Anyone who follows the popular scientific literature knows that fractals are now "in." Commonly employed to "explain" patterns in nature, fractals are, from a simplistic viewpoint, mathematical ways to predict the development of a growing structure, be it a crystalline mass, a plant, or the universe-as-a-whole.

Yes, the universe-as-a-whole, the clouds of stars and clusters of galaxies, may be mimicked by cellular automata (i.e., fractals). Imagine the universe as a cubical lattice, and start in one corner, adding one layer of cubes after another. Galaxy distribution could be simulated by using a rule telling us which of the added cubical cells had galaxies in them and which did not.

"The rule actually used supposes that the question whether each point in a newly added layer will (or will not) be occupied by a galaxy is mostly determined by the occupancy of the five nearest neighbors in the previous layer, but for good measure, there is a random variable to introduce an element of white noise to the system. To make the process a little more interesting, the determination whether a new site is occupied depends on whether a number characteristic of that site, and calculated by simple arithmetic from the corresponding number for the five nearest neighbors in the preceeding layer, exceeds an arbitrarily chosen number."

Comparing this fractal simulation with the observed universe is startling. The agreement is "spectacularly successful."
(Maddox, John; "The Universe as a Fractal Structure," Nature, 329:195, 1987.)

Comment. In biology, too, fractal modelling can be very impressive. But,
doesn't it all verge on numerology? The existence of a galaxy at a point in space is simply dependent on its neighbors; and the law of gravitation is not even mentioned. Are the physical laws that we usually assume as controlling the dynamics of matter now "hidden" beneath a more general property of the universe? One is reminded of R. Sheldrake's theory of morphic resonance, in which the mere existence of a certain structure makes it more easy for the same structure to be duplicated elsewhere in the universe!