Astrid Lindenmayer was a Hungarian theoretical biologist who developed formal languages called Lindenmayer Systems (L-Systems) that create fractals and model the structures of plants. He published "Mathematical models for cellular interaction in development" in 1968, modeling the structure of plant cells. His work is now used to model whole plant structures. L-Systems are sets of strings made by applying rules. They can be used to create all sorts of interesting shapes and patterns and it's uncanny how closely they mimic trees, grasses, weeds and other branching forms. Think of trees as computers building their own structure using code!
Most of the material I've found online has to do with computer science applications. Computer science blogger Christopher Jennings has a very clear explanation of the math and "productions" that are L-Systems. Here's an example from his blog:
The images below are from an article by Allan Pike on his computer science and visualization blog. They show the math or "productions" and the resulting (very plant-like) imagery:
These images (with coresponding "productions") are from algorythmicbotany.com:
The same way artists have recognisable ways of making marks (especially curves and angles), plants seem to have a handwriting that's pretty uniform across all their structures- root systems, leaves, twigs, branches, seeds and flowers all appear to drawn by the same hand; different parts of the same plants seem to be written with the same code but repurposed to fit the different biological and structural needs.