#Fractals

Adam PSome crazy dancing <a href="https://mastodon.r-flash.eu/tags/psychedelic" class="mention hashtag" rel="nofollow noopener" target="_blank">#psychedelic</a> <a href="https://mastodon.r-flash.eu/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> I found pretty 🙂

Some Bits: Nelson's LinkblogElectric Sheep: Long-running collaborative computer art project, using CPU time on multiple machines. Been around 25 years now? <a href="https://electricsheep.org/" rel="nofollow noopener" translate="no" target="_blank">https://electricsheep.org/</a> <a href="https://tech.lgbt/tags/crowdsourcing" class="mention hashtag" rel="nofollow noopener" target="_blank">#crowdsourcing</a> <a href="https://tech.lgbt/tags/generative" class="mention hashtag" rel="nofollow noopener" target="_blank">#generative</a> <a href="https://tech.lgbt/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://tech.lgbt/tags/art" class="mention hashtag" rel="nofollow noopener" target="_blank">#art</a> #+

claude<a href="https://post.lurk.org/tags/Fraktaler" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fraktaler</a> <a href="https://post.lurk.org/tags/Fraktaler3" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fraktaler3</a> v3 <a href="https://post.lurk.org/tags/release" class="mention hashtag" rel="nofollow noopener" target="_blank">#release</a> <a href="https://post.lurk.org/tags/DeepZoom" class="mention hashtag" rel="nofollow noopener" target="_blank">#DeepZoom</a> <a href="https://post.lurk.org/tags/hybrid" class="mention hashtag" rel="nofollow noopener" target="_blank">#hybrid</a> <a href="https://post.lurk.org/tags/EscapeTime" class="mention hashtag" rel="nofollow noopener" target="_blank">#EscapeTime</a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://post.lurk.org/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> binaries for Web, Android and Windows, built from Debian Linux, source for all those platforms<a href="https://fraktaler.mathr.co.uk/" rel="nofollow noopener" translate="no" target="_blank">https://fraktaler.mathr.co.uk/</a>changes since v2.1 (July 2023) are too many for this toot, the main new feature is flexibile colouring with GLSL shader fragment.changes since v3~preview (June 2024) are quite small (a few bug fixes, some enhancements).

bbqshoes<a href="https://mastodon.art/tags/Thursday" class="mention hashtag" rel="nofollow noopener" target="_blank">#Thursday</a> <a href="https://mastodon.art/tags/Fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fractals</a> <a href="https://mastodon.art/tags/DigitalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#DigitalArt</a> <a href="https://mastodon.art/tags/Trippy" class="mention hashtag" rel="nofollow noopener" target="_blank">#Trippy</a>

Daniel PomarèdeCosmography archives1999: Is the Universe Fractal?A perspectives paper by Vicent J. Martinez for Science Magazine <a href="https://www.science.org/doi/10.1126/science.284.5413.445" rel="nofollow noopener" translate="no" target="_blank">https://www.science.org/doi/10.1126/science.284.5413.445</a> <a href="https://mastodon.social/tags/Cosmography" class="mention hashtag" rel="nofollow noopener" target="_blank">#Cosmography</a> <a href="https://mastodon.social/tags/Cosmology" class="mention hashtag" rel="nofollow noopener" target="_blank">#Cosmology</a> <a href="https://mastodon.social/tags/galaxies" class="mention hashtag" rel="nofollow noopener" target="_blank">#galaxies</a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/Universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#Universe</a> <a href="https://mastodon.social/tags/Astrodon" class="mention hashtag" rel="nofollow noopener" target="_blank">#Astrodon</a> <a href="https://mastodon.social/tags/Astronomy" class="mention hashtag" rel="nofollow noopener" target="_blank">#Astronomy</a> <a href="https://mastodon.social/tags/Astrophysics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Astrophysics</a> <a href="https://mastodon.social/tags/science" class="mention hashtag" rel="nofollow noopener" target="_blank">#science</a> <a href="https://mastodon.social/tags/STEM" class="mention hashtag" rel="nofollow noopener" target="_blank">#STEM</a> <a href="https://mastodon.social/tags/archive" class="mention hashtag" rel="nofollow noopener" target="_blank">#archive</a> <a href="https://mastodon.social/tags/archives" class="mention hashtag" rel="nofollow noopener" target="_blank">#archives</a> <a href="https://mastodon.social/tags/CosmographyArchives" class="mention hashtag" rel="nofollow noopener" target="_blank">#CosmographyArchives</a>

Alexandre B A Villares 🐍"Lindenmayer Systems, Fractals, and Plants" (PRUSINKIEWICZ; HANAN, 1989) <a href="https://link.springer.com/book/10.1007/978-1-4757-1428-9" rel="nofollow noopener" translate="no" target="_blank">https://link.springer.com/book/10.1007/978-1-4757-1428-9</a><a href="https://ciberlandia.pt/tags/LSystem" class="mention hashtag" rel="nofollow noopener" target="_blank">#LSystem</a> <a href="https://ciberlandia.pt/tags/Fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fractals</a> <a href="https://ciberlandia.pt/tags/Mandelbrot" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mandelbrot</a> <a href="https://ciberlandia.pt/tags/ComputationalBiology" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputationalBiology</a>

Alexandre B A Villares 🐍I should be working but I got stuck watching this <a href="https://www.youtube.com/watch?v=Ed1gsyxxwM0" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/watch?v=Ed1gsyxxwM0</a><a href="https://ciberlandia.pt/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://ciberlandia.pt/tags/Mandelbrot" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mandelbrot</a> <a href="https://ciberlandia.pt/tags/JuliaSet" class="mention hashtag" rel="nofollow noopener" target="_blank">#JuliaSet</a>

Emlyn<a href="https://mastodon.world/tags/MathArtMarch" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArtMarch</a> Day 18 (Chance) Many of the images I've made are based on known <a href="https://mastodon.world/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> or slight variations of them. This one is not based on anything in particular, I just stumbled upon it by chance as I was playing around in <a href="https://mastodon.world/tags/PowerPoint" class="mention hashtag" rel="nofollow noopener" target="_blank">#PowerPoint</a>. <a href="https://mastodon.world/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mastodon.world/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://mastodon.world/tags/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractalart</a> <a href="https://mastodon.world/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a>

Emlyn<a href="https://mastodon.world/tags/MathArtMarch" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArtMarch</a> Day 6 (Single Line) There are quite a few <a href="https://mastodon.world/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> made by repeatedly modifying a single line. I decided to go for one of the less well known ones (at least to me), the Fibonacci Word Fractal. Again, this is made completely in <a href="https://mastodon.world/tags/PowerPoint" class="mention hashtag" rel="nofollow noopener" target="_blank">#PowerPoint</a>. <a href="https://mastodon.world/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mastodon.world/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mastodon.world/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a>

claude10 years (exactly) on from my unanswered question"Interior Distnace Estimate for Julia Sets - Getting Rid Of Spots" <a href="https://math.stackexchange.com/questions/1153052/interior-distance-estimate-for-julia-sets-getting-rid-of-spots" rel="nofollow noopener" translate="no" target="_blank">https://math.stackexchange.com/questions/1153052/interior-distance-estimate-for-julia-sets-getting-rid-of-spots</a>I think I found the answer: apply l'Hospital's rule to the limit for attracting (not super-attracting) interior distance, take the maximum of all such distance estimates.<a href="https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule" rel="nofollow noopener" translate="no" target="_blank">https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule</a>Not very principled (I haven't checked the necessary conditions for the rule to be valid), but seems to work ok for removing the spots at the preimages of the attractor.<a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://post.lurk.org/tags/JuliaSet" class="mention hashtag" rel="nofollow noopener" target="_blank">#JuliaSet</a> <a href="https://post.lurk.org/tags/DistanceEstimate" class="mention hashtag" rel="nofollow noopener" target="_blank">#DistanceEstimate</a> <a href="https://post.lurk.org/tags/graphics" class="mention hashtag" rel="nofollow noopener" target="_blank">#graphics</a> <a href="https://post.lurk.org/tags/attractor" class="mention hashtag" rel="nofollow noopener" target="_blank">#attractor</a> <a href="https://post.lurk.org/tags/PreImage" class="mention hashtag" rel="nofollow noopener" target="_blank">#PreImage</a>

AI6YR BenFractal cabbage (err... Romanesco broccoli) <a href="https://m.ai6yr.org/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://m.ai6yr.org/tags/farmersmarket" class="mention hashtag" rel="nofollow noopener" target="_blank">#farmersmarket</a>

💧🌏 Greg CocksScaling In Branch Thickness And The Fractal Aesthetic Of Trees [In Art From Da Vinci To Mondrian] -- <a href="https://academic.oup.com/pnasnexus/article/4/2/pgaf003/7996468" rel="nofollow noopener" translate="no" target="_blank">https://academic.oup.com/pnasnexus/article/4/2/pgaf003/7996468</a> <-- shared paper -- [not my usual fare, but love the spatial mathematical components, although the maths is way over my head!] <a href="https://techhub.social/tags/spatial" class="mention hashtag" rel="nofollow noopener" target="_blank">#spatial</a> <a href="https://techhub.social/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://techhub.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://techhub.social/tags/art" class="mention hashtag" rel="nofollow noopener" target="_blank">#art</a> <a href="https://techhub.social/tags/painting" class="mention hashtag" rel="nofollow noopener" target="_blank">#painting</a> <a href="https://techhub.social/tags/representation" class="mention hashtag" rel="nofollow noopener" target="_blank">#representation</a> <a href="https://techhub.social/tags/daVinci" class="mention hashtag" rel="nofollow noopener" target="_blank">#daVinci</a> <a href="https://techhub.social/tags/LeonardodaVinci" class="mention hashtag" rel="nofollow noopener" target="_blank">#LeonardodaVinci</a> <a href="https://techhub.social/tags/MurraysLaw" class="mention hashtag" rel="nofollow noopener" target="_blank">#MurraysLaw</a> <a href="https://techhub.social/tags/tree" class="mention hashtag" rel="nofollow noopener" target="_blank">#tree</a> <a href="https://techhub.social/tags/vegetation" class="mention hashtag" rel="nofollow noopener" target="_blank">#vegetation</a> <a href="https://techhub.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://techhub.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://techhub.social/tags/%CE%B1" class="mention hashtag" rel="nofollow noopener" target="_blank">#α</a> <a href="https://techhub.social/tags/biology" class="mention hashtag" rel="nofollow noopener" target="_blank">#biology</a> <a href="https://techhub.social/tags/artwork" class="mention hashtag" rel="nofollow noopener" target="_blank">#artwork</a> <a href="https://techhub.social/tags/radiusscalingexponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#radiusscalingexponent</a> <a href="https://techhub.social/tags/branches" class="mention hashtag" rel="nofollow noopener" target="_blank">#branches</a> <a href="https://techhub.social/tags/branching" class="mention hashtag" rel="nofollow noopener" target="_blank">#branching</a> <a href="https://techhub.social/tags/nature" class="mention hashtag" rel="nofollow noopener" target="_blank">#nature</a> <a href="https://techhub.social/tags/naturalpatterns" class="mention hashtag" rel="nofollow noopener" target="_blank">#naturalpatterns</a> <a href="https://techhub.social/tags/proportions" class="mention hashtag" rel="nofollow noopener" target="_blank">#proportions</a> <a href="https://techhub.social/tags/physiology" class="mention hashtag" rel="nofollow noopener" target="_blank">#physiology</a> <a href="https://techhub.social/tags/Mondrian" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mondrian</a> <a href="https://techhub.social/tags/aesthetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#aesthetic</a> <a href="https://techhub.social/tags/aesthetics" class="mention hashtag" rel="nofollow noopener" target="_blank">#aesthetics</a> <a href="https://techhub.social/tags/scale" class="mention hashtag" rel="nofollow noopener" target="_blank">#scale</a> <a href="https://techhub.social/tags/scaling" class="mention hashtag" rel="nofollow noopener" target="_blank">#scaling</a>

claudeinspired by tavis' deep field <a href="https://post.lurk.org/tags/nebulabrot" class="mention hashtag" rel="nofollow noopener" target="_blank">#nebulabrot</a> <a href="https://post.lurk.org/tags/DeepZoom" class="mention hashtag" rel="nofollow noopener" target="_blank">#DeepZoom</a> images on <a href="https://post.lurk.org/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener" 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" 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" target="_blank">#math</a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://post.lurk.org/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#proof</a> <a href="https://post.lurk.org/tags/ComplexDynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComplexDynamics</a>

groffTake the parity of the indices of the terms of the continued fraction of Liouville's constant that equal 8. For odd numbers turn left, for even turn right.What do you get?The Dragon curve appears, again. It's everywhere.This works with indices equalling 1 too (for 9 you'll have to ignore the first digit)<a href="https://mastodon.me.uk/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://mastodon.me.uk/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.me.uk/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mastodon.me.uk/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a>

michael16-Jan-2025 New 2D multifractal tools delve into <a href="https://mastodon.social/tags/Pollock" class="mention hashtag" rel="nofollow noopener" target="_blank">#Pollock</a>'s <a href="https://mastodon.social/tags/expressionism" class="mention hashtag" rel="nofollow noopener" target="_blank">#expressionism</a><a href="https://www.eurekalert.org/news-releases/1070719" rel="nofollow noopener" translate="no" target="_blank">https://www.eurekalert.org/news-releases/1070719</a> <a href="https://mastodon.social/tags/science" class="mention hashtag" rel="nofollow noopener" target="_blank">#science</a> <a href="https://mastodon.social/tags/art" class="mention hashtag" rel="nofollow noopener" target="_blank">#art</a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a>

ECHAEAJ'ai acheté ça 3€ en brocante...je l'ouvre et que vois-je ? 😮 <a href="https://mamot.fr/tags/mandelbrot" class="mention hashtag" rel="nofollow noopener" target="_blank">#mandelbrot</a> <a href="https://mamot.fr/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://mamot.fr/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a>

Toni AittoniemiRoses in the breeze Violets are blackMoon is made of cheese Mandelboxes are made of math<a href="https://mastodon.green/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a> <a href="https://mastodon.green/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> <a href="https://mastodon.green/tags/realtime" class="mention hashtag" rel="nofollow noopener" target="_blank">#realtime</a> <a href="https://mastodon.green/tags/raymarching" class="mention hashtag" rel="nofollow noopener" target="_blank">#raymarching</a> <a href="https://mastodon.green/tags/coding" class="mention hashtag" rel="nofollow noopener" target="_blank">#coding</a> <a href="https://mastodon.green/tags/vfx" class="mention hashtag" rel="nofollow noopener" target="_blank">#vfx</a>

Lukas VFN 🇪🇺Never a Dull Enzyme <a href="https://schaechter.asmblog.org/schaechter/2024/05/never-a-dull-enzyme.html" rel="nofollow noopener" translate="no" target="_blank">https://schaechter.asmblog.org/schaechter/2024/05/never-a-dull-enzyme.html</a> <a href="https://mstdn.science/@STCmicrobeblog" class="u-url mention" rel="nofollow noopener" target="_blank">@STCmicrobeblog</a> Emergence of fractal geometries in the <a href="https://scholar.social/tags/evolution" class="mention hashtag" rel="nofollow noopener" target="_blank">#evolution</a> of a metabolic enzyme: Franziska Sendker et al. <a href="https://www.nature.com/articles/s41586-024-07287-2" rel="nofollow noopener" translate="no" target="_blank">https://www.nature.com/articles/s41586-024-07287-2</a>"Citrate synthase from S. elongatus has the peculiar capacity to self-assemble into a type of <a href="https://scholar.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> shape known as a <a href="https://scholar.social/tags/Sierpi%C5%84ski" class="mention hashtag" rel="nofollow noopener" target="_blank">#Sierpiński</a> triangle. This is not a universal feature of citrate synthases, there's something unique about the one from this <a href="https://scholar.social/tags/cyanobacterium" class="mention hashtag" rel="nofollow noopener" target="_blank">#cyanobacterium</a>." <a href="https://scholar.social/tags/bacteria" class="mention hashtag" rel="nofollow noopener" target="_blank">#bacteria</a> <a href="https://scholar.social/tags/microbes" class="mention hashtag" rel="nofollow noopener" target="_blank">#microbes</a> <a href="https://scholar.social/tags/cyanobacteria" class="mention hashtag" rel="nofollow noopener" target="_blank">#cyanobacteria</a> <a href="https://scholar.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a>

sɹɐʎA xɘlA 💻➡🗑Some moron on mastodon.social just reported me to myself because they think <a href="https://genart.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractals</a> are <a href="https://genart.social/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#AI</a>, lol

Eclectic Human<a href="https://zirk.us/tags/ProfilePicture" class="mention hashtag" rel="nofollow noopener" target="_blank">#ProfilePicture</a>: the Phoenix, dreaming of flight, re-creates itself in a <a href="https://zirk.us/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> flame. <a href="https://zirk.us/tags/Avatar" class="mention hashtag" rel="nofollow noopener" target="_blank">#Avatar</a> <a href="https://zirk.us/tags/Fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fractals</a> <a href="https://zirk.us/tags/FractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#FractalArt</a> <a href="https://zirk.us/tags/Metamorphosis" class="mention hashtag" rel="nofollow noopener" target="_blank">#Metamorphosis</a><a href="https://zirk.us/tags/Header" class="mention hashtag" rel="nofollow noopener" target="_blank">#Header</a> photo: View up into the spreading, spiraling branches of a large pine tree at Wallingford Castle Gardens, Oxfordshire.

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