What’s Stephen Wolfram been up to over the past 20 years? Dealing with the implications of his discovery of rule 30.

In this Flash application, every successive row of squares is generated by applying a simple rule to the preceding row. For each square in the new row, the rule looks at the three closest squares in the preceding row. In our case, if all 3 are black, for example, then the new square will be white–and if the one immediately above is black but the other 2 are white, then the new square will be black, etc… There are 256 such possible rules (because a set of 3 squares with 2 states has eight possible permutations, and for each permutation the new square has 2 possible states). Rule 30, displayed here on he right, is special: Wolfram discovered that it is capable of generating completely random behavior from a row containing just a single square.

My implementation of rule 30 does not lead to perfectly random behavior, because–for space reasons–the leftmost square and the rightmost square have been turned into neighbors. Because the amount of squares in a row is fixed (at 30) there is a finite set of possible permutations, and so eventually the combinations must repeat. In our particular case, this happens every 250,000 iterations or so, or about every 2 days at the current pace. Still, not bad for a few lines of code.

[Mon, Jun 10 2002 – 11:54] Felix (www) (email) If this is the best you can come up with after trudging through that monster of a book, I’m definitely not buying it. Besides, your flash thingy looks far from random to me: the human eye likes to search out patterns, and I see a lot of downward-pointing triangles in the animation. Surely if it was truly random there would be a lot of upward-pointing triangles as well — but so far, after looking for a while, I haven’t seen any.

[Mon, Jun 10 2002 – 17:24] Stefan (www) (email) By randomness here, he means that the only way of determining whether a particular square will be white or black is by running the program–there is no equation to provide you with a shortcut. The downward facing triangles are large patterns that evolve–structure inside randomness, if you like, and they make it much more interesting.

Another thing that I noticed today upon staring at it for too long: All the black squares are conneccted and the resulting zig-zag lines slope to the left. When they “fall off” the left edge they reappear on the right; and they all seem to flow together, like rivers confluencing. It’s as if the rule has a memory, making sure it never creates a closed shape.

I’ve only read until chapter 6. I think Wolfram talks about how these rules are computationally equivalent to computers by the end of the book, so the reference to memory might turn out to be salient.

Did I mention it’s a beautiful book?

[Tue, Jun 11 2002 – 19:34] Matthew (email) it’s a sure sign financial armageddon is upon us when an employee of an options trading firm spends all day staring at small white and black squares scroll down a screen.

[Tue, Jun 18 2002 – 04:58] yiarof (email) well i icouldn’t even open it. it was a blank white screen. looks like bollocks to me.

[Wed, Jun 19 2002 – 14:13] Stefan Geens (www) (email) Perhaps Yiarof could drag itself and its computer kicking and screaming into the 21st century by downloading and installing the Flash player, available at http://www.macromedia.com