Technique · Fields
Fractal tree
A dense branching tree drawn by folding space: thousands of branches from a dozen iterations.
Fractal tree is a field drawn for every pixel by the graphics chip. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Benoit Mandelbrot coined the word fractal in 1975, from the Latin fractus, broken.
- A tree crown spreads to fill the light that its neighbours leave, so its shape is half rule and half circumstance.
- Lungs, rivers and lightning branch like trees because branching is an efficient way to reach an area from a single source.
- Leonardo da Vinci noted that the branches of a tree, added together, are as thick as its trunk.
- A fractal looks the same at every scale: here each branch is a smaller copy of the whole tree.
The mathematics
- After 12 rounds of splitting in two, a tree has up to 2^12 = 4,096 tips.
- If each round shrinks the branches by the same factor, the lengths form a geometric series, so the tree has a finite height even if it branches forever.
In art
- Klimt's Tree of Life, designed around 1909 for the Stoclet Palace in Brussels, shows a tree turned into spiralling ornament.
- Between about 1908 and 1913 Piet Mondrian painted a series of trees, reducing them step by step to a lattice of lines.
More ways to use it
Related techniques
Nebula and stars · Liquid · Droplets · Network · Terrain and maps · Neuron · Order to chaos · Radiolarian shell