Random Walk Explorer
A random walk takes one random step after another, and the simple rules hide deep behaviour. This tool runs several flavours at once. A plain 2D walk spreads out as a diffusing cloud whose typical distance grows as the square root of the number of steps. A Lévy flight mixes in rare long jumps and covers ground completely differently, the pattern real foraging animals use. A self-avoiding walk that never crosses its own path grows faster and can trap itself. Run many walkers at once to see the cloud spread, watch a single path meander, and track how far they get versus step count on a live plot.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- For an ordinary walk the mean squared distance grows in proportion to the number of steps, so typical distance scales as √n — slow, diffusive spreading.
- Lévy flights draw step lengths from a heavy-tailed distribution, so occasional huge jumps make them spread far faster than a normal walk and explore new ground efficiently.
- A self-avoiding walk cannot revisit a cell, so it swells faster than a free walk and can paint itself into a corner with no legal move left — a model for polymer chains.
- Runs 100% in your browser — simulations are computed locally on your device.
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