Fractal Formation and Ordering in Random Sequential Adsorption

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, P(R)~R^α-1, R≤Rₘₐₓ. We find that the patterns become more and more ordered as α increases, and that the Apollonian packing is obtained at the α→∞ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.