## 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.

## Most Recent:

# “Berlin 8:00 a.m.”

## The emergence of phantom traffic jams

This explorable features an agent based model for road traffic and congestion. The model captures a phenomenon that most of us have witnessed on highways: * phantom traffic jams*, also known as

*traffic shocks*or

*ghost jams*. These are spontaneously emergent congested segments that move slowly and oppositely to the traffic. The explorable illustrates that phantom jams are more likely to occur if the variability in car speeds is higher:

# “Jujujajáki networks”

## The emergence of communities in weighted networks

This explorable illustrates a dynamic network model that was designed to capture the emergence of community structures, heterogeneities and clusters that are frequently observed in social networks. Clusters are characterized by a high probability that a person's *'friends are also friends'*. In this model not only the connectivity evolves but also the strength of links between nodes. The model was orginally proposed by Jussi Kumpula, Jukka-Pekka Onnela, Jari Saramäki, János Kertész and Kimmo Kaski.

# “Prime Time”

## The distribution of primes along number spirals

This explorable is about **prime numbers**. It illustrates interesting patterns that emerge if you arrange the positive natural numbers \(1,2,3,....\) and so forth in a regular pattern in the plane and look at the * distribution of the primes* in the arrangement. Although prime numbers, as one might expect, don't follow some regular repetitive pattern, they are also not distributed completely at random. Instead, in all arrangements streaks and fragments of neighboring primes emerge. These structures are related to

**prime generating polynomials**like the famous polynomial discovered by Leonard Euler.