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For First Responders · Percolation

Percolation for a zip line

Built for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field. Simulate a zip line 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.

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Frequently asked questions

Is this good for first responders?: Yes — this version of "Percolation for a zip line" is framed for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.