A ibonacci fractal
Lately, I have been toying with sequences related to Fibonacci. Most of my pursuits relate to performing efficient calculations, but a few relate to visualization. In particular, I was looking for a nice way to visualize this sequence.
 1, 3, 8, 21, 55, 144, 377, ... (every other Fibonacci number)

...
 one way to generate the sequence is to triple the current number and subtract the previous to get the next

S_{n+1} = 3 S_{n}  S_{n1}
 or a slightly more additive way to think about it.

S_{n+1} = 2 S_{n} + (S_{n}  S_{n1})

S_{n+1} = 2 full + (partial)
 Note: these partials correspond to the skipped Fibonacci numbers (below count the blue squares)
 Geometrically: look for the two full—grey and lighter blue, and a partial—dark blue. Focus on how a pattern relates to the one previous.

Note: In an alternate fashion, the partial is added below and then right in the following graphic sequence