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_n-1
• or a slightly more additive way to think about it.
  S_n+1 = 2 S_n + (S_n - S_n-1)
  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