These structures are the product of a process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles.

An aggregation grown from a single point by diffusion of material and the concentration gradients thus produced.

I read a paper describing the construction of these forms within weak solutions of gold particles. The particles would adhere when touched and thus be removed from the solution. Concentration gradients lead to the fractal tree form.

The paper suggested that computer simulations of single particles following random walks would accurately duplicate the concentration gradients that led to the structure.

I set out to test this in two dimensions in smalltalk at bit-map resolution. Aggregations grew from a single fixed particle. These would reach a diameter of several hundred pixels within an hour or so of computation on my personal Tektronix 4404.

I learned that an aggregation was easily distorted by any bias in the random numbers driving the walk. I fixed this by choosing a large set of random numbers in advance and normalizing them to zero mean. Table lookup also out performed generating random numbers on the fly.

See 3D Printing of computed objects