“Wolfram code is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized in his book A New Kind of Science.” (Wikipedia)Each row on the horizontal axis is a generation of cells and the
vertical axis shows each successive generation based on the rules.
There are 256 possible rules based on the fact there are 8 possible
states that a cell and it’s neighbours could be in, and two possible
results for each of those states (on or off). Not all of the rules
give interesting results and some are inversions or reflections of
other rules, but the variation is captivating, as is how patterns from
nature jump out in some of them. Most the patterns do not actually
repeat but they seem to make some intuitive sense to our brains. I’d
love to see some of these woven or printed on fabric as giant
non-repeating patterns.
The examples below are all generated live and if you reload the page
you will get new patterns following the same rules.
The above examples all start from a row filled with random cells, the
examples below are the same four rules but starting from a single live
cell.
The potential uses of these rules are really interesting too. Some of the rules (like Rule 90) if started with a single live cell produce a Sierpiński triangle. Rule 30 when started with noise generates a pattern similar to some shells.
Apparently Rule 184 can be used to model traffic flow and others are used to model the dispersal of gas.
The generator I built can render all the rules in the set, I think a good future daily-code could be to make an interface to allow people to interactively play with the different rules and starting conditions. If you have any ideas for things to play with on a daily code hour let me know.
These patterns below almost follow the same rules as above but they are second-order. Which means instead of only looking at the previous generation to generate the next generation (row), you look at the previous two generations; The neighbours from x - 1 and the state of the cell to perform the rules on from x - 2
I find it very interesting that the first order have a very natural feeling and the second order feel a lot more man made.
Below are the same set but this time following third order rules (x - 3)
