Message #3336

From: m_a_kl@yahoo.com
Subject: Re: Research Project
Date: Wed, 20 Apr 2016 06:07:42 -0700

Hello all,

I’m also new to this group. The MC7D program is not the only appropriate way to visualise a 3^7-Rubik’s cube, so you might understand this one (which I hope is equivalent) better. I attached a bitmap picture showing a different method not doubling labels; each non-white pixel stands for one label and vice versa. It is constructed iteratively: To increase dimension by one, the pattern is repeated three times and then "front" (with respect to the new dimension) and "back" labels are added. Start pattern is raster-2.png, in which each of the little squares is a label. If you combine two of these steps by arranging 3x3 patterns and then adding "left", "right" resp. "top", "bottom" labels, you don’t fill a line but a plain, thus obtaining a more compact representation (see raster-4.png for the image of a 3x3x3x3-Cube after one double step).

By the way, the pictures were generated by a program, which I extended to execute moves on the cube, so I use this opportunity to put a question to this group, too. My program only allows "simple" moves: At first, one third of the cubies is selected by fixing one coordinate to be 1 or (-1); then two different coordinates x_i and x_j are chosen and every selected cubie is rotated in the (x_i, x_j) plane, only changing its x_i and x_j coordinate. I hope that this is enough to execute all possible moves by combining simple moves, for any dimension? Please inform me if I’m incorrect or if I have to be more specific.

By the way: The above iteration puts pixels into the plain such that any bounded region receives pixels until a certain dimension is reached, and then it is fixed. By noticing that the way of entering moves described in the previous paragraph does not depend on the total number of dimensions handled by the program, it can be regarded as "arbitrarily-dimensional Rubik’s cube simulator".

Kind regards!