Okay, so far so good. On 6/25/12, Mike Stay <metaweta@gmail.com> wrote:
My ideal measure would still assign 2^{-s|p|} or [...]
|p| looks like "absolute value of p" so I guess that's your shorthand for the measure function. What is s?
[...] or 2^{-s ln(index(p))} to each pattern p, since then I still get a partially random real out at computable s, but the cells would be numbered in a way that makes computing the measure of equivalent patterns relatively easy. Does numbering them in an order traced out by a space-filling curve like a Hilbert curve or a dragon curve give any benefits over using a spiral?
I numbered my cells for a different purpose, but I had a similar motivation (making it so that equivalent rotations and reflections could be somehow ignored, and having the first N integers lie within a roughly sqrt(N) sized part of the grid). At least I think that's your motivation (-: Anyway, I couldn't think of much that was better than "antidiagonals", which is no better than spirals. I always normalized patterns by sliding them into a corner, so antidiagonals makes more sense. If you normalize by "centering" the pattern on the origin, then a spiral centered on the origin would make sense. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com