Essential properties of fractals in mathematics are self-similarity and often existing scale invariance. In the Romanesco Broccoli, self-similarity and scale invariance are evident in the fact that the conical bulges appear again and again in smaller forms.
With mathematical fractals these properties can be exactly fulfilled.
In chaotic structures I look for patterns that are characteristic for the underlying calculation rule.
If they seem interesting enough to me, the next step is the selection of a suitable colouring.
The calculation rules can be redesigned again and again, they often lead to unexpectedly bizarre fractal shapes with self-similar patterns.