[next] [prev] [up] Date: Sat, 19 Jul 80 16:31:00 -0400 (EDT)
[next] [prev] [up] From: Ed Schwalenberg <ED@MIT-AI >
~~~ ~~~ [up] Subject: Nope, I guess we don't understand

First of all, I was sitting here inventing a GOOD cube notation,
when McKeeman's message about his notation came in. I begin
to fear that ACW was right, and we will all die before agreeing
on a notation. I dislike all proposed notations so far, for the
following reasons:
ALAN's labeling of the cube for describing a POSITION is excellent;
however it is not useful for describing transforms, which are
operations and not positions.
ACW's language I find baffling, principally because it lacks
verbosity. I would much rather have a notation like
[doubleswap] than F[X,[Y']] since it is descriptive. An analogy
with Life is useful here; I think that the adoption of names
like "traffic lights" is far more usable in the long run than
any of [the-oscillator-of-period-two-composed-of-three-blots-placed-
orthogonally-adjacent] or | .
... | .
| .
or "if you put 3 blots in a row, the center dot remains alive forever
while the two outer dots appear first horizontally then vertically".
Creating names like "The Christman Cross" is fun, and makes for
interesting wordplay, even if you don't resort to Latin. So my
proposed language is Augmented English, which has the great feature
of being able to put in comments (a feature notably absent in the

I urge people to describe the transform and its result in any
message describing a nifty transform or pattern (provided both are
known, of course!). RP's pretty pattern may not be what I think it
is, since "pretty" is not a good description. I propose that this
be called "swapping-centers-in-triplets" (procedural notation) or
Twelve Squares (which is not a movie by Mel Brooks, but the positional

Bernie's comment about decision-making I think is important: it
seems to me that cubemeisters do in fact approach the problem with
a set of "subroutines", which are defined to NOT contain
conditional branches. Doubleswap and checkerboard-all-faces are
examples of subroutines. Conditional branching is generally simply
the matter of selecting an orientation of the cube before applying
a transformation, "setting up" the subroutine if you will. I think
that in the case of generating patterns from a solved cube,
branches are unnecessary but helpful: rather than say "doubleswap
then rotate the cube 90 clockwise in Z and doubleswap again"
saying "doubleswap, then doubleswap the remaining solid face" much
more clearly indicates what is going on. (the examples above are

I herein announce two patterns I have independently invented; I do
not know if they are elsewhere available. The first is called
Ten Squares by analogy with Twelve Squares, since it is highly related.
Twelve Squares causes the 3 centercubies of three mutually adjacent
faces to move to an adjacent face; three iterations of "swapping-
centers-in-triplets" suffice to return to the solved state. Ten
Squares, on the other hand, is a configuration wherein two opposite
faces are solid, while the other 2 sets of opposing faces each possess
the centercubie belonging to its opposing face. This is created by
first swapping-centers-in-triplets, then swapping-centers-in-triplets
again, only with the cube rotated 90 degrees away from you. Note that
this results in the final centerslice rotation of the first transform
and the first centerslice rotation of the second effectively combining
into a single 180-degree centerslice rotation. To resolve the cube,
simply do swapping-centers-in-triplets without regard to the orientation
of the cube, then you are back to the trivially soluble Twelve Squares.

The second I call Laughter, after the use of the string \/\/ in comlinks
to signify laughter. It leaves the top and bottom faces solid, while
causing pairs of opposing faces to have a diagonal stripe of the
opposing color. (I propose that the color of the face opposite a given
face be called the complementary color; my cube has complementary pairs
of red-white, orange-yellow and blue-green.) To create Laughter, select
a top-bottom pair, which will remain solid. Rotate the left and right
sides clockwise (in "opposite" directions as viewed from the top, thus
resulting initially in the top being 3 differently-colored stripes). I
call this "splaying". Then rotate the cube 90 degrees while preserving
the top/bottom orientation (i.e., rotate it about the Z axis.). Six
iterations of splay/rotate suffice. Laughing the cube again solves it.
Laughing the cube, then Frowning it (same as laughing, only rotate the
faces anticlockwise) results in Four Crosses: 2 complementary pairs
of crosses with the top and bottom solid.

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