Fractal Tree Generator
Draw recursive binary trees from branch angle, length ratio and depth, then measure the canopy dimension by box counting and compare it against the self-similarity prediction.
Last reviewed by the Radiatus Cloud team
Need this done properly for your business?
Radiatus delivers secure cloud, DevOps & compliance engineering.
Two numbers decide what the tree looks like
A fractal tree is built by one rule applied to itself: draw a branch, then draw two shorter branches from its tip at plus and minus some angle, and repeat. Only the angle and the length ratio matter to the shape. A ratio near 0.5 with a wide angle gives an open fan, a ratio near 0.7 with a narrow angle gives a dense plume, and the same code produces both without any change to the drawing logic.
The height converges even though the depth does not
Each level is shorter than the last by a fixed factor, so the total length along any single path from root to tip is a geometric series that sums to the initial length divided by one minus the ratio. That is why increasing the depth past about fifteen adds visible detail but no visible height: the remaining branches are collectively shorter than a pixel. The total ink, by contrast, grows without bound whenever twice the ratio exceeds one, because the branch count doubles faster than the length shrinks.
The canopy has a measurable dimension
The set of branch tips is a self-similar fractal made of two copies of itself scaled by the ratio, which predicts a dimension of log 2 divided by log of one over the ratio. This tool measures the dimension directly by box counting and reports both numbers, so you can see the prediction hold when the two halves stay separate and fail when the ratio passes one half and the copies begin to overlap.
Related tools
- Data Collection Analysis — Analyze app description to infer data collection.
- Dark Pattern Detector — Scan UX text for manipulative patterns.
- AI Risk Disclosure — Generate disclosure text for AI features.
- Maturity Radar — Generate a radar chart of security maturity.
Frequently Asked Questions
What controls the shape of a fractal tree?
The branch angle and the length ratio, and essentially nothing else. Depth adds detail rather than changing the form, because each level is smaller than the last by a fixed factor.
Why does the tree stop getting taller?
Because the lengths form a geometric series. The longest path from root to tip sums to the initial length divided by one minus the ratio, so the height converges to a finite limit no matter how deep you go.
What is the canopy dimension?
The branch tips form a self-similar set made of two copies of itself at the length ratio, giving a predicted dimension of log 2 over log of one over the ratio. This tool also measures it by box counting so you can compare.
Why does the prediction fail above a ratio of 0.5?
The self-similarity formula assumes the two half-copies do not overlap. Past a ratio of one half they intersect, so the measured dimension falls below the formula and eventually saturates as the canopy fills area.
Does total branch length converge too?
No. Total length is the initial length times the sum of two-times-ratio to each power, which diverges whenever twice the ratio exceeds one, even though the height stays finite.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Set the branch angle and length ratio, then generate.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.