This explorable illustrates a process known as diffusion-limited aggregation (DLA). It’s a kinetic process driven by randomly diffusing particles that gives rise to fractal structures, reminiscent of things we see in natural systems. The process has been investigated in a number of scientific studies, e.g. the seminal paper by Witten & Sander.

The Model:

The system is initialized by say 300 diffusing particles that move about randomly in the plane. In the center of the system is a tiny nucleus (dark red dot in the simulation panel). When a diffusing particle touches this nucleus it gets stuck an becomes part of the structure so that later on additional particles can get stuck, too, and the structure grows. There’s also a continuous supply of new particles that are injected in the periphery of the system. If particles are just diffusing it usually takes a while for a structure to emerge in the center because only rarely particles collide with it. So, in addition to the isotropic and homogeneous diffusion we added a bit of drift to the model: particles are weakly attracted to the center. There’s also a bit of swirl going on, so particles are spiraling to the center.

Try this:

With the sliders on the right you can manipulate the parameters of the system. Try this: Scale the attaction parameter just a bit so that particles accumulate in center. If you move the twist parameter up, particles start swirling and the emergent structure should also have a twist to it, an imprint of the motion of the particles. The twist-mix parameter controls the proportion of particles moving clockwise or counter-clockwise, when centered the split is 50/50. This parameter has an interesting effect on the emergent structure, especially if you turn the wiggle parameter down to zero. If you are impatient, increase the speed and attraction.

References:

• T. A. Witten, Jr. and L. M. Sander, Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, [Phys. Rev. Lett. 47 (1981), 1400] (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.1400)
• T. A. Witten and L. M. Sander, Diffusion-limited aggregation, Phys. Rev. B 27, 5686 – Published 1 May 1983