid" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>grid</span></a> <a href="https://mathstodon.xyz/tags/newton" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>newton</span></a> <a href="https://mathstodon.xyz/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractal</span></a> <a href="https://mathstodon.xyz/tags/complexnumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>complexnumbers</span></a> <a href="https://mathstodon.xyz/tags/complexplane" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>complexplane</span></a> <a href="https://mathstodon.xyz/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>glsl</span></a> <a href="https://mathstodon.xyz/tags/shader" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>shader</span></a></p>
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Colin the Mathmo<p>Every polynomial with real coefficients factors into linear and quadratic terms.</p><p>How much machinery is needed to show this?</p><p>If it crosses the X-axis then it has a linear term.</p><p>If it doesn't cross the X-axis then it is of even degree, and the roots come in complex conjugate pairs.</p><p>What the minimum needed to see this?</p><p><a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <br><a href="https://mathstodon.xyz/tags/algebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algebra</span></a> <a href="https://mathstodon.xyz/tags/ComplexNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ComplexNumbers</span></a> <br><a href="https://mathstodon.xyz/tags/MathsChat" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathsChat</span></a> <a href="https://mathstodon.xyz/tags/MathChat" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathChat</span></a></p>
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