# “Anomalous Itinerary”

## Lévy flights

This explorable illustrates the properties of a class of random walks known as Lévy flights.
To get the most out of this explorable, you may want to check out the explorable **Albert & Carl Friedrich** on ordinary random walks and diffusion first.

# “Hopfed Turingles”

## Pattern Formation in a simple reaction-diffusion system

With this explorable you can discover a variety of spatio-temporal patterns that can be generated with a very famous and simple autocatalytic reaction diffusion system known as the **Gray-Scott model**. In the model two substances \(U\) and \(V\) interact and diffuse in a two-dimensional container. Although only two types of simple reactions occur, the system generates a wealth of different stable and dynamic spatio-temporal patterns depending on system parameters.

# “Albert & Carl Friedrich”

## Random Walks & Diffusion

This explorable illustrates the geometric and dynamic properties of the physical process of **diffusion** and its intimate relation to a mathematical object known as a **random walk**. It also illustrates graphically the implications of the **central limit theorem** that explains why we so often (* normally*) observe

**Gaussian distributions**in nature. In the context of random walks this means that in the long run and from a great distance the paths of different types of walks become statistically indistiguishable.

# “Flock'n Roll”

## Collective behavior and swarming

This explorable illustrates of an intuitive dynamic model for collective motion (swarming) in animal groups. The model can be used to describe collective behavior observed in schooling fish or flocking birds, for example. The details of the model are described in a 2002 paper by Iain Couzin and colleagues.

# “Particularly Stuck”

## Diffusion Limited Aggregation

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.