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This solution won't be accepted without a lot more work. Flipping a coin is not guaranteed to produce an aperiodic tiling, since, in the trivial case where the
by cvoss 3y ago
This solution won't be accepted without a lot more work. Flipping a coin is not guaranteed to produce an aperiodic tiling, since, in the trivial case where the coin comes up heads indefinitely, you'll be producing a periodic tiling. (You will argue it's not likely to do this, and I'd agree. In fact, I'd conjecture you'll only produce a periodic tiling with measure zero probability.) But what's required is to actually show an aperiodic tiling. If you have a proof that coin flipping will produce such a tiling with non-vanishing probability, then, presumably, embedded in your proof, you will likely find a decision procedure for producing an aperiodic tiling deterministically.
- JadeNB 3y ago> If you have a proof that coin flipping will produce such a tiling with non-vanishing probability, then, presumably, embedded in your proof, you will likely find a decision procedure for producing an aperiodic tiling deterministically. I'm not sure it's obvious to expect a proof that something happens with positive probability to embed a constructive proof of existence (which seems to be what you mean). The difference between these two ideas in combinatorics is exploited with the probabilistic method (https://en.wikipedia.org/wiki/Probabilistic_method https://en.wikipedia.org/wiki/Probabilistic_method).