09 August 2008

7x7 Blinky, Inky, and Clyde

Dario suggested I try to depict the four monsters (aka: "ghosts") from Pac-Man on four sides of a V-CUBE 7, but this was as close as I could get. I tried lots of color combinations, but most of them were impossible to make out. With the color scheme shown above you can almost see Blinky (the red one) if you squint and use your imagination.

I couldn't draw Pinky because the V-CUBE doesn't have a pink side. So my pattern ended up with an un-named green monster on the fourth side.

05 July 2008

6x6 Proud Python

This extends the 4x4 Quad Color Python concept to six colors on a 6x6 cube.

03 July 2008

4x4 Quad Color Python

Four colors per side on a 4x4!

This pattern surprised me. My 5x5 Quad Color Python demonstrated 4 is the maximum number of colors per side for a 'python' type pattern on a 5x5 cube due to combinitoric constraints imposed on the centers and middle-edge pieces. I later reproduced the pattern on a 4x4 by just eliminating the center string, yielding the 4x4 Tricolor Python pattern.

While exploring how the pattern might be extended onto a 6x6 cube I realized I had overlooked a better implementation of the pattern on the 4x4. Instead of eliminating the center stripe I moved it and replaced one of the edge stripes. The picture at right compares the 4x4 and 5x5 versions of the improved 'python' pattern, showing that the sides of each cube have the same four colors although they appear in a different order.

30 June 2008

6x6 Cube in Cube in Cube in Cube in Cube in Cube

This is a straightforward expansion on the common Cube-in-Cube pattern. I tried to arrange the colors carefully so the same colors wouldn't touch each other at the edges, since this tended to make the pattern look like a broken spiral. Every side has all six colors.

26 June 2008

4x4 Power Series

The number of stripes on the first three sides of the 4x4 represent the first three entries in an even power series: 1, 2, 4. As a simple exercise I extended the pattern to a custom-built 2x2x6 cube, but as the series 1, 2, 6.

17 June 2008

5x5x5 Dado Rail

The varying-width stripes remind me of the way a chair rail divides a wall between the dado below and the...uh... non-dado part.

But when viewed from a different angle it's easy to see this is just a simple 3-cycle pattern. (More precisely, it's two slightly different 3-cycle patterns.)

16 March 2008

5x5 Grecian Urn 2

This string pattern has the same layout as my previous Grecian Urn 1 but with a somewhat more complicated arrangement of colors, so the side faces have four colors each. No two string fragments on the same face are the same color.

Too complicated? Here's a schematic showing how the pieces are laid out on the cube.

05 March 2008

5x5 M.C. Escher's Pretzel

M.C. Escher used to draw all sorts of pictures of impossible objects like stairways that ascended in loops and waterfalls that drained into their own tributaries.

If M.C. Escher tried to draw a pretzel, it just might have looked something like this cube pattern.

06 January 2008

5x5 Parallels

This string pattern wraps around 4 sides of the cube, leaving the top & bottom blank. The string rises and descends on alternate sides. On the 3x3 there's one string, but on the 4x4 there are two parallel strings, and on the 5x5 there are three parallel strings.

The picture at right shows the reverse sides.