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pythagoras-fractal

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​

  1. Pick parameters — Angle (default 45° for classic; 30° / 60° produce asymmetric trees). Depth (5-12). Colors. Stroke width.
  2. Render — Recursive draw: square → two children at angle → recurse.
  3. 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.

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.

Try it now​

The full pythagoras-fractal runs in your browser at https://ztools.zaions.com/pythagoras-fractal — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-06 · Author: Ahsan Mahmood · Edit this page on GitHub