Collatz Cube Decorative Ornament!
Collatz in 3D! Along the bottom row, all the odds that are not equivalent to 5 mod 8. Above them, columns of numbers of the form 8x+5 associated with each of these "base" odds (ie 5, 21, 85,... all stacked above 1, 13, 53, 213, ... all stacked above 3, etc). Extending back from each odd on the face of the cube are the 2^n multiples of each odd.
Picture a crystal cube, with one blue, one yellow and one green light representing each number in its proper cell. Light one blue and one yellow light at random. The cube is programmed so that every half second (or whatever), the lights jump to the next number in the Collatz mapping. The yellow chain stays yellow and the blue chain stays blue UNLESS they reach the same cell/number at the same time, in which case the green light comes on instead!
Hold races!
Perfect holiday gift!
