3 ms·
When it came to the description of "einsteins" (a single tile aperiodic tessellation), I couldn't help but think of the images in the 3rd edition of The Scheme
by GregBuchholz 9y ago
When it came to the description of "einsteins" (a single tile aperiodic tessellation), I couldn't help but think of the images in the 3rd edition of The Scheme Programming Language:
http://www.scheme.com/tspl3/binding.html#./binding:h0 http://www.scheme.com/tspl3/binding.html#./binding:h0
http://www.scheme.com/tspl3/examples.html#./examples:h0 http://www.scheme.com/tspl3/examples.html#./examples:h0
...Are there holes in those "tilings", or are the tiles not all the same shape, or am I misunderstanding what non-periodic means in this context?
And what is the name for those types of "self-surrounding" tiles on the cover:
http://www.scheme.com/tspl3/canned/large-cover.png http://www.scheme.com/tspl3/canned/large-cover.png
- dwringer 9y agoThe spiral images have tiles that are reflected, not just rotated. You'd otherwise need a third dimension to do another rotation. I think that might be considered two different tiles by the rules laid out in the article.
- shmolyneaux 9y agoThe banner image in the article appears to include reflected tiles.
- markegli 9y agoThe tiles in an aperiodic tiling must guarantee that the tiling is not periodic simply by their shape. https://en.wikipedia.org/wiki/Aperiodic_tiling https://en.wikipedia.org/wiki/Aperiodic_tiling All three of the Scheme examples can be tiled periodically even though they aren't tiled periodically in the examples. How to tile them periodically is left as an exercise to the reader, but it's not hard.
- GregBuchholz 9y agoGot to love this quote from the "Einstein Problem" page on Wikipedia: https://en.wikipedia.org/wiki/Einstein_problem https://en.wikipedia.org/wiki/Einstein_problem "Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved."
- Infernal 9y agoThere's definitely something Douglas Adams-esque about that phrasing.