Interactive Models

A selection of models studied by our group was implemented in Javascript to make them accessible for everyone to study. You can explore those directly on this website.


A model of financial markets based on the Ising Model.

The agents are given two possibilities: To buy or to sell a given stock. Each agent is influenced by the price as well as its nearest neighbors. The conflicting character of a minority game combined with a ferromagnetic Ising model causes frustration across scales and emerges expectation bubbles and volatility clustering known from real markets.

S. Bornholdt, Expectation bubbles in a spin model of markets: Intermittency from frustration across scales, Int. J. Mod. Phys. C, Vol. 12, No. 5 (2001) 667-674.


A model of scientific paradigms

Scientists suggest ideas to each other and accept those new ideas with a probability proportional to their popularity. Once a scientists has scrapped an idea he cannot reconsider it. An innovation rate controls how often scientists come up with new ideas.

S. Bornholdt, M. H. Jensen and K. Sneppen, Emergence and Decline of Scientific Paradigms, Phys. Rev. Lett. 106 (2011) 058701.


A model of multiple epidemics

This is a minimal model of how epidemic spreading interacts with immunity of individual hosts: Every agent only gets infected once by each disease. Older diseases thus face a harder time while new diseases sweep over the system.

K. Sneppen, A. Trusina, M.H. Jensen, and S. Bornholdt, A Minimal Model for Multiple Epidemics and Immunity Spreading, PLoS ONE 5 (2010) e13326.


A model for how the brain may keep itself between silence and chaos

This is a simple neural network model which exhibits self-organized criticality (SOC). Based on local rules only, the network evolves towards criticality, showing typical scale-free avalanches matching those recently observed in the brain.

S. Bornholdt and T. Rohlf, Topological evolution of dynamical networks: Global criticality from local dynamics, Phys. Rev. Lett. 84 (2000) 6114-6117.

S Landmann, L Baumgarten, S Bornholdt, Self-organized criticality in neural networks from activity-based rewiring,  Phys. Rev. E 103 (2021) 032304.


Social evolution of structural discrimination

We ask: “Could a social hierarchy emerge and persist between two groups distinguished by easily observable characteristics, even if they are identical in terms of intrinsic properties?”

G. Gruner, S. Bornholdt, Social evolution of structural discrimination, arXiv/1703.06311

In contrast to the implementations listed above the following programs make use of the full features of the SpiMoSim library. These implementation are meant for advanced users and those who are familiar with Javascript and might want to use SpiMoSim for their projects.

MARKET MODEL (advanced version)  

A model of financial markets based on the Ising Model.

This implementation features more plots, higher dimensional lattices, CSV export, downloads of animated GIFs, upload of initial states, export of the current state (JSON format) and more.

S. Bornholdt, Expectation bubbles in a spin model of markets: Intermittency from frustration across scales, doi:10.1142/S0129183101001845

Models powered by SpiMoSim – A modular javascript library for interactive physical models by Pascal Grafe. Find out more!


The 50-50-Stalemate Model simulates the formation of two different opinions in contrversial debate using pairwise interaction between agents. Controversial meaning that people tend to have strong opinions about the topic and maybe repel the opposite instead of convincing them. The original paper shows that for larger values of the repel parameter the system tends towards an equilibrium, where the two opinions are trapped in a stalemate. On this interactive website the model is implemented using the spiMoSim library from Pascal Grafe.

The paper can be found here: “Repulsion in controversial debate drives public opinion into fifty fifty stalemate” (2019), Sebastian M. Krause, Fritz Weyhausen-Brinkmann, Stefan Bornholdt