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Fractal KittyA print has started<a href="https://mathstodon.xyz/tags/penplotter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#penplotter</a> <a href="https://mathstodon.xyz/tags/creativecoding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#creativecoding</a> <a href="https://mathstodon.xyz/tags/generative" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#generative</a> art <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/recurseCenter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#recurseCenter</a> <a href="https://mathstodon.xyz/tags/p5js" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#p5js</a> <a href="https://mathstodon.xyz/tags/d3" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#d3</a>

Zeno RoguePorted Seuphorica (Scrabble solitaire deckbuilder) to RogueViz for a more intuitive and powerful interface!(1) Infinite square grid, with standard Seuphorica special powers. Letters E and R (inverse colors close to the gigantic EE top left) are "reversing", hence "RE" is accepted and "EE" is accepted multiple times. Note the word GEESE which uses a portal to get a multiplier for gigantic 'E' two times in a single word. "PETER" uses a mirror.But since this is RogueViz, let us make the board geometry abstract, to have even more fun with geometry and topology!(2) Usually, words can only go "right" and "down". In hyperbolic geometry, we have holonomy, so "right" and "down" are not globally defined. So we have to accept both directions. (Or, optionally, only accept words if they are valid both ways.)(3) In this one, "right" and "down" are not globally defined either, but "horizontal" and "vertical" are (in a somewhat twisted way), so Seuphorica "horizontal" and "vertical" multiplier powers can work.Although the hexagons somehow turn a horizontal word into a vertical one...<a href="https://mathstodon.xyz/tags/RogueViz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RogueViz</a> <a href="https://mathstodon.xyz/tags/NonEuclideanGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclideanGeometry</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/noneuclidean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#noneuclidean</a> <a href="https://mathstodon.xyz/tags/HyperbolicGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperbolicGeometry</a> <a href="https://mathstodon.xyz/tags/Seuphorica" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Seuphorica</a> <a href="https://mathstodon.xyz/tags/scrabble" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#scrabble</a>(to be continued...)

foldworksTiled entrance to a “buzzy gathering place” (eatery) in Lancaster, England. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</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/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pattern</a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#architecture</a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#design</a>

n-gons<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> Snub Flower Tiling RevisitedI found a beautiful egg shape hidden in my previous design.Also note: Today, new versions of the mac apps I use for most of my tiling designs are released!! That is <a href="https://mastodon.cc/@zellige" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@zellige</a>, which I used for the egg, as well as <a href="https://mastodon.social/@girih" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@girih</a> (for equilateral shapes), thank you Stefan!<a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/Egg" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Egg</a> <a href="https://mathstodon.xyz/tags/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a>

Gwen FisherI was commissioned to remake an old painting, Doodle No. 57, for someone to gift to their advisor. It’s always fun revisiting old subjects with new skills. Shading has gotten a lot easier for me since then. Of course, there’s still room for improvement but I think the illusion of depth here is reasonably convincing. Pigeon Hole Principle Doodle No. 145 8” square Watercolor on Arches cotton paper If there are more pigeons than holes, at least one hole must have more than one pigeon. <a href="https://mathstodon.xyz/tags/watercolor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#watercolor</a> <a href="https://mathstodon.xyz/tags/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</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/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>

n-gonsSnub Flower TilingIf you look careful you can see the snub square tiling and its cairo cousin hiding in the geometry.<a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</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/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂<a href="https://mastodon.gamedev.place/tags/4d" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#4d</a> cartesian product of 2 of ðese fancy pentagonal tilings + 🔄2d✝️sections = 🤔🤔🤔<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/mastoart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mastoart</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#abstract</a> <a href="https://mastodon.gamedev.place/tags/monochrome" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#monochrome</a> <a href="https://mastodon.gamedev.place/tags/animation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#animation</a> <a href="https://mastodon.gamedev.place/tags/creativecoding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#creativecoding</a>

n-gonsA <a href="https://mathstodon.xyz/tags/pentagon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pentagon</a> <a href="https://mathstodon.xyz/tags/flower" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#flower</a> for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> This tiling uses 931 equilateral tiles.<a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</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/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a>

Dani Laura (they/she/he)Artistic rendering of a <a href="https://mathstodon.xyz/tags/CairoTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CairoTiling</a> . <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a>

foldworksSeat upholstery, Stockholm, Sweden <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</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/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pattern</a>

Fractal KittyI am super excited to host the 238th Carnival of Mathematics. Please submit your beautiful mathy thoughts, art, and musings (prior to 4/1/25)<a href="https://aperiodical.com/carnival-of-mathematics/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://aperiodical.com/carnival-of-mathematics/</a>This includes <a href="https://mathstodon.xyz/@Ayliean" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@Ayliean</a> 's <a href="https://mathstodon.xyz/tags/mathArtMarch" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathArtMarch</a> prompts - I hope to have a section for what everyone does this month. I am grateful to know any interesting tidbits about the number 238 as well - Why is this number special to you?<a href="https://mathstodon.xyz/tags/carnivalOfMathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#carnivalOfMathematics</a> <a href="https://mathstodon.xyz/tags/indieWeb" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#indieWeb</a> <a href="https://mathstodon.xyz/tags/personalBlog" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#personalBlog</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/aperiodical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#aperiodical</a> <a href="https://mathstodon.xyz/tags/blogger" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#blogger</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a>

NaomiOrigami pentakis dodecahedron!I decided a few weeks ago that I wanted to make a truncated isocahredron out of sonobe units. I made some and started assembling them into triangles and then (what I now know to be) a hexapentakis truncated icosahedron. I soon decided to actually calculate how many sonobe modules I would need and decided 270 was far too many so rethought my plan and settled on a pattern that only requires 90 modules. I then set various rules for the colours and spent a lot of last week playing with different options and trying to find one which satisfied my conditions. I was working on colouring the graph of a truncated isocahredron and wanted: (1) all edges around a face to be a different colour to each other and (2) all edges coming out of a face (spokes?) to be different colours to each other too (and of course any adjacent edges must be different but this is covered by condition (1)). After many failed attempts of doing this by hand and beginning to doubt it was possible, I eventually numbered the edges and made this into a graph colouring problem on a graph with 90 vertices and stuck it into Sage which confirmed the chromatic number of the 90-vertex graph was in fact 6 and gave me a possible colouring. Then several hours later at the end of last week, the modules had been put together. Due to the way each edge from my diagram was rotated, the resulting shape is made of triangular faces (if you imagine filling in the gaps) and is in fact the dual of the truncated icosahedron - i.e. the pentakis dodecahedron.<a href="https://mathstodon.xyz/tags/MathsArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathsArt</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/Origami" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Origami</a>

n-gonsThis is a tiling of different size 90-36-54 triangles. <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a>

Andrew D. HwangIf \(\alpha\) is irrational, the path \[ (x, y) = (\cos t + \cos(\alpha t), \sin t + \sin(\alpha t)) \] maps the real line to a dense subset of the disk of radius \(2\). If we plot points for regularly-spaced \(t\), with spacing not a rational multiple of either \(2\pi\) or \(2\pi/\alpha\), we get some indication of the geometry of this path, and how sensitively it depends on \(\alpha\).If you have a minute (60 frames at one frame per second), each image shows the result of plotting points with \(t\) an integer, starting at \(0\) and with \(100\) points in each of \(60\) shades from red to gold. As we step through the frames, the real parameter \(\alpha\) increments along an interval of length \(1/10\) centered at \(\sqrt{3}\).<a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a>

Dani Laura (they/she/he)Another version starting with a square, blue palette. <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂(9.9.6/2-ish) when u can't decide if u want to call ur cat lizard or broadsword 🤔<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/why" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#why</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mastoart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mastoart</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#abstract</a> <a href="https://mastodon.gamedev.place/tags/animation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#animation</a>

Dani Laura (they/she/he)Artwork based on dividing a rectangle into two rectangles, depending on the shape of the rectangle, and iterating recursively. Colors are computed from the shapes of the parent rectangles. The ratio in this case is √3, which has special properties for the procedure. <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a>

foldworksDoor with grille, Argos, Greece <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</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/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#architecture</a>

n-gons<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> Sprials from right triangles<a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/Triangle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Triangle</a> <a href="https://mathstodon.xyz/tags/Sprial" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sprial</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a>

Gwen Fisher3 by 3 Skew-Symmetric Mew Tricks Doodle No. 142 Watercolor and pigment ink on cotton paper 6 inches squareA skew-symmetric matrix is a square matrix where its transpose is equal to its negative. One property of such a matrix is all of the diagonal elements are zero.<a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/watercolor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#watercolor</a> <a href="https://mathstodon.xyz/tags/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a>

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