Active Motion Cross Scans

Active Diffusion Speed Three-Row Scan

spread follows speed squared

Changing speed at fixed persistence time separates linear motion from squared spread. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One metre per second gives one square metre per second

Hold persistence time at 2 s. Speed 1 m/s gives active spread scale 1 square metre per second.

12⋅2/2=11^{2}\cdot2/2=1
Active diffusion scale ledgerA deterministic active spread scale uses speed squared times time.speedactive spread

Two metres per second gives four

At speed 2 m/s, the squared speed makes active spread 4 square metres per second.

22⋅2/2=42^{2}\cdot2/2=4
Active diffusion scale ledgerA deterministic active spread scale uses speed squared times time.speedactive spread

Three metres per second gives nine

Speed 3 m/s gives active spread 9 square metres per second. The time is still fixed at 2 s.

32⋅2/2=93^{2}\cdot2/2=9
Active diffusion scale ledgerA deterministic active spread scale uses speed squared times time.speedactive spread