We call Brownian particles with the ability to generate a field active Brownian particles if the
produced field self-consistently determines the motion of the particles or defines their rates
of chemical reactions. We worked out examples where this stochastic approach shows
behaviour like well known reaction-diffusion models: periodic pattern, spirals, travelling
spots.

We call Brownian particles with the ability to generate a eld Active Brownian Particles if the
produced eld self-consistently determines the motion of the particles or de nes their rates of
chemical reactions. We worked out examples where this stochastic approach shows
behaviour like well known reaction-di usion models: periodic pattern, spirals, travelling
spots. In his work on Brownian motion Einstein 1] emphasized the Janus face of di usion. On
the one hand di usion is the macroscopic transport coecient, connecting the gradient of …