It seems so easy for nature to produce forms of great beauty--as so often imitated in art. But how does nature manage this? And must we be content with just imitating nature? Or can we perhaps capture whatever fundamental mechanism nature uses to produce the forms it does, and use this mechanism directly for ourselves?

My work in science has led me to the conclusion that for the first time in history, we are finally now at the point where this has become possible. And the key lies in the idea of computer programs. For a computer program, like a natural system, operates according to definite rules. And if we could capture those rules we should be able to make programs that do the kinds of things nature does.

But in fact we can do vastly more. For nature must follow the laws of our particular universe. Yet programs can follow whatever laws we choose. So we can in effect make an infinite collection of possible universes, not just our particular universe.

In the past, however, it has seemed difficult to get programs to yield anything like the kind of richness that we typically see in nature. And when one hears of images made by programs, one tends to think of rigid lines and simple geometrical figures. But what my work in science suggests is that people have created programs with too much purpose in mind: they have tried to make sure that their programs are set up to achieve specific goals that they can foresee.

But nature--so far as we know--has no goals. And so the programs it runs need not be chosen with any particular constraints. And what my work in science has shown is that programs picked almost at random will often produce behavior with just the kind of complexity--and sometimes beauty--that we see in nature. All that is necessary is that we go beyond the narrow kinds of programs whose behavior we, as humans, can readily foresee.

When I created Mathematica my goal was to build an environment in which one could easily set up programs of essentially any kind. And indeed the language that underlies Mathematica is based on concepts more general and more fundamental than even those of standard logic or mathematics. And by using these concepts it is possible to create programs that correspond to the kinds of rules that seem to operate in nature--or in anything like nature.

In fact, with the Mathematica language, remarkably simple programs can often produce pictures of such intricacy and unexpected detail that we would never imagine that they could ever have been made just by following any set of rules.

Sometimes the pictures one gets remind one of some familiar system in nature. And sometimes they look like the creations of a human artist. But often they are something different. They have parts reminiscent of nature. And parts that one could imagine being created by human artists. But then they have unexpected elements, like nothing seen before, together with a vast range of details far beyond what any unaided artist could ever produce.

And this is the essence of the images in Graphica.

Stephen Wolfram
scientist and creator of Mathematica