Wear Your Favourite Cellular Automaton As A Scarf
Written by Lucy Black
Sunday, 19 July 2015

KnitYak is a KickStarter with the aim of bringing you your very own custom cellular automata scarf. You select the 1D automaton and the machine knits it for you.

The KickStarter is aiming for \$100,000 to buy an industrial knitting machine. According to  Fabienne "fbz" Serriere the knitting mathematician who started all of this, only an industrial knitting machine has any hope of making a high quality product fast enough. At the time of writing the pledge stands at \$63,135 and there are only five days to go. So if you decide you want one pledge at least the \$150 for a custom scarf or even the \$390 needed for a wrap.

What is the idea?

If you know about 1D cellular automata then you will understand completely where this project is coming from. The basic idea is that you start off with an initial pattern of black and white pixels and you have a rule that generates the next row. The rule changes each pixel to black or white depending on its two neighbours.

For example the pattern:

specifies a rule that if a pixel is white and has two black neighbors then the cell below should be black.

As there are only eight possible states of the three cells a complete rule that specifies exactly what should happen in any situation only has to list if the result for each combination of the eight as black or white.

By thinking of black as 1 and white as 0 you can give each neighbor pattern a number between 0 and 7 and then read off the resulting black or white cell on the next row as a set of eight zeros or ones, i.e. a binary number. This can be used as an index to specify the rule.

This may seem very restrictive, but this is the point. The big surprise is that such simplicity leads to very complex behaviour.

Some are boring, true, but there are two classes of behavior - seemingly random and complex - that are impressive. You can extend the rules to include colors, but at the moment the knitting pattern is limited to black and white. Don't let this worry you, however, because rule 110 is, in a sense, Turing complete and can produce enough patterns to keep you happy all on its own:

So all you have to do is pick your rule, from the set known to produce good patterns, and your starting configuration and your scarf will be knitted. You not only get the scarf; the program is included as well.

KnitYak: Custom mathematical knit scarves

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