About this falling cube simulation

This simulation visualizes a simple physical system that can exhibit Self-Organizing Criticality (SOC). Identical cubes are released one by one from above and fall under gravity onto a flat ground plane. As more cubes accumulate, they form a pile whose structure and stability emerge purely from local interactions: gravity, collisions, friction, and restitution. There is no global controller arranging the cubes or enforcing a shape. Order, instability, and sudden rearrangements arise on their own.

As the pile grows, it naturally approaches a critical state where small perturbations—such as the addition of a single cube—can lead to disproportionately large effects, like local collapses or avalanches. This is characteristic of self-organizing critical systems: the system continuously organizes itself near a threshold between stability and instability without external tuning.

The time graph shows an approximation of the pile’s height over time, measured as the highest cube that has effectively come to rest. This allows you to observe how growth is not smooth or linear, but punctuated by sudden reorganizations as the pile settles and reshapes itself.

You can interactively explore the system by adjusting parameters such as gravity, restitution (bounciness), drop height, spread radius, and drop frequency. These controls change the local interaction rules, which in turn alter the emergent global behavior of the pile.

The 3D view is fully interactive. You can change the viewpoint using the mouse:

This makes it possible to closely inspect local structures, overhangs, and instabilities, or to step back and observe the pile as a whole as it evolves toward and fluctuates around a critical state.