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Víctor<a href="https://mastodont.cat/tags/mandelbrotset" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mandelbrotset</a> (autosimilaritat fractal, on en les parts, ensopegues de sobte, amb la totalitat 😃)

N-gated Hacker NewsBehold, the "Mandelbrot Set Explorer"—a dizzying kaleidoscope for the mathematically obsessed 🌀, perfect if you're into endless options for color palettes that make Paint look high-tech 🎨. Just when you thought you had enough ways to procrastinate, here comes a <a href="https://mastodon.social/tags/UI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#UI</a> with more drop-downs than an Excel spreadsheet on steroids 📊. <a href="https://mandelbrot.site" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://mandelbrot.site</a> <a href="https://mastodon.social/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> <a href="https://mastodon.social/tags/Explorer" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Explorer</a> <a href="https://mastodon.social/tags/ColorPalettes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ColorPalettes</a> <a href="https://mastodon.social/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mastodon.social/tags/Procrastination" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Procrastination</a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/ngated" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ngated</a>

claudeI made a small page about my <a href="https://post.lurk.org/tags/conjecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#conjecture</a> on iteration count vs distance estimate bounds in the <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> <a href="https://mathr.co.uk/web/m-iteration-count-vs-distance-estimate.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://mathr.co.uk/web/m-iteration-count-vs-distance-estimate.html</a>

claudeinspired by tavis' deep field <a href="https://post.lurk.org/tags/nebulabrot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nebulabrot</a> <a href="https://post.lurk.org/tags/DeepZoom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DeepZoom</a> images on <a href="https://post.lurk.org/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractals</a> forums, I did a little shader that for each c in the complement of the <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.<a href="https://post.lurk.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://post.lurk.org/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://post.lurk.org/tags/ComplexDynamics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ComplexDynamics</a>

Oscar CunninghamWhat is the conjectured topology of the Mandelbrot set?My understanding is that for each p and k there's a certain number of bulbs, each centred around a point which becomes periodic with period p after k steps. But how do they all stick together?<a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/Mandelbrot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mandelbrot</a> <a href="https://mathstodon.xyz/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> <a href="https://mathstodon.xyz/tags/Fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fractal</a>

Víctorsí, el <a href="https://mastodon.cat/tags/mandelbrotset" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mandelbrotset</a> és encisador!... no serà perquè també ens permet visualitzar com d'interrelacionat està tot?

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