## Splinterfields: Mathematickal Arts #3

A third and final update on the Mathematickal Arts Workshop – following the previous outline, some more detail on the process of going from software to textile using plain weave.

First create a program and choose the colours:

Axiom: O
Rule: O => : O O :
Repeat 5 generations

: = Green
0 = Orange

Then “compile” the code to expand the pattern:

1= O
2= : O O :
3= : : O O : : O O : :
4= : : : O O : : O O : : : : O O : : O O : : :
5= : : : : O O : : O O : : : : O O : : O O : : : : : : O O : : O O : : : : O O : : O O : : : :

The resulting weave can be previewed in ASCII as described earlier. This was useful to discover the range of patterns possible. When done, install the compiled code on the loom as a warp thread colour sequence.

Then you follow the same sequence for the weft threads, choosing the colour based on the code generated. In this way you become a mere part of the process yourself.

This is another, more complex program with 2 rules. This expands rather quicker than the last one, so only three generations are required:

Axiom: O
Rule 1: O => O : O :
Rule 2: : => : O :
Run for 3 generations

This technique draws comparisons with Jacquard looms, but obviously it’s far simpler as the weave itself is the same, we are only changing between 2 colours (and a human is very much required to do the weaving in this case). However, one of the activities I would have tried with more time available would have been reverse engineering Jacquard woven fabric – to attempt to decode the rules used.

During the workshop it was also suggested that a woven quine may be possible – where the pattern somehow contains the instructions for it’s own manufacture.

## Splinterfields: Mathematickal Arts #2

For my contribution to the Mathematickal Arts workshop, I wanted to explore weaving, specifically plain weave. This is the simplest form of weaving, but when combined with sequences of colour it can produce many different types of pattern.

Some of these patterns when combined with muted colours, have in the past been used as a type of camouflage – and are classified into District Checks for use in hunting in Lowland Scotland. This is, I guess, a kind of less prestigious form of Tartan.

I started off by trying to understand how the patterns emerge, beginning with the basic structure:

The threads running top to bottom are the warp, those running across are the weft. If we consider the top most thread as visible, we can figure out the colours of this small section of weave. A few lines of scheme calculate and print the colours of an arbitrarily sized weave, by using lists of warp and weft as input.

```; return warp or weft, dependant on the position
(define (stitch x y warp weft)
(if (eq? (modulo x 2)
(modulo y 2))
warp weft))

; prints out a weaving
(define (weave warp weft)
(for ((x (in-range 0 (length weft))))
(for ((y (in-range 0 (length warp))))
(display (stitch x y
(list-ref warp y)
(list-ref weft x))))
(newline)))
```

I’ve been visualising the weaves with single characters representing colours for ascii previewing, here are some examples:

```(weave '(O O O O O O O) '(: : : : : : : : :))
=>
O : O : O : O
: O : O : O :
O : O : O : O
: O : O : O :
O : O : O : O
: O : O : O :
O : O : O : O
: O : O : O :
O : O : O : O

(weave '(O O : : O O : : O O) '(O : : O O : : O O :))
=>
: O : : : O : : : O
O : : : O : : : O :
O O O : O O O : O O
O O : O O O : O O O
: O : : : O : : : O
O : : : O : : : O :
O O O : O O O : O O
O O : O O O : O O O
: O : : : O : : : O
```

This looked quite promising as ascii art, but I didn’t really know how it would translate into a textile. I also wanted to look into ways of generating new patterns algorithmically, using formal grammars – this was actually one of the simpler parts of the project. The idea is that you begin with an axiom, or starting state, and do a search replace on it repeatedly following one or more simple rules:

```Axiom: O
Rule: O -> :O:O

Generation 1: O
Generation 2: :O:O
Generation 3: ::O:O::O:O
Generation 4: :::O:O::O:O:::O:O::O:O
```

We can then generate quite complex patterns for the warp and the weft from very small instructions, next I’ll show what happens when some of these are translated into real woven fabric…

## Splinterfields: Mathematickal Arts #1

Textiles and mathematics have a long but sometimes easy to ignore shared history. The Mathematickal Arts workshop at FoAM in Brussels last weekend celebrated and brought this history to the fore with Tim Boykett and Carole Collet taking us on an exploration including knots, origami, group theory, mobius strips, donut making, weaving, symmetry, crochet and non-euclidean geometry systems.

This workshop underlined the importance of applying a hypothesis led process to creative work – testing your assumptions, recording experiments well and attempting classification to further understanding and avoid repeating mistakes. Right at the start we were confronted by the strange things that happen when you cut a moebius strip in half, a good reminder of the fragility of intuition and common sense.

As always with FoAM, the food blended seamlessly into the workshop with woven, rolled and knotted dishes being provided by Annabel Meuleman. We also contributed to the sugar intake by making donuts from knotted and pleated dough and observing the transformations undertaken while cooking (and shortly after, eating).

This workshop was one of the first activities connected with the resilients project which is engaged with promoting long term thinking. One of the things we discussed related to this was the way that textiles are used to store memory. For example knots were used as a language in the Inca civilisation in order to communicate using Quipu. Carole also introduced us to Ikat, a weaving technique where warp and weft fibres are tie dyed prior to weaving. This is a very complex process, and the accumulation of slight errors results in a hazy look (It’s known as “abra”, or Ã¢â‚¬Å“cloudÃ¢â‚¬Â in Central Asia). The knowledge of the precise technique – where to tie the fibre to achieve a desired pattern, are passed down the maternal line from mother to daughter.

Many many more pictures here, and another post soon on what I ended up making.