Many years ago, I had a student investigate plant growth computationally using fractals. But he was also interested trying to develop and model environmental conditions to see if he could then model what effect(s) different environmental conditions would have on different plants and their structures. It is a challenging problem!
But it got me thinking since a lot has happened in such an area of study, and it is more important as climate change continues to change conditions around the world. I went to ChatGPT to get some ideas on this, and at the end are some initial ideas for high school project ideas:
Prompt: Is it possible to accurately model different types of plants using fractals?
ChatGPT:
Yes—up to a point. Fractals are remarkably good at modeling many aspects of plant growth because plants often exhibit self-similarity, where a structure repeats at different scales. However, no fractal model can perfectly capture all the biological complexity of a real plant.
Why fractals work well for plants
Many plants grow through repeated branching processes:
Tree trunks branch into limbs, then branches, then twigs.
Fern leaves contain smaller leaflets that resemble the entire leaf.
Root systems often exhibit branching patterns similar to the above-ground structure.
Vein networks in leaves can display fractal-like organization.
Because of this repeated geometry, fractal mathematics can reproduce many plant forms surprisingly well.
Examples of fractal plant models
1. L-Systems (Lindenmayer Systems)
Developed by Aristid Lindenmayer in the 1960s, L-systems use simple growth rules that are repeatedly applied.
For example:
A stem grows.
The stem splits into two branches.
Each branch repeats the same rule.
After many iterations, realistic trees, shrubs, and ferns emerge.
Many computer-generated forests in movies and video games use L-systems.
2. Iterated Function Systems (IFS)
These use geometric transformations:
Scale
Rotate
Translate
Repeated thousands of times, they can create realistic-looking:
Ferns
Pine trees
Bushes
The famous Barnsley Fern is generated from only a few mathematical equations.
3. Fractal Dimension Analysis
Scientists use fractal dimensions to quantify plant structure.
For example:
A simple line has dimension 1.
A flat surface has dimension 2.
A highly branched tree may have a fractal dimension between 1 and 2.
Different species often have characteristic fractal dimensions that correlate with:
Light capture efficiency
Water transport
Growth strategies
For a high school research project
This is actually a rich area for student research. One could:
Photograph different tree species.
Use image analysis software.
Calculate the fractal dimension of each branching pattern.
Compare species.
Investigate whether fractal dimension correlates with:
Growth rate
Shade tolerance
Leaf area
Habitat
This would combine mathematics, biology, computer science, and physics into a genuine research study.