I Ching Memory Wheels

Sixty-four digits can be arranged to represent all the hexagrams of the I Ching in an overlapping sequence.  The sequence wraps around, like beads on a circular string; one could use such a string of beads to select hexagrams.  I have illustrated the concept for one sequence below following the example in 64 bit I Ching Binary Loop / Wheel in the Abrahadabra.com forum; please see The Changes and the Bruijn sequence on the Clarity site for more information.

0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001 0000001010001001011000011001101001110001111010101110110111111001

Here are 892 memory wheel sequences.  They are all topologically unique, both shifted and reversed.  If each were connected end-to-end, they would all be different, whether you rotated or flipped them.

If you have a real need, here are 222,539 unique sequences, in zipped format (uncompressed file size is 14.0 MB):

222539memorywheels.zip (986 KB).  [Woo!  Got the time down to 13 minutes.]

If there are 2^2n-1-n different memory wheels for binary n-tuples, then as I understand it there are 2²⁶ = 67,108,864 different I Ching memory wheels.  Given a total of 2⁶⁴ = 18,446,744,073,709,551,616 different sequences of 64 digits, that means that only 1/274,877,906,944 of the sequences are memory wheels.