[next] [prev] [up] Date: Thu, 24 Feb 83 06:18:00 -0700 (PST)
~~~ ~~~ [up] From: JAY <JAY@USC-ECLB >
~~~ ~~~ [up] Subject: NxNxN: Finite N

I have a program, not finished, which allows manipulation of a NxNxN
(N^3) cube. Presently it WILL manipulate any NxNxN cube (i tried up
to 23) but it has a VERRY BAD user interface. I plan to improve the
interface in the near future (this morning?) I hope to be able to
parse the Cube-Talk mentoined in the first message in the archive
alan;cube mail1 (or 2?), or a super-set of it (like being able to save
cube's on disk, save move seq's (macros), defining macros with
parameters, and make logfiles of especialy hairy session). As for
output... For small cubes (up to 8^3) i can use the normal air-plane
pattern of display, for medium cubes (8^3 <= size <= 12^3) i can put it
all on the normal terminal, but for larger cubes (24^3 >= cube >=
12^3) all i can do is display a face, or maybe two.


I am interested in a, WORKING, N^3 simulator, not speed or space. As
a result my representation of the cube is loosing on both counts.
(yes it realy is a NxNxN array of cubes (a record of six integers!))
It is written in CLU for TOPS-20 os.

However my rep. brought up an interesting super-groop, immagin a cube
realy made of N^3 cubies. Each of these cubies would be a 'Miniature'
N^3 in color scheme. Now this new device (a 'compleatly colored'
cube) is solved only when ALL cubies are oriented correctly (ie. all
have red up and blue forward), and positioned correctly. In the 3^3
we would not only have to solve the centres, but also the imaginary
inside cubie (is it ever un-solved?)

What do you (readers) think is a good display scheme for a N^3,
remember it should be useable on a 24x80 h19? Is a N^3 simulator even
interesting? What sort of speed improvement could be gained from a
comp-cube? with or without macros?

Is the 'compleatly colored' cube interesting? For what sizes is it
similar to the 'partialy colored' (normal) cube (1^3 and 2^3 for
sure...)? Could the solution of compleat-5^3 be a solution of the
outer shell, and the inner 3^3?

Is a simulation of a 'compleatly colored' cube interesting? How
would one view the manny inside faces?

What other reps for the cube are there? (other than the obvious two;
an array of color tabs, or a 3d array of cubies..) Which reps
optimize storage, time, or simplicity to compute a twist, or even ease
of compairison? Just occured to me that each cubie could be rep'd as
a number twixt 1 and 24 (as a cube has only 24 orientations). This
optimization would reduce storage by a factor of 6 (not too bad!)

enough..... enough.....

j'  <jay@eclc>

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