bolha.us

1 post1 participant0 posts today

claudedid some experiments tracing <a href="https://post.lurk.org/tags/ExternalRay" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExternalRay</a> in <a href="https://post.lurk.org/tags/InflectorGadget" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InflectorGadget</a> Julia morphing.the <a href="https://post.lurk.org/tags/ExternalAngle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExternalAngle</a> (expressed as binary expansion) of the rays of the inflection nodes in the <a href="https://post.lurk.org/tags/JuliaSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JuliaSet</a> have unchanging periodic part corresponding to the starting minibrot, while the length of the preperiodic part increases linearly with each morph (e.g. adding a constant number of bits each time), zoom depth is constant, but the stretching dynamics sometimes need precision to be increased.compare with <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> morphs by deep zooming, where the length of the periodic part (and thus iteration count) increases exponentially with each morph (e.g. doubling each time), and zoom depth goes up typically by 150% (requiring 150% higher precision).<a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractals</a>

claudeJust published: web version of <a href="https://post.lurk.org/tags/InflectorGadget" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InflectorGadget</a> inflection mapping gadget for <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> <a href="https://post.lurk.org/tags/JuliaSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JuliaSet</a> <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> <a href="https://post.lurk.org/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathr.co.uk/ig/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://mathr.co.uk/ig/</a>Pro-tip: keep the Add tool selected and use mouse wheel to zoom if available, otherwise (e.g. touch screen) you need to keep switching between toolsClick the hash button in the top left to update the address bar URL before sharing (otherwise it might not be up to date), here's one I did today (3 things in a rabbit: right-handed tree, left-handed tree, line):<a href="https://mathr.co.uk/ig/#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" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://mathr.co.uk/ig/#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</a>

claudetoday I added a quantization option to <a href="https://post.lurk.org/tags/InflectorGadget" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InflectorGadget</a>, to snap inflection points to <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> nucleus (first one) and preimages of <a href="https://post.lurk.org/tags/JuliaSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JuliaSet</a> attractor (later ones) - this makes all the nodes as circular as possiblethis also makes the structure exactly reproducible (by a human, no automation yet) from instructions as there's no fuzzy variation coming from imprecise mouse click locationsthe human touch adds a certain pleasant softness, so quantum mode is optional

bbqshoes<a href="https://mastodon.art/tags/Monday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Monday</a> <a href="https://mastodon.art/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mastodon.art/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> <a href="https://mastodon.art/tags/Mood" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mood</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>

Microfractal<a href="https://mathstodon.xyz/tags/fractalfriday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractalfriday</a> A silent treeThe triangle inequality average coloring method also works for non-Mandelbrot fractals.Formula: \(z_{n+1} = |re(z_n^2)| +im(z_n^2) + c\) Coordinates: x: -1.7463650472347604109617 y: 0.00128414711414212653456240 size: 3.814697265625e-06<a href="https://mathstodon.xyz/tags/digitalart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#digitalart</a> <a href="https://mathstodon.xyz/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a> <a href="https://mathstodon.xyz/tags/fractalart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractalart</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/mandelbrotfractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mandelbrotfractal</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/tree" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tree</a>

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