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#fractalart

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Mental Health Art<p>Light is the center 🌌 <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractal</span></a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractals</span></a> <a href="https://mastodon.social/tags/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mastodon.social/tags/consciousness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>consciousness</span></a> <a href="https://mastodon.social/tags/universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>universe</span></a></p>
Mental Health Art<p>Spin into stillness 🌌 <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractal</span></a> <a href="https://mastodon.social/tags/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractals</span></a> <a href="https://mastodon.social/tags/energyart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>energyart</span></a> <a href="https://mastodon.social/tags/consciousness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>consciousness</span></a> <a href="https://mastodon.social/tags/universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>universe</span></a></p>
Mental Health Art<p>Shine. Expand. Repeat. 🌌 <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractal</span></a> <a href="https://mastodon.social/tags/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractals</span></a> <a href="https://mastodon.social/tags/sacredgeometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sacredgeometry</span></a> <a href="https://mastodon.social/tags/energyart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>energyart</span></a> <a href="https://mastodon.social/tags/consciousness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>consciousness</span></a> <a href="https://mastodon.social/tags/universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>universe</span></a> <a href="https://mastodon.social/tags/trippy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>trippy</span></a></p>
Mental Health Art<p>The universe breathes through you 🌠 <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractal</span></a> <a href="https://mastodon.social/tags/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mastodon.social/tags/fractals" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractals</span></a> <a href="https://mastodon.social/tags/sacredgeometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sacredgeometry</span></a> <a href="https://mastodon.social/tags/energyart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>energyart</span></a> <a href="https://mastodon.social/tags/consciousness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>consciousness</span></a> <a href="https://mastodon.social/tags/trippy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>trippy</span></a> <a href="https://mastodon.social/tags/universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>universe</span></a></p>
Flame Reactor<p>Latimama's possibility space.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Meet Latimama, child of Parlagher and Orlens.<br>They are the product of 1 generations of breeding.<br>Latimama wishes they had more colors.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Risto A. Paju<p>2D circle inversion fractals on the spherical surface. This was a fun offshoot of my recent Apollonian endeavours, again using the Riemann sphere mapping to go from 3D to 2D for the iterations.</p><p>The inversion circle centres come from a tetrakis hexahedron and a triakis icosahedron, so the circles form approximations of a truncated octahedron and a truncated dodecahedron.</p><p><a href="https://mathstodon.xyz/tags/apolloniancircles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniancircles</span></a> <a href="https://mathstodon.xyz/tags/apolloniangasket" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniangasket</span></a> <a href="https://mathstodon.xyz/tags/inversion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>inversion</span></a> <a href="https://mathstodon.xyz/tags/circleinversion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>circleinversion</span></a> <a href="https://mathstodon.xyz/tags/riemannsphere" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>riemannsphere</span></a> <a href="https://mathstodon.xyz/tags/geometricart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometricart</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/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mathstodon.xyz/tags/pythoncode" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>pythoncode</span></a> <a href="https://mathstodon.xyz/tags/opengl" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>opengl</span></a> <a href="https://mathstodon.xyz/tags/algorithmicart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorithmicart</span></a> <a href="https://mathstodon.xyz/tags/algorist" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorist</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/laskutaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>laskutaide</span></a> <a href="https://mathstodon.xyz/tags/ittaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ittaide</span></a> <a href="https://mathstodon.xyz/tags/kuavataide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>kuavataide</span></a> <a href="https://mathstodon.xyz/tags/iterati" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>iterati</span></a></p>
Mental Health Art<p>Cosmic spark ignites the night 🌌✨ <a href="https://mastodon.social/tags/Fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Fractal</span></a> <a href="https://mastodon.social/tags/Universe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Universe</span></a> <a href="https://mastodon.social/tags/FractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FractalArt</span></a></p>
Risto A. Paju<p>In the last post, I noted how the incremental iterates of the Apollonian gasket look like the output of an iterated function system. There's indeed such an IFS, and it's a system of circle inversions. It's how I've made a lot of fractal art over the years, but I've usually started directly with the inversion circles/spheres themselves.</p><p>Now that I've worked with the "classical" approach to the Apollonian gasket, I thought I'd translate a given Apollonian setup to the language of inversions. It was a fun little exercise and the math was surprisingly simple, just playing with vectors and solving linear equations. I then used my old inversion shaders from the late 2010s to show the results.</p><p>The first part shows it all together: the 3 largest coloured circles are the initial Apollonian circles, and the 4 inversion circles can be seen in the darkest grey in the background. (The initial Apollonian circles also include a 4th one, but here we can only see it as the perimeter of the coloured area.)</p><p>The second part uses a pointillist process, and it shows essentially the incremental iterates of the previous post. The inversion circles are not seen, but the Apollonian circles are all there as the empty space.</p><p><a href="https://mathstodon.xyz/tags/apolloniancircles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniancircles</span></a> <a href="https://mathstodon.xyz/tags/apolloniangasket" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniangasket</span></a> <a href="https://mathstodon.xyz/tags/iteratedfunctionsystem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>iteratedfunctionsystem</span></a> <a href="https://mathstodon.xyz/tags/inversion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>inversion</span></a> <a href="https://mathstodon.xyz/tags/circleinversion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>circleinversion</span></a> <a href="https://mathstodon.xyz/tags/geometricart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometricart</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/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mathstodon.xyz/tags/pythoncode" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>pythoncode</span></a> <a href="https://mathstodon.xyz/tags/opengl" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>opengl</span></a> <a href="https://mathstodon.xyz/tags/algorithmicart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorithmicart</span></a> <a href="https://mathstodon.xyz/tags/algorist" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorist</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/laskutaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>laskutaide</span></a> <a href="https://mathstodon.xyz/tags/ittaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ittaide</span></a> <a href="https://mathstodon.xyz/tags/kuavataide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>kuavataide</span></a> <a href="https://mathstodon.xyz/tags/iterati" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>iterati</span></a></p>
Risto A. Paju<p>The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.</p><p><a href="https://mathstodon.xyz/tags/apolloniancircles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniancircles</span></a> <a href="https://mathstodon.xyz/tags/apolloniangasket" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>apolloniangasket</span></a> <a href="https://mathstodon.xyz/tags/riemannsphere" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>riemannsphere</span></a> <a href="https://mathstodon.xyz/tags/archimedeansolid" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>archimedeansolid</span></a> <a href="https://mathstodon.xyz/tags/truncatedoctahedron" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>truncatedoctahedron</span></a> <a href="https://mathstodon.xyz/tags/geometricart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometricart</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/fractalart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalart</span></a> <a href="https://mathstodon.xyz/tags/pythoncode" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>pythoncode</span></a> <a href="https://mathstodon.xyz/tags/opengl" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>opengl</span></a> <a href="https://mathstodon.xyz/tags/algorithmicart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorithmicart</span></a> <a href="https://mathstodon.xyz/tags/algorist" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorist</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/laskutaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>laskutaide</span></a> <a href="https://mathstodon.xyz/tags/ittaide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ittaide</span></a> <a href="https://mathstodon.xyz/tags/kuavataide" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>kuavataide</span></a> <a href="https://mathstodon.xyz/tags/iterati" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>iterati</span></a></p>
Flame Reactor<p>Bowraly in flight.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>This is Bowraly, child of Chichtel and Natts.<br>They are a Generation 6 fractal.<br>They are a bit shy.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Freedel wiggles.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Meet Freedel, child of Thof and Ostron.<br>They are a Generation 4 fractal.<br>They like simple fractals.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Bearton spins.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>This is Bearton, child of Subi and Hirschel.<br>They are the product of 5 generations of breeding.<br>Their favorite color is blue.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Machani flows.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>This is Machani, child of Stuckhum and Mazro.<br>They are a Generation 13 fractal.<br>They like geometric fractals.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>Stristen spins.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
Flame Reactor<p>This is Stristen, child of Obell and Arvine.<br>They are the product of 16 generations of breeding.<br>They like fancy fractals.</p><p>If this flame is beautiful, ⭐ or boost this post to improve its chances for future breedings.<br><a href="https://mastodon.social/tags/fractalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fractalArt</span></a></p>
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