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Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/
#aperiodicMonotile #til
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Taking some time away from the herd.
#sea #cow
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As a follow up to last week's post on Markov partitions for Hat (hat and turtle) and Spectre (hats in turtles and turtles in hats) tilings (https://mathstodon.xyz/@pieter/116484517078239617), here is a way of colouring such tilings. For each control point, we colour the tile according to its distance from the boundary of the fractal window it lies in.
The first image shows a patch of a turtle tili
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#textureTuesday
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🔥 Top post: Peter Selinger now has an app https://www.mathstat.dal.ca/~selin · 27 likes + reposts
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Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog po…
#SilentSunday
I saw my first whales of the season yesterday, a lone mother and calf. Pretty sure these are Southern Rights, which are much less common around here than Humpbacks.
They were fairly close to shore, but as usual, my phone camera did a lous…
Jarkko Kari, Sébastien Labbé and I have a pre-print on the arXiv on a sufficient condition for proving non-periodicity of Wang tiles with vertical and horizontal stripes: https://arxiv.org/abs/2606.24693
There's a nice connection to quadr…
#textureTuesday
The old milkwoods growing next to the Mncwasa river estuary have some really interesting lichen growing on them.
#lichenSubscribe
#silentSunday
Here is the same idea applied to a Spectre tiling.
(2/2)
As a follow up to last week's post on Markov partitions for Hat (hat and turtle) and Spectre (hats in turtles and turtles in hats) tilings (https://mathstodon.xyz/@pieter/116484517078239617), here is a way of colouring such tilings. For ea…
Taking some time away from the herd.
#sea #cow
Lastly, we turn our attention to the Spectre tiling. Things are much the same as before, although since the deflation involves a reflection, we need to use a vector \(v\) such that \(𝑣𝑀=λ𝑣̅,\)
instead of a left eigenvector.
The two image…
To get the turtle Markov partition I started off with, you can follow the same steps, but using the projection along \((1, \xi^2)\) instead of \((1,-1)\), and them moving the control point to the underside of the turtle's shell. By good fo…
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