At some level the situation will no doubt be a little like in the evolution of a typical class 4 cellular automaton, as illustrated below. Given some initial set of persistent structures, these can interact to produce some intermediate pattern of behavior, which then eventually resolves into a final set of structures that again persist.

In the intermediate pattern of behavior one may also be able to identify some definite structures. Ones that do not last long can be very different from ones that would persist forever. But ones that last longer will tend to have properties progressively closer to genuinely persistent structures. And while persistent structures can be thought of as corresponding to real particles, intermediate structures are in many ways like the virtual particles of traditional particle physics.

So this means that a picture like the one below can be viewed in a remarkably literal sense as being a spacetime diagram of particle interactions—a bit like a Feynman diagram from particle physics.

One immediate difference, however, is that in traditional particle physics one does not imagine a pattern of behavior as definite and determined as in the picture above. And indeed in my model for the universe it is already clear that there is more going on. For any process like the one in the picture above must occur on top of a background of apparently random small-scale rearrangements of the network. And in effect what this background does is to introduce a kind of random environment that can make many different detailed patterns of behavior occur with certain probabilities even with the same initial configuration of particles.

The idea that even a vacuum without particles will have a complicated and in some ways random form also exists in standard quantum field theory in traditional physics. The full mathematical structure of quantum field theory is far from completely worked out. But the basic notion is that for each possible type of particle there is some kind of continuous field that exists throughout space—with the presence of a particle corresponding to a simple type of structure in this field.

In general, the equations of quantum field theory seem to imply that there can be all sorts of complicated configurations in the field, even in the absence of actual particles. But as a first approximation, one can consider

A collision between localized structures in the rule 110 class 4 cellular automaton.

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