This explorable illustrates how strong heterogeneities, cluster-like structures and high variability in node connectivities can naturally emerge in growing networks. The mechanism explored here is very simple: When a new node is added to the network it picks another target node at random. Instead of linking to it, the new node establishes a link to one of the target’s neighbors.

This explorable illustrates a dynamic model for pattern formation in a growing community of microbes. Many microbial organisms exhibit collective behavior when a community of them expands say on a surface with nutrients. These patterns are often very beautiful and rich in structure.

This explorable is about pattern formation in a model system for the growth of a bacterial population in a petri dish in which the bacterial population is made up of a mix of two or three mutant strains that have identical fitness and reproduction properties. In the model system, an initially well mixed drop of bacteria with an equal amounts of every mutant strain is positioned in the center of the petri dish. After that, the bacteria start replicating, the population expands radially and a pattern will emerge.

This explorable illustrates network growth based on preferential attachment, a variant of the Barabasi-Albert model that was introduced to capture strong heterogeneities observed in many natural and technological networks. It has become a popular model for scale-free networks in nature.

Preferential attachment means that nodes that enter the network during a growth process preferentially connect to nodes with specific properties. In the original system, they preferentially connect to existing nodes that are already well connected, increasing their connectivity even further. This rich get richer effect generates networks in which a few nodes are very strongly connected and very many nodes poorly.

This explorable illustrates a process known as diffusion-limited aggregation (DLA). It’s a kinetic process driven by randomly diffusing particles that gives rise to fractal structures, reminiscent of things we see in natural systems. The process has been investigated in a number of scientific studies, e.g. the seminal paper by Witten & Sander.

This explorable illustrates how fractal patterns observed in natural systems, particularly structural properties of some plants, can approximately be modeled by simple iterative models. Sometimes these models are refered to as Lindenmayer systems.