Date: 24 Feb 1983 0618-PST From: JAY Subject: NxNxN: Finite N To: cube-lovers@MIT-MC 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. [Implementation] 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?) [Questions] 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' -------