Alternative hypothesis: The first several bits (of each 64-bit chunk) are less chaotic than the middle bits due to repetitive border behavior of a 1-D cellular automaton. This hypothesis also accounts for the observation that the final seven bits of each chunk are always either 1000000 or 0111111.
If you were instead removing the last n bits from each chunk, you’d find another clear phase transition at n=7, as the last seven bits only have two observed configurations.
If you calculate the entropy p0log2(p0)+p1log(p1) of each of the 64 bit positions (where p0 and p1 are the proportion of bits 0 and 1 among 2095 at that position), then you’ll see that the entropy depends much more smoothly on position if we convert from little endian to big endian, namely if we sort the bits as 57,58,...,64, then 49,50,...,56, then 41,42,...,48 and so on until 1,...,8. That doesn’t sound like a very natural boundary behaviour of an automaton, unless it is then encoded as little endian for some reason.
Now that I know that, I’ve updated towards the “float64” area of hypothesis space. But in defense of the “cellular automaton” hypotheses, just look at the bitmap! Ordered initial conditions evolving into (spatially-clumped) chaos, with at least one lateral border exhibiting repetitive behavior:
Alternative hypothesis: The first several bits (of each 64-bit chunk) are less chaotic than the middle bits due to repetitive border behavior of a 1-D cellular automaton. This hypothesis also accounts for the observation that the final seven bits of each chunk are always either
1000000or0111111.If you were instead removing the last n bits from each chunk, you’d find another clear phase transition at n=7, as the last seven bits only have two observed configurations.
If you calculate the entropy p0log2(p0)+p1log(p1) of each of the 64 bit positions (where p0 and p1 are the proportion of bits 0 and 1 among 2095 at that position), then you’ll see that the entropy depends much more smoothly on position if we convert from little endian to big endian, namely if we sort the bits as 57,58,...,64, then 49,50,...,56, then 41,42,...,48 and so on until 1,...,8. That doesn’t sound like a very natural boundary behaviour of an automaton, unless it is then encoded as little endian for some reason.
Now that I know that, I’ve updated towards the “float64” area of hypothesis space. But in defense of the “cellular automaton” hypotheses, just look at the bitmap! Ordered initial conditions evolving into (spatially-clumped) chaos, with at least one lateral border exhibiting repetitive behavior: