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To: cube-lovers@life.ai.mit.edu
Subject: Cube Patterns
From: mark.longridge@canrem.com (Mark Longridge)
Message-Id: <60.305920.104.0C188656@canrem.com>
Date: 	Thu, 28 Oct 1993 19:20:00 -0400
Organization: CRS Online  (Toronto, Ontario)

        Comments on Rubik's Cube Patterns
        ---------------------------------

First some positions of theoretical interest:

(F R B L)^5 = F1 L3 D2 F3 B2 R1 L3 F2 B3 R2 B1 U2 D2 R3 D2 L2
                 B2 L2 F2  (19 moves)

So in the ht metric this is compressible.

I've been thinking about new approaches to finding new patterns.
To improve on the "old-fashioned" method of simply taking a cube
and twisting it I wrote a module to test for legality of position
and another module for arrangement entry. Thus I can doodle around with
a cube pattern much more efficiently.

This approach led to the discovery of the ML Checkerboard, which is
to date the most involved of the pretty patterns:

ML's Checkerboard =  B1 U2 R1 L1 D2 B3 L2 F2 R1 F3 U3 D3 F3 B3 R2 U1
                        R2 D3 L2   (19 moves)

Also by combining the 8 twist and the first discovered square's
group antipode, a new corner's only pattern:

Antwist = R1 F2 B2 D2 R1 L3 B2 R1 B2 U1 F2 U2 F2 D2 F2 R2
             L2 D3   (18 moves)

Also I have re-evaluated what is a complex cube position. Cube positions
have different degrees (or types) of difficulty.

A. A position is difficult if it is visually hard to recognize, e.g.
    no pattern is apparent, the cube is well mixed and random.
    However the pattern superfliptwist, although being 20 moves
    deep, IS easy to recognize.

B. A position is easy with respect to computer analysis if it is
    cyclically decomposable. That is to say it by looking at a
    position a program finds it is generated by (F R B L)^5,
    so this position is EASY.

C. A position is easy with respect to the human hand if the sequence
    required to solve the position can be executed rapidly. To a
    degree such positions are similar to positions in point (B)
    in that only a subset of all cube operators are required, and
    the sequence does not require turning all 6 sides and so the
    sequence is easier to memorize as well.

As a result of thinking along these lines I am going to write a
module to do cyclic decomposition.

-> Mark <-
Email:  mark.longridge@canrem.com

....more patterns to follow...