Twistedspinster

hmmm.. random cogitations on Fibonacci

Marcy commented on Fibonacci sequences in knitting- go see Fuzzy Galore for more details. I've used Fibonacci many, many times, but it just now occurs to me that it's a binary system. In other words, there are two colors (or parts of the daisy or chambered Nautilis or whatever) that are going back and forth in the sequence.

What if you want to use THREE colors? Or (gasp) more? Methinks I need to consult a mathemetician. OK, yes. Wikipedia has an article on Fibonacci sequence ... but it makes my head hurt. (yeah, the sinuses again. I gotta admit that Sudafed sends me down some pretty amazing paths, while simultaneously making me incapable of higher reasoning. Strange, but there you go. Rather, there I go.)

Can somebody mathematical give me a SIMPLE formula for a 3-color Fibonacci sequence?

hmm - maybe I could just go from this (where A is the first color, and B is the second)

A1, B1, A3, B5, A8, etc

to having colors A, B and C do this:

A1, B1, C3, A5, B8, C13, etc.

It's boring (and not fun to count) to have knitted stripes of more than 5 or 8 rows. I wish I could remember (and thank!) whoever told me that you can go up and down the sequence, as long as you don't skip numbers.

In other words, 1, 1, 3, 5, 3, 5, 3, 1, 3, 1 etc. Don't go from 5 to 1, or 8 to 3.

I ought to sit down and try this with 3 colors!!

posted by Ruth S. @ 12:06 PM