#monotile — Public Fediverse posts

Well this is, indeed, fun.
I have lots of tweaks to do to the final output, but it works.
My only challenge now is knowing when to stop, ie have I covered the rectangle I want? Slightly harder than it sounds, but I have a plan #spectre #monotile

Some of my patterns are based on tilings with can be thought of as having overlapping parts, this overlap often consists of something that looks like a border.

An example is this sequence in which the “borders” are unclear until they resolve into borders of a snub square tiling, or its Cairo-type tiling dual.

https://mathstodon.xyz/@HypercubicPeg/109043217999286054

————

Often when I do something like this, I can find an infinite class of “tiles” where the pattern along the border can be incremented in some predictable way.

A little while back, I had a go at trying to interpret the Hat tile in a similar way using edge-touching dodecagons. Here is one of the versions that I liked.

#mathart #mathsart #aperiodicMonotile #monotile #tiling #tilingTuesday

What do you get when your #ADnD #Dungeon master is a #maths nerd? You get a #MathsPuzzle like this: there's a weirdly shaped hole in the wall, and a bunch of puzzle pieces on the floor looking all the same... #monotile

Note: I'm not looking for a solution, we want to figure it out in our next session!

Hats on a soccer ball by @jonpaulsballs #BridgesMathArt #aperiodic #monotile #tiling #geometry

When it comes to debugging, I have a bad habit of sometimes guessing parameters when I think that all that prevents me getting the output I expect is something simple, like an incorrect sign. Invariably I end up wasting far too much time making increasingly complicated guesses, when a few minutes thought and some pen and paper would have revealed the bug. I don't recommend this habit to anyone, but in one instance it led me to discover a series of tilings that I probably wouldn't have found otherwise.

Take a tiling of turtle tiles (a version of the chiral aperiodic monotile), throw away the tiles with less frequent handedness, and flip the other tiles about the axis shown in the first image. This doesn't produce a new tiling, since there will be overlaps. However, the tiles can be grouped in roughly triangular clusters of 1, 3 or 6 tiles, all with the same orientation modulo \(120^\circ\), and the tiles in each cluster don't overlap after flipping. In addition, the clusters of flipped tiles can be translated in a consistent manner to avoid overlaps, leaving a partial tiling whose gaps all have the same shape - the 'rooster'.

(1/n)
#tilingTuesday #aperiodic #monotile #tiling

I doodled a spectres tonight (image is here, tiles are on my blog post).

https://fractalkitty.com/2023/06/07/spectre-tiles/

#spectre #aperiodic #monotile #mathart #fresco #jellyfish #tiling #chiral #ocean #hat

@jchyip
Great!
"[...] a pattern that never repeats".
"The einstein sits in a weird purgatory between #order and #disorder."
An aperiodic #monotile.

Before: periodic monotiles.

My guess:
the #Triangle (prime number 3) is the key element to order (in terms of 'arrange') such an asymetric existence.

#Thx4sharing, @gerritbeine !

https://www.architonic.com/es/product/valence-design-monotile-concrete-light-grey/1501310

Monotile is the name of my heavy metal nerdcore theremin band. The songs have a time signature of π/4.

#monotile #AperiodicMonotile #HeavyMetal #nerdcore #theremin #pi #math #mathematics #mathtodon #music #musictodon