Showing Text From Page | View Full page with images

The Intrinsic Generation of Randomness

In the past two sections [3, 4], we have studied two possible mechanisms that can lead to observed randomness. But as we have discussed, neither of these in any real sense themselves generate randomness. Instead, what they essentially do is just to take random input that comes from outside, and transfer it to whatever system one is looking at.

One of the important results of this book, however, is that there is also a third possible mechanism for randomness, in which no random input from outside is needed, and in which randomness is instead generated intrinsically inside the systems one is looking at.

The picture below shows the rule 30 cellular automaton in which I first identified this mechanism for randomness. The basic rule for the system is very simple. And the initial condition is also very simple.

Yet despite the lack of anything that can reasonably be considered random input, the evolution of the system nevertheless intrinsically yields behavior which seems in many respects random.

As we have discussed before, traditional intuition makes it hard to believe that such complexity could arise from such a simple

Captions on this page:

The rule 30 cellular automaton from page 27 that was the first example I found of intrinsic randomness generation. There is no random input to this system, yet its behavior seems in many respects random. I suspect that this is how much of the randomness that we see in nature arises.

From Stephen Wolfram: A New Kind of Science [citation]