In 1952, Alan Turing published a paper, "The Chemical Basis of Morphogenesis," which mathematically demonstrated the main phenomena of morphogenesis. In the paper he introduced a concept of morphogens, which is a system of chemical substances reacting together and diffusing through a tissue, and demonstrated the morphogenesis phenomena with series of equations that morphogens obay for its interaction. Due to an instability of the homogeneous equilibrium, a reaction-diffusion system can produce a pattern or structure. This section will get into the emergent phenomenon in patterns.
Gray Scott model describes the variation of u and v, which represent the concentration of chemical U and V respectively. U and V react according the following equation:
This model can be seen as a simulation of the behavior of diffusive living things reproducing under conditions of limited food. Different patterns emerge for slight changes in feeding and death rates.
This pattern can be seen in Hawaiian Whitespotted Toby.
Figure 1: Hawaiian Whitespotted Toby (retrieved from MAUI OCEAN CENTER)
This pattern can be seen in Puffer Fish.
Figure 2: Puffer Fish (retrieved from FSN)
This pattern can be seen in Spotted Eagle Ray.
Figure 3: Spotted Eagle Ray (retrieved from Animal Spot)
This pattern can be seen in Brain Coral.
Figure 4: Brain Coral (retrieved from OCEANA)
This pattern can be seen in Burrfish.
Figure 5: Burrfish (retrieved from South Carolina Aquarium)
The following pattern represents the distribution of f and k parameters over x-y axes. We can exploit this map to re-create mona lisa with the Gray Scott model.
