The branches of trees show fractal patters, each splitting into two new branches of which each split into 2 new branches and so on.
This principle was first discovered by Leonardo DaVinci in the 15th century and it became known as “Leonardos rule for branching”:
“All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk below them.”
The rules for branching are incredible simple and with just a few parameters you are able to generate realistic and complex trees – try it yourself in your browser
Treebark also shows fractal characteristics. The fractal dimension of tree bark can be used to determine the age of a tree. 1
Further Reading & Sources
Adventures into the mathematical forest of fractal trees – Wolfram Alpha article
Uncovering DaVinci’s tree rule – Inside Science, American Institute of Physics