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always to have the same overall rounded form, essentially independent of their orientation with respect to the underlying grid.

And indeed what happens is similar to what we have seen many times in this book: the evolution of the cellular automaton generates enough randomness that the effects of the underlying grid tend to be washed out, with the result that the overall behavior produced ends up showing essentially no distinction between different directions in space.

So should one conclude from this that the universe is in fact a giant cellular automaton with rules like those of case (c)?

It is perhaps not impossible, but I very much doubt it.

For there are immediately simple issues like what one imagines happens at the edges of the cellular automaton array. But much more important is the fact that I do not believe in the distinction between space and its contents implied by the basic construction of a cellular automaton.

For when one builds a cellular automaton one is in a sense always first setting up an array of cells to represent space itself, and then only subsequently considering the contents of space, as represented by the arrangement of colors assigned to the cells in this array.

But if the ultimate model for the universe is to be as simple as possible, then it seems much more plausible that both space and its contents should somehow be made of the same stuff—so that in a sense space becomes the only thing in the universe.

Several times in the past ideas like this have been explored. And indeed the standard theory for gravity introduced in 1915 is precisely based on the notion that gravity can be viewed merely as a feature of space. But despite various attempts in the 1930s and more recently it has never seemed possible to extend this to cover the whole elaborate collection of forces and particles that we actually see in our universe.

Yet my suspicion is that a large part of the reason for this is just the assumption that space is a perfect continuum—described by traditional mathematics. For as we have seen many times in this book, if one looks at systems like programs with discrete elements then it immediately becomes much easier for highly complex behavior to emerge. And this is fundamentally what I believe is happening at the lowest level in space throughout our universe.

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