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꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂♻️<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/gonefractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#gonefractal</a> <a href="https://mastodon.gamedev.place/tags/redundant" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#redundant</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/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</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/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a>

safest_integer``` library(Matrix) n = 2^7 a = 0.022 b = 0.051 I = Diagonal(n) D = bandSparse(n, k=0:1, diag=list(rep(-2,n), rep(1,n-1)), sym=TRUE) Au = I-.08*D Av = I-.04*D v = matrix(0,n,n) j = n/2+(-n/4):(n/4) v[j,j] = 0.5 u = 1-v while(1) { uvv = u*v^2 u = u-uvv+a*(1-u) v = v+uvv-(a+b)*v u = as.matrix(solve(Au,u)) u = as.matrix(t(solve(Au,t(u)))) v = as.matrix(solve(Av,v)) v = as.matrix(t(solve(Av,t(v)))) image(u);dev.flush();dev.hold() } ``` <a href="https://mastodon.social/tags/rstats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rstats</a> <a href="https://mastodon.social/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> <a href="https://mastodon.social/tags/generativeart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#generativeart</a>Details👇

Bojidar MarinovThere are 8 possible moves knight moves on a chessboard, ignoring direction gives us 4. We can map those to 4 rhomboids formed out of such knight moves (fig. 2), which we can then define rules for to map to multiple smaller shapes (fig. 3). Recursively applying those rules nets us an aperiodic tiling of <a href="https://mastodon.social/tags/KnightPolygons" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KnightPolygons</a> for <a href="https://mastodon.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>! (fig. 1, 4) ✨

n-gonsI don’t have a submission for today’s <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a> but be sure to check post for other amazing contributors! Also, you are warmly encouraged to submit something - everyone is welcome!

foldworksFloor tiles, <a href="https://mathstodon.xyz/tags/Saigon" class="mention hashtag" rel="tag">#Saigon</a> Central Post Office, Ho Chi Minh City, <a href="https://mathstodon.xyz/tags/Vietnam" class="mention hashtag" rel="tag">#Vietnam</a> <a href="https://en.m.wikipedia.org/wiki/Saigon_Central_Post_Office" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://en.m.wikipedia.org/wiki/Saigon_Central_Post_Office</a> <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="tag">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="tag">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="tag">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="tag">#photography</a> <a href="https://mathstodon.xyz/tags/pattern" class="mention hashtag" rel="tag">#pattern</a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="tag">#architecture</a>

Malwen<a href="https://toot.wales/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> Created in <a href="https://toot.wales/tags/OneLab" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OneLab</a> for Android

TimemiTSome wiggly repeating structures surrounding a minibrot. UF6 Kate02 in EV / Distance estimator in SPR <a href="https://mastodon.scot/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> <a href="https://mastodon.scot/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a>

Alexandre MuñizFound an actual edgematch solution for these without a mistake this time.<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a>

safest_integer``` library(tidyverse) z = function(n) { bb = function(i) { x = y = 0 for (k in 0:(n - 1)) { x = x + ((floor(i/2^(2 * k))) %% 2) * 2^k y = y + ((floor(i/2^(2 * k + 1))) %% 2) * 2^k } c(x, y) } as.data.frame(t(sapply(0:(4^n - 1), bb))) } ggplot(z(6)) + geom_path(aes(x=V1, y=V2, col=sin(V1/4)+cos(V2/4)), show.legend=F) + scale_colour_gradient(low='orange', high='blue') + theme_void() ```<a href="https://en.wikipedia.org/wiki/Z-order_curve" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Z-order_curve</a> <a href="https://mastodon.social/tags/rstats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rstats</a> <a href="https://mastodon.social/tags/generativeart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#generativeart</a> <a href="https://mastodon.social/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> <a href="https://mastodon.social/tags/rtistry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rtistry</a> <a href="https://mastodon.social/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a>

Alexandre MuñizThere are 12 ways to tile a 3×3 square with an L tromino, two dominoes and two monominoes. These tilings seemed like a promising set to use in an edgematching puzzle. Here they are in a 2×6 edgematching configuration. (I added the dotted green lines to mark edges that have no match as an aid in solving.) [Edit: This one is bad: there's a mismatch on the rightmost column. I have a terrible eye for detail. But there are solutions.]<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a>

sɹɐʎA xɘlA 💻➡🗑<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

Bojidar MarinovFollowing up on last week's note on prime <a href="https://mastodon.social/tags/KnightPolygons" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KnightPolygons</a> (polygons formed by chess knight moves that cannot be subdivided into smaller such polygons), this week I decided to try tiling the plane with a tile formed out of the 14 prime knight polygons with area 6. Unfortunately, tiling was stymied by failure to enumerate all such polygons at the start as well as many, many failed attempts, so here is my two best almost-results, plus a prime knight polygon classification. 😅😊 <a href="https://mastodon.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂雲雲雲雲雲 雨雨雨雨雨 雨雨雨雨雨 雨雨雨雨雨 傘傘傘傘傘 人大人大人 凸凹道凹凸<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/superposition" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#superposition</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>

Viktor Tokariev 🇺🇦<a href="https://fosstodon.org/@BrunoLevy01" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@BrunoLevy01</a> 🫴 <a href="https://twiukraine.com/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

n-gons<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a> Tiling from <a href="https://mathstodon.xyz/tags/squares" class="mention hashtag" rel="tag">#squares</a> and <a href="https://mathstodon.xyz/tags/triangles" class="mention hashtag" rel="tag">#triangles</a><a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="tag">#MathArt</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="tag">#Geometry</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="tag">#Art</a>

foldworksPatterned carpet, Loughborough University, England <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="tag">#Tiling</a> <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="tag">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/Pattern" class="mention hashtag" rel="tag">#Pattern</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="tag">#Geometry</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="tag">#MathArt</a> <a href="https://mathstodon.xyz/tags/MathsArt" class="mention hashtag" rel="tag">#MathsArt</a>

Dani Laura (they/she/he)Tessellations with quarter of octagons and two sizes of squares. <a href="https://mathstodon.xyz/tags/tilingtuesday" class="mention hashtag" rel="tag">#tilingtuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="tag">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="tag">#tiling</a>

curved-rulerPerturbed grid for <a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

TimemiTIrregular things For <a href="https://mastodon.scot/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> UF6 Iterated Function Syndrome 21 in OM

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