steiza_

For those looking to create patterns like these in real life, I've had some success describing aperiodic tiling expansion rules in PostScript: https://github.com/steiza/postscript_fractals

From there you can send it to a laser cutter (see link for pictures), vinyl cutter, plasma cutter, CNC machine, etc.

PostScript is particularly great because it's a stack based language, and aperiodic tilings are often defined by expansion rules that are basically recursive algorithms. Just don't go too deep or you'll blow the stack!

Many aperiodic tilings rely on "substitutions" which let you express very complicated patterns with some simple recursion.

I've found this maps well to express them in programming languages, like PostScript (although most implementations limit the stack at some point).

For an example of expressing these patterns in PostScript, and what it looks like on closet doors, check out https://github.com/steiza/postscript_fractals

You might enjoy http://tilings.math.uni-bielefeld.de/