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
Sn+1 = 3 Sn - Sn-1
- or a slightly more additive way to think about it.
Sn+1 = 2 Sn + (Sn - Sn-1)
Sn+1 = 2 full + (partial)
- Note: these partials correspond to the skipped Fibonacci numbers (below count the blue squares)
Note: In an alternate fashion, the partial is added below and then right in the following graphic sequence