A mathematical sequence consists of a series of numbers, usually starting at 0 or 1, all of which are derived from preceeding ones according to formal rules. In other words, no matter where you are in the sequence you ought to be able to deduce what the following number should be.
One of the most well-known sequences was one derived by the Italian medieval mathematician known today as Fibonacci. In his Liber Abaci, published in 1202, he explained a simple sequence, where every number is the sum of the two numbers preceeding it. So the result is:
1 1 2 3 5 8 13 21 34 ...The fascinating thing about it is that this sequence is actually found in nature with amazing frequency. Fibonacci himself used the cute (pre-Australian cute) example of the multiplication of rabbits in his book. Since then, it's also been found to apply to such varied things as shell spirals, branching plants, flower petals, seeds, pine cones, leaves... It seems almost everywhere you look there is lurking a Fibonacci sequence.
So what does all this have to do with fiber? There are easy ways to use the Fibonacci sequence in designs, both for color and texture. And the results somehow always manage to look pleasing to the human eye, which is probably because the sequence looks so... natural! See for instance this improvised sock - doesn't it look like someone racked her brain to come up with something so sophisticated? And you don't need to use a whole lot of the sequence for the effect to take hold visually - instead of using 3 uniform thin stripes for instance, make the 3rd twice as wide, and see the result...
So let's think of some obvious ways to use the sequence:
a...a aa bbbbb aa bbb aa bb aa b aa b a...aor when both colors work together:
aa bbbbb aa bbb aa bb aa b aa b
aaaaaaaa b aaaaa b aaa bb aa bbb a bbbbb a bbbbbbbb
Here is a Fibonacci rib - a 4x4 ordinary rib is livened up by changing the pattern every Fibonacci number of rows.
aaaa bbbb aaaa bbbb bbbb aaaa bbbb aaaa aaaa bbbb aaaa bbbb bbbb aaaa bbbb aaaa aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa bbbb aaaa
And this is a Fibonacci doodle - switch rows every Fibonacci number of rows.
abbbbbbbbbbbbbbbbbbbbbbbb babbbbbbbbbbbbbbbbbbbbbbb bbaabbbbbbbbbbbbbbbbbbbbb bbbbaaabbbbbbbbbbbbbbbbbb bbbbbbbaaaaaabbbbbbbbbbbb bbbbbbbbbbbbbaaaaaaaabbbb
There is nothing original about this, it's all been very well known for a long time, and once your eye gets tuned to it you'll notice uses of the sequence in many designs. But it all works so well to give pleasing designs that there's no reason not to make use of it liberally...
References:
First published: 01/21/03
Modified: 4/27/06
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