The histogram approaches a Gaussian as N and t grow -- the Central Limit Theorem in action.

Einstein (1905): <r²> = 4Dt. The RMS distance grows as the square root of time.

In 1827, Robert Brown observed pollen grains jittering in water. Einstein explained it in 1905: invisible molecules bombard the particle from all sides. Each step is random, yet at scale, beautiful order emerges -- Gaussian distributions, predictable diffusion rates, and the square-root law. Randomness, paradoxically, is one of the most orderly things in nature.