Hosts are green, parasites are red, empty squares are black.
The famous ''Life'' game of Conway is an example. The picture above shows an example of such spirals. The two papers referenced above contain many futher literature references on other systems in which these spirals were observed, and also give pictures of spirals in their systems. It seems that the reason why these spirals are formed up to now is regarded as somewhat of a mystery. I believe that I can explain why these spirals are formed.