A linked article about an einstein (one-piece) aperiodic tile contains a beautifully simple animation of the continuum of tiles that morph as you scroll down the page.<p><a href="https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/" rel="nofollow">https://www.quantamagazine.org/hobbyist-finds-maths-elusive-...</a>
> it’s impossible to tell any two tilings apart by examining any local area. That’s because every finite patch of any tiling, no matter how large, will show up somewhere in every other tiling<p>I was about to pose a question but it turns out that's what the article is about!
> edges of tilings don’t fall at regular intervals, so specifying their distribution requires continuous real numbers rather than discrete integers.<p>Surely they mean <i>algebraic</i> numbers not <i>real</i> numbers.
love how that piece quotes Tony Cubitt, a stunning coincidence for somebody who works in quantum computing-related science.<p>His website is a fun read too:<p><a href="https://www.dr-qubit.org/qubit.html" rel="nofollow">https://www.dr-qubit.org/qubit.html</a>