In fractal theory, self-similarity and scalability go hand in hand. When you look closely at this shape, you can clearly see that the smaller shapes… or branches… are just scaled replicas of the “whole” object and that THIS same pattern is repeated over and over again at all scales.
This is nice for the plant because it only has to remember how to make ONE shape… and a few simple rules and voila, a broccoli head.
What are these simple rules you ask?
When you look at the spiraling branches near the top of this plant, you can see that they are very SIMILAR to the ones near the bottom, only they are SCALED smaller so scaling must be one of the rules.
Also, you will notice that they are orientated differently so rotation must be a “rule”. Then you will notice that they appear in different locations within the plant so translation must also be one of the “rules”.
These are the main “rules” or transformations that are used to make most if not all fractals, Scaling, Rotation and Translation. No calculus required.