Pythagoras Tree Fractal — SVG Generator, Free
Generate the Pythagoras tree fractal — recursive squares forming a tree. Customize angle, depth. Browser-only.
About Pythagoras Tree Generator
The Pythagoras tree is a fractal constructed from squares: place a square, attach two smaller squares on top at right angles forming a triangle (the Pythagorean theorem visualised), repeat on each child. The result resembles a stylized tree. Different angles produce dramatically different shapes — 45° gives the symmetric classic; other angles produce asymmetric "windswept" forms. The ZTools Pythagoras Tree generator builds the fractal in SVG up to depth 12 with configurable angle, color, and size.
Use cases
- Decorative SVG. Background or hero element with mathematical / organic feel.
- Teach the Pythagorean theorem. Visual demonstration of a² + b² = c² in fractal form.
- Generative art. Tweak angles for unexpected shapes.
- CS teaching — recursion. Each level is a recursive call. Watch the tree grow as depth increases.
How it works
- Pick parameters. Angle (default 45° for classic; 30° / 60° produce asymmetric trees). Depth (5-12). Colors. Stroke width.
- Render. Recursive draw: square → two children at angle → recurse.
- Export SVG. Vector for scaling / printing.
Examples
Input: angle 45°, depth 10
Output: Classic symmetric Pythagoras tree.
Input: angle 30°, depth 10
Output: Asymmetric "leaning" tree.
Input: angle 60°, depth 8
Output: Wide, bushy variant.
Frequently asked questions
Why does depth 12 freeze?
Depth N produces 2^N squares. Depth 12 = 4,095 squares; depth 15 = 32,767. Beyond ~12, SVG path count slows.
Privacy?
All in browser.
Pro tips
- 45° is the classic — most recognisable.
- For posters, depth 11+ at high resolution gives stunning detail.
- Combine with color gradient (depth-based) for added visual interest.
Reviewed by Ahsan Mahmood · Last updated 2026-05-06 · Part of ZTools.
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