Interactive Simulations

This page is a growing collection of interactive models for exploring ideas from complexity science, nonlinear dynamics, and collective behaviour. Some simulations are already playable below, and more will be added over time.

Simulation Library

Select a model to load it into the interactive workspace.

Available Now

Forest Fire Model

Explore how a single fire spreads through a forest as tree density changes, revealing threshold-like behaviour in fire size.

Available Now

Forest Fire (SOC)

Explore the growth-lightning forest-fire model, where slow regrowth and rare ignitions generate intermittent fire avalanches.

Available Now

Vicsek Flocking Model

Explore how local alignment rules give rise to collective motion and phase transitions between order and noise.

Coming Soon

More Simulations

Future additions may include models related to network dynamics, diffusion, synchronization, and educational demonstrations.

In development

Forest Fire Model

A simplified forest-fire model in which a single ignition spreads through a forest with density rho, highlighting how fire size changes near the critical region.

Choose Simulation

Forest Fire Model

This version focuses on a single fire event in a randomly generated forest. It is useful for exploring how fire size depends on tree density.

Try this: Explore values of rho around 0.55. Below that threshold, fires are usually local; above it, they can spread across much of the forest.

Tree Density (rho): 0.55

Grid Size

Ignition Mode

How to Explore

Choose a value of rho and reset the forest.
Click Start to ignite one tree and let the fire run.
Use Single Step to follow the spread one update at a time.
Compare what happens below, near, and above rho around 0.55.

Actual Density 0.55

Active Fire 0

Burned Trees 0

Burned Fraction 0.000

Last Fire Size 0

Last Fire Fraction 0.000

Duration 0

Status Ready

Model Assumptions

Spread uses the four cardinal neighbors only.
Periodic boundary conditions are used.
One fire is ignited at a time, then allowed to burn out.

Forest Fire (SOC)

This version follows the slow-growth, rare-lightning forest-fire model. Instead of one ignition only, the lattice evolves continuously and produces fire events of different sizes over time.

Try this: Keep lightning rare, then compare slower and faster regrowth. You will see long quiet periods interrupted by bursts of burning.

Growth Probability (p): 0.010

Lightning Probability (f): 0.00010

Grid Size

Sweeps per Animation Frame

How to Explore

Reset the model to begin with a fresh lattice.
Click Start and let the forest grow for a while.
Watch how rare ignitions trigger fire events of different sizes.
Compare how the event pattern changes when p grows faster or f becomes rarer.

Tree Density 0.000

Burning Cells 0

Fire Events 0

Last Fire Size 0

Largest Fire 0

Mean Fire Size 0.0

Time Step 0

Status Ready

Model Assumptions

Trees regrow on empty sites with probability p.
Lightning ignites trees with probability f.
Spread uses the four nearest neighbors.
Burned sites become empty again, allowing repeated fire events.

Vicsek Flocking Model

This model shows how self-propelled particles align with nearby neighbors. It is useful for exploring how collective motion emerges from local interaction and noise.

Try this: Increase noise to break alignment, then lower it again to watch ordered motion re-emerge.

Rotational Diffusion (Dr): 0.10

Aligning Interaction Range: 10

Particle Count

How to Explore

Start with low rotational diffusion and watch particles align into collective motion.
Increase diffusion to see the ordered state break down.
Change the interaction range to test how far alignment information spreads.
Increase particle count and compare the order parameter through time.

Order Parameter 0.000

Regime Initializing

Mean Neighbors 0.0

Clustered Fraction 0.000

Particle Count 50

Time Step 0

Status Ready

Model Assumptions

Particles move with constant speed in a square domain.
Each particle aligns with neighbors inside the chosen interaction range.
Rotational diffusion perturbs the local mean direction at each update.
Periodic boundaries are used.

Tree Burning Burned Empty

The chart shows the instantaneous size of the active fire front and the cumulative burned fraction through time.

The chart tracks tree density and the active burning fraction as the growth-lightning dynamics generate repeated fire events.

The chart tracks both the order parameter and a simple clustering measure, showing whether the particles are aligning and gathering into denser groups.