#hitomezashi — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #hitomezashi, aggregated by home.social.
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On an infinite square grid, paint vertical segments yellow, and horizontal segments blue.
In each iteration, take every "path" of edges of the same color (in iteration 0 these will be horizontal/vertical lines, in later iterations they will be cycles). Simultaneously, for every such path, every second edge becomes yellow and every second segment becomes blue. Which half gets which color is decided randomly.
Iterations 0 and 1 look clearly different than others, iterations 2 and 3 also look somewhat different, but it is harder to pinpoint the difference. To check my intuitions that they are different, I have written a "blind test" game in which you have to guess the number of iterations in a random picture, and I was not able to consistently guess correctly. With even more iterartions it would be even harder.
But it is actually possible to guess consistently (as in, for any p<1 there is a method to guess the number of iterations correctly with probability at least p, after looking at a finite part of the pattern). How to do so is left as an exercise to the reader.
