Welcome to Complexity Explorables

This site is designed for people interested in complex systems and complex dynamical processes. Complexity Explorables hosts different collections of interactive illustrations of models for complex systems in physics, mathematics, biology, chemistry, social sciences, neuroscience, epidemiology, network science and ecology.

Topics include pattern formation, synchronization, critical phenomena, chaotic dynamics, evolutionary dynamics, fractals, collective behavior, reaction-diffusion systems and more.

The main collection is Explorables. Each explorable contains one interactive component and describes a single system. The models are chosen in such a way that the key elements of a system’s behavior can be explored and explained without too much math (there are a few exceptions) and with as few words as possible.

The site also features Flongs (short for “foot longs”). These are mini tutorials on specific and paradigmatic complex systems that go a bit deeper, feature more interactive elements but usually require a bit more math.

If you want to use Explorables in teaching or presentations, we have a Slide section. A slide only contains an Explorables’ interactive element, without the text, and can easily be used as part of a presentation or lecture.

For a great summary, introduction and background information on complexity and complex systems I recommend the site “What is Complexity Science?” by Manlio De Domenico and Hiroki Sayama.

Recently added:

“T. Schelling plays Go”

The Schelling model

July 1, 2019

“Janus Bunch”

Dynamics of two-phase coupled oscillators

May 20, 2019

“Nah dah dah nah nah... (Opus, 1984)”

Conway's Game of Life

April 24, 2019

“Berlin 8:00 a.m.”

The emergence of phantom traffic jams

March 28, 2019

T. Schelling plays Go

The Schelling model

Janus Bunch

Dynamics of two-phase coupled oscillators

Berlin 8:00 a.m.

The emergence of phantom traffic jams

Jujujajáki networks

The emergence of communities in weighted networks

Prime Time

The distribution of primes along number spirals

I sing well-tempered

The Ising Model

Anomalous Itinerary

Lévy flights

Hopfed Turingles

Pattern Formation in a simple reaction-diffusion system

Albert & Carl Friedrich

Random Walks & Diffusion

Critically Inflammatory

A forrest fire model

Dr. Fibryll & Mr. Glyde

Pulse-coupled oscillators

Facebooked Flu Shots

Network vaccination

The Blob

A network's giant component

Stranger Things

Strange attractors

I herd you!

How herd immunity works

Scott's World*

Microbial growth patterns

Yo, Kohonen!

Kohonen's Self-Organizing Map

Echo Chambers

A model for opinion dynamics


A stochastic cellular automaton

Surfing a Gene Pool

Expansion of clones with idential fitness


Growing complex networks

If you ask your XY

The XY model of statistical mechanics

Ride my Kuramotocycle!

The Kuramoto model

Maggots in the Wiggle Room

The dynamics of evolution

A Patchwork Darwinge

Evolution: Variation and Selection

Into the Dark

Collective intelligence

Barista's Secret

Percolation on a lattice

Lotka Martini

The Lotka-Volterra model

Double Trouble

The double pendulum

Critical HexSIRSize

The stochastic, spatial SIRS model

Flock'n Roll

Collective behavior and swarming

Hokus Fractus!

Famous fractals

Particularly Stuck

Diffusion Limited Aggregation


The spatial rock-paper-scissors game

Kick it like Chirikov

The kicked rotator (standard map)


The SIRS epidemic model

Keith Haring's Mexican Hat

Pattern Formation by Local Excitation and Long-Range Inhibition

Spin Wheels

Phase-coupled oscillators on a lattice

Weeds & Trees

Lindenmayer Systems

Flock'n Roll

Collective behavior and swarming