Exhibition · Series IX · Many Scales
A Walk Becomes Diffusion
When does a crowd of random steps become a continuum law?
What to notice
Individual walkers move by local random steps. At larger scales, the population density approaches the heat equation and the measured mean-square displacement recovers the expected diffusion constant.
Everyday analogy. Imagine thousands of people each taking random left-or-right steps from the same doorway. Individual paths look erratic, but the crowd as a whole spreads into a smooth, predictable shape.
Fixed-seed stochastic reference model. The public visual is pre-rendered from the declared random-walk process and continuum comparison.