It is a little over one year a ago when I created a mobile version of cellular automata in 256 rules in Tableau. Recently in the thought of a similar project, I went back to understand how I did it last year. Oh boy, I almost have to retrain myself to understand all the gory details.

I made some optimization along the way (i.e., simplified calculation and used 2 rows of data instead of 4). Suddenly it came to my mind that I can put 256 rules of the cellular automata in a single sheet. It's a bit more complex but not that much. Voila a small multiple rendition of the all the 256 varieties. Click image to go to the interactive viz.

Note that
- each rule is rendered with 2 rows of data plus data densification.
- the total number of rows is 512.
- I could have done it with 2 rows of data plus densification. Due to the need of driving the pop ups, I need the rule dimension to slice the entire chart.
- hover mouse on each cell to pop up a bigger view of the same automaton.
- for each rule or cell, width and height can be adjusted via parameters.

By laying all of 256 rules in a 16x16 grid in a raster, we observed many similarities:
- 1st column and 8th column are identical
- every other rule in 1st and 8th columns down the rows are identical
- in the 4th column, rows of odd numbers are identical. Rows 2,4,10,12 (rules 20,52,148,180) are identical. Rows 6,8,14,16 (rules 84,116,212,244) are identical.
- and many other similarities. This can be a topic of research. I guess that the research is already done somewhere.

It's a great fun to explore the different results of the simple cellular automata. Many computer pioneers such as Von Neumann and in recent times, Stephen Wolfram have done a great deal of work. Tableau has provided a great way to visualize and explore those amazing patterns. Voila the results. Feel free to download the workbook and explore the details. Leave comments if you have questions.