On 12/17/94 at 22:46:08 txr@alumni.caltech.edu said:
>In mlist.cube-lovers you write:

For each cube position, we only need to store the depth, assuming
we have some way to index to the proper cell in a data structure
containing the depth for each cube position. As long as the depth
does not exceed 31, then 5 bits will suffice for each cell.

I think depth modulo 3 is enough, since depth of adjacent positions
will differ by at most one -- just move in the direction of depth
getting less. So we could get by with 2 bits per cell.

regards,

Tim Rentsch

You are certainly correct. And as Dan Hoey pointed out to me via
private E-mail once upon a time, for Q turns you can get it down
to only one bit by storing (depth modulo 4)/2 because you can infer
the state of the low order bit from the parity of cube position.
(Parity of the cube position equals the parity of the depth for Q turns,
but not for Q+H turns.)

But I tend to think that certain kinds of interesting analyses
of a data base for the entire God's Algorithm
would be greatly assisted by storing the entire depth.

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