"Lower trimming" is one technique for determining if a sequence is a fractal sequence. 1 is subtracted from each element, and all the zeroes are thrown away. If the resulting sequence is the same is the original, then it is a fractal sequence. This is an example of a fractal sequence: 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, ... If we subtract 1 from each element, we get: 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, ... and removing all the zeroes leaves us with: 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, ... Which is the beginning of the original sequence. This sequence is also self-descriptive, in that each element gives the number of zeroes that were removed before it. And, for reasons I haven't figured out, the indices where the sequence hits a new maximum value (2 at the 2nd position, 3 at the 5th position, 4 at the 13th, 5 at the 34th, etc.) are every second Fibonacci number. Here's another one: 1, 2, 1, 3, 2, 1, 4, 1, 3, 2, 5, 1, 2, 4, 1, 3, 1, 6, 2, 3, 5, 1, 2, 1, 4, 2, 7, 1, 3, 4, 1, 6, ... This sequence gives the number of numbers that are retained between zeroes that are dropped. Alternatively, each element is the number of numbers between 1's in the original sequence. This last fractal sequence combines both ideas. 1, 2, 1, 1, 3, 2, 1, 2, 1, 4, 1, 1, 1, 3, 2, 3, 1, 1, 2, 5, 1, 2, 1, 1, 2, 2, 1, 4, 1, 1, 1, 1, ... Each element gives the number of zeroes dropped before it and the number of elements written before the next zero. Nothing too terribly earth-shaking, but enough to keep me occupied on a Saturday night. :-) Kerry