alive. But with the development of machines having even the most primitive sensors it became clear that this was not correct.

Work in the field of thermodynamics led to the idea that perhaps living systems could be defined by their ability to take disorganized material and spontaneously organize it—usually to incorporate it into their own structure. Yet all sorts of non-living systems—from crystals to flames—also do this. And Chapter 6 showed that self-organization is actually extremely common even among systems with simple rules.

For a while it was thought that perhaps life might be defined by its ability for self-reproduction. But in the 1950s abstract computational systems were constructed that also had this ability. Yet it seemed that they needed highly complex rules—not unlike those found in actual living cells. But in fact no such complexity is really necessary. And as one might now expect from the intuition in this book, even systems like the one below with remarkably simple rules can still manage to show self-reproduction—despite the fact that they bear almost no other resemblance to ordinary living systems.

If one looks at typical living systems one of their most obvious features is great apparent complexity. And for a long time it has been thought that such complexity must somehow be unique to living systems—perhaps requiring billions of years of biological evolution to develop. But what I have shown in this book is that this is not the case, and that in fact a vast range of systems—including ones with very

A two-dimensional cellular automaton that exhibits an almost trivial form of self-reproduction, in which multiple copies of any initial pattern appear every time the number of steps of evolution doubles. The rule used is additive, and takes a cell to be black whenever an odd number of its neighbors were black on the step before (outer totalistic code 204). The same basic self-reproduction phenomenon occurs in elementary rule 90, as well as in essentially any other additive rule, in any number of dimensions.