Abstract The flagellar beat of bull spermatozoa and C.Reinhardtii are modelled by Baby Food a minimal, geometrically exact, reaction-diffusion system.Spatio-temporal animated patterns describe flagellar waves, analogous to chemical-patterns from classical reaction-diffusion systems, with sliding-controlled molecular motor reaction-kinetics.The reaction-diffusion system is derived from first principles as a consequence of the high-internal dissipation by the flagellum relative to the external hydrodynamic dissipation.Quantitative comparison with nonlinear, large-amplitude simulations shows that animated reaction-diffusion patterns account for the experimental beating of both bull sperm and C.
Reinhardtii.Our results suggest that a unified mechanism may exist Dipping Bowls for motors controlled by sliding, without requiring curvature-sensing, and uninfluenced by hydrodynamics.High-internal dissipation instigates autonomous travelling waves independently of the external fluid, enabling progressive swimming, otherwise not possible, in low viscosity environments, potentially critical for external fertilizers and aquatic microorganisms.The reaction-diffusion system may prove a powerful tool for studying pattern formation of movement on animated structures.