Issue 13 launch art project

Chalkdust

1 May 2021

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We are very excited to launch issue 13 of Chalkdust which we have jam packed with articles lovingly crafted by our authors and editors. This issue is something of an homage to the late great John Conway who is featured as our significant figure. The issue also includes some favourite mathematical games and cellular automata, both of which Conway was very interested in.

In order to celebrate the release of Chalkdust issue 13, we have decided to do something a little different. Alas we cannot yet invite you to join us for an in-person celebration, but we thought it would be fun to join with you in a little community art and maths project inspired by our cover feature for this issue on cellular automata. In short, an automaton is a simple machine which follows a set of rules, perhaps to produce a pattern of coloured squares. These patterns can turn out to be surprisingly complex given the unassuming rules which generate them. You should read up about elementary cellular automata in our cover article, before reading on below.

A marriage of maths and art

What is it exactly we would like you to do? Produce a piece of art inspired by a cellular automaton. Quite deliberately we are not being proscriptive about the medium of the art, or exactly which automaton you choose. We would however recommend that you stick to an automaton which is a variation on the elementary automata discussed in our cover feature, in particular a one-dimensional automaton which allows you to represent the time-evolution of the pattern in two-dimensions. To get you started, here are some ideas which you might want to explore.

Art medium ideas:

• No need to overcomplicate things, you could stick to colouring pencils or paint on paper
• You could try forming your square grid using paper weaving, or get other ideas from the Art Assignment YouTube channel
• Maybe you want to push the boundaries to traditional media, and try plaiting an automaton into someone’s hair, using coloured beads to make the pattern
• Creating some form of digital art could be the most straightforward option, as the computer can do the drawing for you—just make sure you add your own flair so that it becomes art and is not just a maths plot
• Choose some way to use your automaton to encode musical notes and turn the pattern into a piece of music

Automaton ideas:

• The 256 elementary automata are well studied and you can find examples of each online, why not pick one you like the look of and run with it?
• Starting with a row of eight, say, 1s and 0s, you could glue the two ends together and then run your automaton on a cylinder rather than expanding out into the plane
• If you like the idea of ternary, or other base $b$, automata but feel a bit intimidated by the $b^{b^3}$ possible rules, try one of the $b^{3(b-1)+1}$ totalistic rules, where the value of each cell in the next generation depends only on the total sum of the three cells above it, not their individual values and configuration
  

  Ternary totalistic rule 2101001$_3$ which is 1729 in decimal.

• Stephen Wolfram’s book A new kind of science (available for free online) has a whole chapter (chapter 3) on one-dimensional cellular automata and their variations, including totalistic rules, substitution systems, and Turing machines—pick one you like and have a play

We are very excited to see what imaginative things you can come up with. When you’re happy with your piece(s) of art, send them to us on Twitter (@chalkdustmag) using the hashtag #chalkdust13, or via email (contact@chalkdustmagazine.com) and we’ll feature the best ones on our blog.