Turing’s diffusion/reaction algorithm involved this. As you intuited, it is a good system for making fractal-like designs and patterns. Cheetah spots, zebra stripes, maybe even 3D structures like capillaries...

But, such a system can’t make discrete forms—like a nose.

There’s something else going on.

For instance... deer grow antlers every season (antlers are not horns; rather, they are complex structures with tissue, bone, skin, nerves, etc) Anyway, if a growing antler is nicked, scar tissue will form... no big deal, right? But, this is where it gets weird... When the antlers fall off and then grow the following year, the scar will be present on the new antlers. Let that sink in.