This chapter explores how naturally occurring inanimate structures grow by accretion of smaller-sized components, focusing on one specific accretion process: diffusion-limited aggregation (DLA). In DLA, particles move about in random fashion, but stick together when they come into contact. Clumps of particles then form and grow further by colliding with other individual particles, or clumps of particles. Over time, one or more aggregates of individual particles will grow. After providing an overview of how DLA works, the chapter describes its numerical implementation and shows a representative simulation of a two-dimensional DLA aggregate. It then considers two peculiar geometrical properties of aggregates resulting from the DLA process, namely self-similarity and scale invariance, and shows that rule based growth through DLA can lead to the buildup of complex structures, sometimes exhibiting fractal geometry. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.
Self-similar resistive circuits as fractal-like structures