November 9, 2018

How a sock met a maths sequence.


Socks, yes socks! Sarah is a great knitter and I responded to her call out and the results are so cool! Sarah's wrote about this project but let's get some more details on the design.

Fibonacci?
This video inspired some thinking https://youtu.be/mOMLRMfIYf0.
If the Fibonacci sequence can be incorporated into music then maybe it would be a cool sock design!
The swirl is deceptively simple but needed some work to go onto the graph paper.
This number sequence makes a swirl that appears in nature. An image of a storm pattern gave Wendy
the final design of opposing swirls as in the eye of the storm.

Why love a maths sequence?
Fn=Fn-1+Fn-2
Fibonacci numbers follow an integer sequence. Possible shown in early Indian work of poetry formed
by words of two syllables. The design here took the sequence this far:
1,1,2,3,5,8,13
(see diag below for sock pattern)


How are the stripes worked out?
Sarah had already made one pair of socks using the Fibonacci sequence of numbers.
Wendy produced the spirals based on two opposing swirls. Sarah thought about incorporating some
stripes as well,.

Running up and down through the sequence throughout the sock.  Wendy’s spiral pattern spanned
over 65 rows, a good number of rows for a sock is roughly 100, so Sarah played around with some
numbers to make this fit. She ended up with stripes above and below the main spiral pattern in blue
and green, using a sequence of: 8 blue, 5 green, 3 blue, 2 green, 1 blue, 1 green for the stripes above
the spiral pattern, and stripes of 1 green,1 blue, 2 green,3 blue, 5 green under the spiral pattern and
above the heel. The heel is knitted over 32 stitches, so Sarah emphasised the beginning of the
Fibonacci sequence by using a stripe of alternate stitches in blue and green across the whole heel,
before returning to a full sequence for the foot and toe.The foot sequence was 1 blue, 1 green, 2 blue,
3 green, 5 blue, 8 green,13 blue, 8 green, 5 blue, 3 green, 2 blue, 1 green, 1 blue; and the toe
sequence was 2 green, 3 blue, 5 green, 3 blue, 2 green, 1 blue, 1, 2 blue, 1 green, then joined with an
invisible grafting stitch.


What about entropy?
Nick Sousanis is an inspiration in his writings and visual work. The swirl on the entropy page here:
http://spinweaveandcut.com/sketching-entropy/ is eerily familiar to the Fibonacci spiral.
This page talks about the inevitable change in things and the downward flow of the river of life.
“Each of us, during our brief time in the stream, has the opportunity to reflect on the forces that s
et this in motion, and reach in to send up something uniquely our own against the flow.” (Sousanis, 2013)

This collaboration provided that opportunity.


All images: Sarah Honeychurch