Brownian Step Ledgers

Step Variance Adds

Brownian spread is represented by a checked mean-square ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The diagram counts steps, not random draws

There are 4 steps, each with length 2 metres.

4 steps,ℓ=2 m4\ \text{steps},\quad \ell=2\ \text{m}
Random walk ledgerStep count and step size set mean-square spread and diffusion.spreaddiffusionrms

Mean-square displacement adds

The mean square is 16 square metres.

4⋅22=16 m24\cdot2^{2}=16\ \text{m}^{2}
Random walk ledgerStep count and step size set mean-square spread and diffusion.spreaddiffusionrms