Investigate the best randomization methods for big cubes and Megaminx.

[lgarron]

4x4x4-7x7x7 and Megaminx are the only puzzles without random-state scramblers. Except maybe for 4x4x4, such scramblers are likely to remain infeasible (or at least impractical) for a while.

3x3x3 random-turn scrambling (I think) is more random if we alternate axes every turn. There are a couple of such ways to vary scrambling on higher-order cubes, e.g.

• Alternating axes vs. doing a lot of consecutive R, 2R, Rw moves, etc.
• Double turns vs. single turns.
• Slice turns vs.
• On megaminx:

We should come up with some decent randomness metrics (e.g. distribution of centers among faces) and figure out what makes for a good distribution according to reasonable metrics. (Question: how much should we bias this to existing cube methods?)

See Stefan's 3x3 scramble analyzer. This would probably good to generalize; a tool to analyze arbitrary permutation puzzle (a la ksolve) and metrics for all state-machine scramblers seems very feasible and useful, though a bit tricky.

[lgarron]

Issue #62 meant in message for commit 2580fcf.