Fractal trees are an example of how self-similarity is used in fractals because each branch is repeated by using the original shape of the trunk and each time is rotated and down-sized.
“All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk.”
-Leonardo Da Vinci
-Leonardo Da Vinci
Pattern
This was known as Leonardo Da Vinci's rule for branches. Fractal trees can have no randomness, so each branch is identical to the one before. The pattern consists of a line and two separate lines, known as the branches that continuously repeats until the shape of the tree begins to form. If randomness is added, then it could make the tree appear more realistic, although the original fractal tree uses a formula where the rotation only occurs around the origin. At the end of each segment, rotate right and left the same degree from the line and draw congruent shorter segments.
self similarity
Each branch of the fractal tree is a replica of the base of the tree. Also, fractal trees are symmetrical, unless randomness is used, like in the image below.