Holding step length fixed while count changes makes mean-square spread readable. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two steps make eight square metres

Hold step length at 2 metres. With 2 steps, mean-square spread is 8 square metres.

222=82\cdot2^{2}=8
Random walk ledgerStep count and step size set mean-square spread and diffusion.spreaddiffusion

Four steps double the spread ledger

The same step length over 4 steps gives mean-square spread 16. The diffusion coefficient remains 1 square metre per second.

422=164\cdot2^{2}=16
Random walk ledgerStep count and step size set mean-square spread and diffusion.spreaddiffusion

Six steps make twenty-four square metres

With 6 steps, the checked spread reaches 24 square metres. This is count times step length squared.

622=246\cdot2^{2}=24
Random walk ledgerStep count and step size set mean-square spread and diffusion.spreaddiffusion