Most Fiendishly Difficult Maze

[Bruce_Shapiro]

A friend who knows I like fractals and one-line drawings, just sent me a link about this:

It references this paper on Hamiltonian Cycles on Ammann-Beenker Tilings.

I find this space-filling curve strangely appealing, and would love to be able to recreate it. I’m hoping one or more of this forum’s amazing tiling-gurus might be able to shed some light – like they did very soon after the discovery of the Einstein tiling was published.

[Joseph_Oster]

From the paper you cited, which has many more images.

See full size original image

[laurent_delrieu]

Nice holiday problem. I don’t know if I’ll manage to do something but the recursive tiling is done.

Recursion 4 (30520 tiles)

[laurent_delrieu]

Hello
I published a tool in Nautilus (1.9.1) that is able to subdivide Ammann Beenker tiles. But there is no tools at the moment to generate the Hamiltonian Cycles

AmmaanBeenkerTiliing.gh (13.9 KB)

[laurent_delrieu]

Same color = same area