Three real mean-square-displacement rows from a real physim Brownian-motion simulation (scenario brownian-motion-diffusion, D=0.5, N=2000 particles, seed=11), each fitting back a D close to, not exactly, the real input value. 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 real MSD rows each fit back a D close to the input
A real physim Brownian-motion simulation tracks 2000 independently diffusing particles with input diffusion coefficient D=0.5000 square metres per second. At real time t=2 seconds, the real mean-square displacement is 1.9487, fitting back D=0.4872. At t=5 seconds, real MSD=4.9167 fits back D=0.4917.
1.9487/(2⋅2)≈0.4872
The third real row is still close, not exact
At real time t=10 seconds, real MSD=9.3242 fits back D=0.4662 — within a real 6.7580 percent of the input D, the largest gap of the three because a single real seeded run is one finite sample, not an infinite ensemble.