Bacterial motility: ballistic runs interrupted by random reorientations (tumbles)
Run-and-tumble: Bacterium (E. coli) swims in straight line (run) then randomly reorients (tumble). Tumble rate λ → persistence time 1/λ → effective diffusion D_eff = v²/(2λ·d) in d dimensions.
Motility-induced phase separation (MIPS): At high density, particles slow in crowds → spontaneous clustering without attractive forces.
Chemotaxis (χ > 0): Bias toward chemical gradient (simulated toward center). Biased run length → drift velocity v_drift = χ·v/(2λ).
Tail shows recent trajectory. Heat map shows density distribution.