I've been reading Stephen Wolfram's A New Kind of Science, and plan to write a few comments about his theories later. First, though, one of the questions the book asks: what is the origin of randomness?

In a deterministic system, random events seem to come from "outside". But it's surprisingly easy to create very, very simple systems which appear to create highly random data. Here's an example.

I've only tested this in IE6, so your mileage may vary considerably (!).

This graph is really really simple. Begin with the number One. For each iteration: Display the digits of the number. Then multiply the number by (say) three. Repeat.

Is the pattern random? It this real-randomness? Or pseudorandomness? Or are we simply looking at it through the wrong lens (for example, displaying log(n) would give a very different picture)? If pseudorandom, and if simple iterative processes in nature are as widespread as Wolfram asserts, then what is "true" randomness?