Given a particular underlying program, it is always in principle possible to work out what it will do just by running it. But for the whole universe, doing this kind of explicit simulation is almost by definition out of the question. … But to invert this in any systematic way is probably even in principle beyond what any realistic computation can do.

For the model does not say that such sequences are impossible—it merely says that they should occur only about 1% of the time. … If one does not decide in advance how long the blocks are going to be, however, then things can become more complicated. … Needless to say, such a model would for most purposes not be considered particularly useful—and certainly it does not succeed in providing any kind of short summary of the data.

Human Thinking When we are presented with new data one thing we can always do is just apply our general powers of human thinking to it. And certainly this allows us with rather modest effort to do quite well in handling all sorts of data that we choose to interact with in everyday life. … How does general human thinking do with this?

What does it take to find the outcome in this case? It is always possible to do an experiment and explicitly run the system for a certain number of steps and see how it behaves. … Yet from the picture on the facing page it is certainly not obvious how one might do this.

But one of the major features of the new kind of science that I have developed is that it does not have to make any such restriction. … It has in the past couple of decades become increasingly common in practice to study systems by doing explicit computer simulations of their behavior. But normally it has been assumed that such simulations are ultimately just a convenient way to do what could otherwise be done with mathematical formulas.

As soon as we say that a system achieves a definite purpose this means that we can summarize at least some part of what the system does just by describing this purpose. So if we have a simple description of the purpose it follows that we must be able to give a simple summary of at least some part of what the system does. But does this then mean that the whole behavior of the system must be simple?

The first case specifies what to do if both connections from a particular node lead to the same node; the second case specifies what to do when they lead to different nodes. … Even if this restriction is removed, however, more complicated behavior does not appear to be seen.

What one sees is that when the perturbations are sufficiently large, the sequence of colors of the center cell does indeed change. … With only 2 or 3 black cells, the sequence in the center of the pattern does not change. But as soon as more black cells are added, it does change.

So why does the procedure not work better? … As a first example, consider a procedure that at each step picks a square at random, then reverses its color whenever doing so reduces the total number of squares that violate the constraint. … Although the fraction of squares that violate the constraints is less than 20% after 100,000 steps, the overall patterns still do not look much like the exact results.

So how can one do better? … It is also easy to extend block-based encoding to two dimensions: all one need do is to assign codewords to two-dimensional rather than Examples of one-dimensional pointer-based encoding applied to patterns produced by cellular automata. … In the last example, large regions contain no such repeats, and therefore appear in the output just as they do in the input.