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Daniel Piker
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@JuhaniHalkomaki Super cool!
@KangarooPhysics would it be possible to do a similar simulation using Kangaroo?
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#generative #creativecoding #p5js #blobs
Made a new softbody "simulation" from scratch. It's more stable than the previous version, and feels even squishier.
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@sl2c @bengineer8u Ah yes, quite right you are. 6R with 1dof is the one that doesn't fit the mobility criterion.
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@KangarooPhysics @bengineer8u If you calculate the number of variables and constraints, I'm pretty sure that with 6 you should expect 0dof and 7 you should expect 1dof
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Here's a fun little kinematic toy that's easy to make - an equilateral orthogonal hexagon linkage with 1 degree of freedom:
GIF
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@dodecahedra Interesting to see which of those you chose match the best known solutions for the
en.wikipedia.org/wiki/Thomson_p…
(the 'equivalent polyhedra' in the table there are for N vertices, so you'd need to take the duals for N faces)
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Not even going to tell you how much time I spent trying to come up with the iconic shape with n sides while repeating as little as possible.
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This clock makes no sense. Let's fix it!
1. Sphere
2. Circular cone
3. Circular cylinder
4. Tetrahedron
5. Triangular prism
6. Cube
7. Szilassi polyhedron
8. Octahedron
9. Obelisk
10. Square antiprism
11. Elongated pentagonal pyramid
12. Dodecahedron
(From @ihartblair)
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@RonAvitzur @alytile You can have strips of finite width which are periodic in one direction
twitter.com/cs_kaplan/stat…
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@alytile Is the tape genuinely aperiodic or is there a finite section which repeats with a seem? (Or does an aperiodic space filling tiling contain a periodic strip?)
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Forbidden aperiodic monotile masking tape.
禁断の非周期モノタイルのマスキングテープ
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@hamish_todd This all started many years ago (flickr.com/photos/32q2/49…) with thinking about the equivalent of a loxodrome in one dimension up. A Hopf link does make the most direct analogue for the 2 poles, with the surface twisting from one to the opposite one through the 3 sphere.
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@bennywahwah Not exclusively. 3 parts Real + 1 part Imaginary.
Just the real part would look like this
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@garciadelcast I think
@BathshebaSculpt
uses precisioncrystal.com
crystalproteins.com
bathsheba.com/crystal/
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Hello nerdy friends: anyone knows of any company that does custom orders for "subsurface laser engravings", aka #bubblegrams? Asking for a friend :)
en.wikipedia.org/wiki/Bubblegram
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@alytile Number 2 there doesn't connect up across adjacent tiles.
If connecting midpoints, and we want closed curves, I believe we need to include either all the red pts below, all the green points, or all of both.
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Inspired by .@KangarooPhysics I have two questions on the enumeration of einstein decoration especially hat and turtle.
Q1: Enumerate all decorated tiles with connected lines on their tiling for hat(8-kite) and turle(10-kite) using two gems. But use at least one A-gem.
Daniel Piker@KangarooPhysics
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@alytile Oh that's nice. I hadn't looked at patterns on the turtle yet. It seems there are several possibilities for connecting tangent arcs across the long edges
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Imagine it through your mind's eye! Let the new mathematical discovery take on familiar shapes as M.C. Escher did. #AperiodicTileMaker 登場！
数学の新発見「非周期タイル」を身近な形に見立ててみよましょう！
t3puzzle.com/a
GIF
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The Smith-Myers-Kaplan-Strauss monotile is composed of four double-kites. Colouring each double-kite either yellow or green depending on the parity of its orientation, each monotile is half-green and half-yellow; this induces a balanced yellow/green pattern on the hexagonal grid:
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@m_u_s_h_r_o_o_m @TylerGlaiel There's a whole class of equivalent arrangements extremely close to the optimal one. You'd need some precision manufacturing and stiff material to make it impossible to fit them into the same frame
twitter.com/KangarooPhysic…
Daniel Piker@KangarooPhysics
Also - it's not that there aren't any symmetric arrangements possible for 17. It's just that they're not as compact as the one on the right.
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@TylerGlaiel Also - i'd be interested to see if my solution fits in your tray! I think the main issue isn't just size tolerance, it's the corners, which we can't optimize much. I've been thinking of getting it cut out of metal, but sharp corners might be hard on the fingers anyway.
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I turned that cursed "optimal way to pack 17 squares into a square" thing into a physical puzzle
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.@KangarooPhysics
Could you share your truchet-like decoration on Twitter, too?
aperiodical.com/2023/03/an-ape…
これはやりたかった装飾デザイン。さすがpickerさん。
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今朝ビックニュースが飛び込んできました。ついに数学のアインシュタイン問題が解かたというのです。第一発見者のDave Smithさんはアーティストティックにテセレーションを探究する同志です。非周期にしか敷きつめられない不思議なタイルを自分でも理解しようと描いたが下のフラクタルタイルの図です
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Similar to what @alytile showed for the H/T/P/F metatiles (twitter.com/alytile/status…) these are the 2 fractal tiles for the substitution system in figure 2.11 of the new aperiodic monotile paper (arxiv.org/pdf/2303.10798…).
Yoshiaki Araki 荒木義明@alytile
今朝ビックニュースが飛び込んできました。ついに数学のアインシュタイン問題が解かたというのです。第一発見者のDave Smithさんはアーティストティックにテセレーションを探究する同志です。非周期にしか敷きつめられない不思議なタイルを自分でも理解しようと描いたが下のフラクタルタイルの図です
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