Regruntled.com

Deal Extreme has conjoined Rubik’s cubes.  This is the triple version, but there are quad, pentad and hexad versions as well.

The lattice above is almost entirely connected to the border. There is only one “extra piece” that is woven into the lattice and could be pulled out without cutting anything. The lattice below is almost entirely disconnected from the border. There is one giant piece in the center that could be removed.

I keep saying “almost”.  I have the computer grinding out thousands and millions of variations and then tracing out what’s connected to what (which is an interesting programming problem in itself).  One would think that one or the other condition would be possible (completely connected or completely disconnected).  However, I’ve been unable to go all the way in either direction.

I saw this at Math Morph.  It looks like someone crossed a 3D printer with a pasta machine and loaded the extruders with tomato- and spinach-flavored pasta.  Look at all the surface area for the sauce to cling to!  Think of the texture as you bite your way through two interlocking space-filling lattices.

Another Tile lattice experiment.  The basic tile is used in all 8 orientations (rotated and/or mirrored) in 12 rows of 8 columns.  The rotations are generated randomly, and then selected programmatically to remove certain combinations of tiles.  Finally I select visually using criteria that I don’t understand well enough to program.

I made a special edge tile and a special corner tile, and rotated them 4 ways to provide a border.  After I did this, I realized that it solves a visual problem: tiling schemes are designed to repeat indefinitely, but in the end one has to generate a finite image, leading to an abrupt termination.  Here the border tiles contain the chaos.

I think this would make a great carpet.

The colors in the image on the left are from a pentad color harmony; the colors are 72 degrees apart on the color wheel like the points of a pentagon inscribed in a circle.  Actually, I just made that up in analogy to the hexad harmony I read about in a book on color theory.  The hexad harmony has 6 colors spaced 60 degrees apart, and since I only have 5 colors, why not invent the pentad?

The colors on the right are from a hexad harmony, but a color (cyan) is missing.  I call it hexad minus one.  The conventional wisdom from Pythagorean Tarot is:

The Impulse of the Pentad is unbalanced - so it may aim for the Heavens and neglect the Abyss, or aim for the Abyss and neglect the Heavens; but the Hexad balances it: as Above so Below. Thus the Hexad brings the New Dimension into the Realm of the Known and into the Cosmos.

This is what happens when I make something up and google it.

Another experiment.  The lattice is made from 48 identical tiles (6 rows of 8).  The tiles are asymmetric, but line up no matter how they are rotated.  The corners are always blue and the middle segments are always orange.