  Spatiotemporal patterns are often modeled using reaction-diffusion equations,
which combine complex reactions between constituents with ideal diffusive
motion. Such descriptions neglect physical interactions between constituents,
which might affect resulting patterns. To overcome this, we study how physical
interactions affect cyclic dominant reactions, like the seminal
rock-paper-scissors game, which exhibits spiral waves for ideal diffusion.
Generalizing diffusion to incorporate physical interactions, we find that weak
interactions change the length- and time-scales of spiral waves, consistent
with a mapping to the complex Ginzburg-Landau equation. In contrast, strong
repulsive interactions typically generate oscillating lattices, and strong
attraction leads to an interplay of phase separation and chemical oscillations,
like droplets co-locating with cores of spiral waves. Our work suggests that
physical interactions are relevant for forming spatiotemporal patterns in
nature, and it might shed light on how biodiversity is maintained in ecological
settings.
