I’m quite fond of cellular automata, in particular the simple 1D cellular automata.

I was playing around, drawing them on graph paper, when I decided to make something a bit more easy for newcomers to see how it worked, and how to make their own.

By the way, if these sorts of patterns seem familar, you’re right:

(https://commons.wikimedia.org/wiki/File:Textile_cone.JPG)

Conus Textile shell – (photo taken shortly before animal declared bankrupcy over royalties to Stephen Wolfram)

There’s a space for the 8 possible cases, and for you to write the rule in Wolfram notation, and they layout hopefully makes it obvious how the two are related.

Circular version (PDF) — cellular-automata-practice-sheet-circles-v01

Square version (PDF) — cellular-automata-practice-sheet-v02

I’d suggest starting with something like either:

• rule 30 – ( 0 0 0 1 1 1 1 0), or 
• rule 110 – (0 1 1 0 1 1 1 0)

Since they’re regarded to be pretty interesting examples of behavior. (Fun fact, rule 110 has been proven to be Turing complete!)

You can also check out all the examples here: http://mathworld.wolfram.com/ElementaryCellularAutomaton.html

I spent a while playing with having the pattern begin at the bottom, rather than the top. (‘Tree’ vs ‘Mountain’). I liked the growing vertically aspect, but for drawing with a pen I found it difficult to read the lower rows while covering in the cells above them, so I eventually settled on the conventional ‘Mountain’ style.

I was also tempted to make the working area more like a truncated diamond. Since the limited area of the page eventually means getting to a stage where working out the next cell depends on cells that are off the page and unknown. That cell’s daughter is similarly unknown, etc. The result of these forwards and backwards ‘light cones’ looks like a diamond shaped worksheet.

However it started looking weird, and I figured I’d keep it rectangular, and let people figure out about that by themselves 🙂

It was also cute to play around with times when a cell was unknown, but would still not affect the daughter’s result. The boundaries of the known automata can be pushed back a little, in that case. Also if you make spot a mistake, you can track how it would affect the daughter rows.

Oh, and I’m sure I’ve made more than one error in my colouring in. No points for correcting me, but if you do use these sheets I’d be happy to share a pic here. 🙂