Constructing New Fractal-like Particle Aggregates Using Seeded DLA and Concentration Gradient Diffusion Approaches

Hybridization of existing fractal aggregate construction methods has been used to obtain new fractal-like structures, with different properties and fractal dimensions to aggregates obtained using the hybridized methods alone. In this paper we propose the hybridization of the Diffusion-Limited Aggregation (DLA) approach with other methods for constructing fractal-like aggregates, such as Iterated Function Systems (IFSs), Lindenmayer systems (L-Systems), Strange Attractors (SAs) or Percolation-based fractal construction approaches. The proposed approach is a variation of the seeded DLA algorithm used previously in the literature, which consists of considering existing fractal aggregates as condensation nuclei before the DLA simulation. In this case, we revisit the seeded DLA scheme and test different existing fractals as nuclei, such as Strange Attractors or different IFS fractals. We also introduce a simple algorithm for simulating the diffusion of particle aggregate structures, based on concentration gradient diffusion. We show how different fractal aggregates diffuse using this model, and how the diffused versions of the fractal aggregates can then be used themselves as condensation nuclei for the seeded DLA algorithm, obtaining new fractal aggregates. We characterize the new fractal-like aggregates constructed by means of their fractal dimensions, calculated by using the box-counting approach. The obtained fractal-like aggregates have potential applications in computer graphics and multi-media art, due to their esthetic and visually attractive structures based on particles. Applications of the aggregates in statistical and material physics, as well as the modeling of new aggregate types using condensation nuclei and their applications in the development of algorithms, mathematical operators or antenna design, are also reported.