Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Researchers · Percolation

Percolation for a bouncing ball

Built for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model. Simulate a bouncing ball live below — adjust the inputs and watch it respond, right in your browser.

Percolation StudioLive

phase transition · spanning clusters

Controls

Each cell is open with probability p. Water poured on top (cyan) seeps through connected open cells. Near p ≈ 0.59 a spanning path suddenly appears — a phase transition.

Presets

Open probability p

▶ Run in Python

Data Inspector

p0.60

Percolates?no

p_critical≈ 0.593

Governing equation

P (open) = 0.60, p_{c} \approx 0.5927 \Rightarrow spanning cluster

Reading this result: Right at the critical point p_c ≈ 0.5927: a spanning cluster first appears. This is a continuous (second-order) phase transition — the crossing probability rises sharply here and the connected cluster is fractal.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Percolation

Percolation for a projectile from a cannon Percolation for a pendulum clock Percolation for a car braking Percolation for a roller-coaster loop Percolation for a satellite orbit Percolation for a mass on a spring Percolation for a skydiver's free fall Percolation for a two-cart collision

Frequently asked questions

Is this good for researchers?: Yes — this version of "Percolation for a bouncing ball" is framed for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.