Yoshiaki Araki 荒木義明 Profile picture
May 30 19 tweets 11 min read Twitter logo Read on Twitter
[BREAKING] A chiral aperiodic monotile finally discovered!
[速報] 鏡像なしの非周期モノタイルが発見される。
それも前回のTile(1,1)にマッチングルールをつけた形とな!辺を変形できるのでデザインしがいがありそう
何に見える?身近な何かに見立てみよう!
#aperiodic Image
早速亀の辺を曲げて描いてみました
Now, I am curved!
もっと変形させたら変な妖怪が出てきました
カマキリ?ロックダンサー?あなたなら妖怪タイル(Spectres tile)を何に見立てる?
#aperiodic #chiral

.@apu_yokai さんのdesmosを使っていろんな形を想像してみよう! Image
ドラゴン?タツノオトシゴ?
What do you imagine from this shape, a newly discovered Spectres tile? Dragons? Sea dragons? Draw inside the shape to make your imagination to recognizable to everyone!
#aperiodic #chiral #spectres Image
渦巻き巻き巻き
What do you imagine from this shape, a newly discovered Spectres tile? Draw inside the shape to make your imagination to recognizable to everyone! #aperiodic #chiral #spectres Image
一ついい感じ形ができると、その双子が存在します。
これは先の逆巻きバージョン What do you imagine from this shape, a newly discovered Spectres tile? Draw inside the shape to make your imagination to recognizable to everyone! #aperiodic #chiral #spectres Image
カマキリ?Mantis?
What do you imagine from this shape, a newly discovered Spectres tile? Draw inside the shape to make your imagination to recognizable to everyone! #aperiodic #chiral #spectres Image
可愛いモンスターをゲット?Cute monster?
What do you imagine from this shape, a newly discovered Spectres tile? Draw inside the shape to make your imagination to recognizable to everyone! #aperiodic #chiral #spectres Image
ステゴサウルス?stegosaurus?
What do you imagine from this shape, a newly discovered Spectres tile? Draw inside the shape to make your imagination to recognizable to everyone! #aperiodic #chiral #spectres #dino #dinosaur Image
象とも目が合いました
I saw eye-to-eye with elephant during deforming the Specture tile.

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More from @alytile

May 30
[Now curved!] The substitution system of chiral aperiodic spectres turtles.
鏡像なしの非周期モノタイルは辺を変形できます。早速、亀の輪郭をちょっと曲げてみたよ(ちょっとだけど曲がってます)。今回の置換ルールはなんか複雑?!
30度傾くタイルがあったり、塊同士が重なって嵌るみたい(続 Image
新論文のFig2.2の置換システムはちょっと不思議。
初期値は一匹の亀。次のステップで全部を裏にしてから並べています。このうち緑の亀だけ30度分ズレている。
この30度のズレは前回の非周期タイリングには現れない置き方で、これが今回の鍵なんだろうか?青は論文の薄緑に対応arxiv.org/abs/2305.17743 Image
ちなみに緑と青の亀の塊を「Mystic」(神秘?)と呼ぶそうです。さて置換システムの2回目では9匹の亀の塊を8つ作り全部裏にして並べます。このときピンク色の部分が1箇所重なります(ナゼ!) Image
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