Message #861

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Fractal cubes
Date: Wed, 10 Mar 2010 19:41:57 -0800

Chris & David,

Both of your suggestions allow for twists on elements such as a 9x9x1
slice which are not part of any sort of standard cube of any scale.
Also, twists in both of your designs have only local effects. I don’t
want to put them down because I’m actually very happy to see some folks
giving this problem some thought. While we might come up with a hard yet
solvable puzzle this way, these aspects just don’t get me excited. As
you both point out, these purely local operations are not very
fractal-like and therefore don’t exploit the fundamental nature of this
geometry.

Yes, I was thinking of interactions very much like Roice’s Magic Tile in
which portions of the geometry are not just copies of other portions but
in actual fact *are* the same bits of geometry. I was hoping to do the
same thing but with in scale as well as in position, but maybe that’s
not the best approach. At least it didn’t seem to be generating anything
terribly new.

Well here is yet another possible design that I would like to offer: A
click on a given sticker will affect all twistable 3^n x 3^n x 3^(n-1)
faces that contain that sticker. IOW, clicking on a sticker will twist
the face of its level 1 void cube as well as the level 2 cube that
contains it, and then level 3 cube that contains that one, and so on up
to some maximum (probably ending right there). If we don’t allow twists
on "inner" stickers, then not all faces in every such chain will be
twistable. I’m fine with whichever design makes more sense. This gives a
puzzle that is sort of a combination of local and fractal.

Thoughts?
-Melinda