Indeed, reaction-diffusion equations give rise to fractals through their bifurcations. The most famous of those fractals are the ones given by bacterial colony growth: see also this beautiful gallery (ok, the colours are artificial, but they do look very nice also in black and white).
This is how they are made, basically: take a Petri-dish, put in its center a point-like colony of bacteria, and let it evolve. The colony will split, and the "daughters" will create some bifurcating paths through the petri dish, giving rise to a snowflake-like pattern.
Before today I would think these snowflakes are, however, quite artificial (where do you find a point-like colony of bacteria put in a "sterile" medium like a Petri dish, in nature??) .. however here is an example!!!
It is a chinese food ( the "century egg") made of an egg, which is put in a clay coat for a long period. Bacteria penetrate through some pores of the egg crust, and form exactly the snowflake patterns seen in a lab.. very amazing!
here are other photos of century eggs
here Happy easter to you!! ^.^