Message #326

From: Melinda Green <melinda@superliminal.com>
Subject: Lower dimensional cubes
Date: Sun, 20 Aug 2006 22:19:27 -0700

FYI, I added a reference to David Vanderschel’s MC3D program to the main
page today. In the process, I got to musing about the 2D analog which,
while rather trivial, still seemed not so completely obvious that it
just needed to be implemented. So, a couple of hours and less than 150
lines of code later, you can now try it out here:
http://www.superliminal.com/cube/mc2d.html. It automatically scrambles
fully on initialization and beeps when solved. There is no animation or
any controls other than twist-clicking. Refresh your browser to rescramble.

I’m not sure how many unique positions it has but I bet that it’s less
than 10. Considering color symmetry, it may be quite a bit less than
that. It’s so small that I had to make sure that the number of
scrambling twists was odd otherwise scrambling would sometimes randomly
leave it in the solved state!! I’d love to see the complete state graph
laid out graphically. God’s algorithm length seems to be 2 though it
sometimes takes 3 in the applet since I didn’t implement a middle slice
twist.

So do I get the prize for the first person to solve the 2D cube? :-) I
wonder whether anyone has ever bothered to implement this puzzle before.
-Melinda