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) similar to R(alpha-1), R less than or equal to R(max). We find that the patterns become more and more ordered as alpha increases, and that the Apollonian packing is obtained at the alpha --> infinity 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.