Larger spirals in the Rock-Paper-Scissors reaction-diffusion equation
Like the video this simulation shows a solution of a reaction-diffusion equation behaving in a similar way as the Belousov-Zhabotinsky chemical reactions, but which is easier to simulate. The diffusion coefficient D has been chosen larger than in the previous simulation (10 instead of 0.5), creating broader spirals.
At each point in space and time, there are three concentrations u, v, and w of chemicals, which are represented by the red, blue and green components of an RGB color scheme. Denoting by rho = u v w the total concentration, the system of equations is given by
d_t u = D*Delta(u) u*(1 - rho - a*v)
d_t v = D*Delta(v) v*(1 - rho - a*w)
d_t w = D*Delta(w) w*(1 - rho - a*u)
where Delta denotes the Laplace operator, which performs a local average, and the parameter a is equal here to . The terms proportional to a*v, a*w and a*u denote reaction terms, in which Red is beaten by Blue, Blue is beaten be Green, and Green is beaten by Red. The situation is thus simil
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