Heavy elements are produced by supernovas. Some of the resulting clouds of hot gases slowly coalesce, their centers collapsing under gravity to form stars. Somehow parts of the outer regions of these clouds form planets. How does this happen?
A cartoon of the standard model asserts some of the remaining gas condenses into dust, dust forms grains of sand, and grains of sand form rocks. The rocks collide and stick together to form larger rocks. Eventually some heaps of rocks get massive enough to gravitationally attract other stuff, and these growing rock piles form planets. A problem is that by the time the rocks have appeared, they are in Keplerian orbits about the young star and so they collide at velocities of kilometers per second. Smacking two rocks together at several km/sec will not give a larger rock, but rather a cloud of much smaller rocks moving wildly off in all directions. The problem is to get from dust to rock piles.
Experience with growth models suggested to physicists David Peak and Burt Donn that Diffusion Limited Aggregation (DLA) could mediate the growth at some early (and small) stage of development. Instead of forming hard grains of sand, the dust motes diffuse through the cloud and form wispy, filamentary fractal dust balls. Physical measurements of DLA clusters in 3-dimensional space suggest the dust balls should have mass dimension about 2.5, so
mass = radius2.5
Yet the dust ball sweeps out a space with
volume = radius3
So
density = mass/volume = 1/radius0.5
That is, the larger the bust ball, the more tenuous it is. The paths of these large dust balls are slowed by friction against the gas cloud, guaranteeing the relative speed of interaction is much smaller than the Keplerian orbital speed. Consequently, these fractal wisps can collide and stick together, forming larger wisps. When large enough wisps collide, there can be some restructuring, melting at the collision sites. Larger and larger cosmic dust balls colliding will experience more restructuring, more melting and compacting. Eventually these will form solid objects, planetisimals. If the transition from fractal to rock occurs when the resulting rock is large enough to grow by gravitationally accreting other stuff from the gas and dust cloud, then the rest of the standard model can be applied. That is, fractals may provide the transition between dust motes and planetisimals.
There is some evidence to support this view. Comets are thought to be fossils from the very early solar system. During the last flyby of Halley, the density was estimated at about 0.2 gm/cm3 - that is, this comet is not a huge snowball, but rather is very fluffy, possibly with a fractal structure.
Many details of this model remain unclear. In particular, the mechanical properties of fractal dust is an area of active research. If we observe the sorts of restructuring necessary to make the transition from cotton ball to planetisimal, then fractals may take on a very important role in our history.
