Pythagoras Fractal

Generate, interact with, and export the classic Pythagoras tree fractal online. Based on squares and right triangles satisfying the Pythagorean theorem. Customize bend angles, foliage color schemes, and export crisp PNG or vector SVG.

Private • In-browser processing • Zero server uploads

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How to Use Pythagoras Fractal

1
Select Recursion Depth
Adjust the depth slider between 1 and 10 to configure the tree density.
2
Tune Tilt Angle
Adjust the branch tilt angle between 20° and 70° to bend branches left or right.
3
Choose Color Scheme
Select Foliage (wood trunk and green canopy), Rainbow, or Neon Blue.
4
Export Image
Click Download or Copy to obtain your graphic as PNG or vector SVG.

Key Features

Pythagorean Theorem Geometry
Construct recursive squares and right triangles with exact mathematical compliance.
Adjustable Bend Angle
Explore classic 45° symmetric canopies or wind-swept asymmetric angles (20° to 70°).
Foliage and Rainbow Themes
Beautiful procedural color modes ranging from natural wood-and-canopy to spectral rainbow gradients.
Dual SVG & PNG Export
Download vector SVG files ready for printing or raster PNG files with touch pan/zoom interaction.

Common Use Cases

  • Geometry education, demonstrating the Pythagorean theorem ($a^2 + b^2 = c^2$) and self-similarity in fractal planes.
  • Architectural and graphic patterning, generating organic geometric canopies.
  • Procedural art and wallpapers for mathematics enthusiasts.
  • Laser cutting, CNC milling, and vector plotter art.

Frequently Asked Questions

A Pythagoras tree is a plane fractal constructed from squares invented by Dutch mathematics teacher Albert E. Bosman in 1942. The three squares touching each junction enclose a right triangle, illustrating the Pythagorean theorem.

At depth $d$, the tree consists of $2^d - 1$ total squares. Depth 1 has 1 square, Depth 6 has 63 squares, and Depth 10 has 1,023 squares.

Because square count doubles with each level ($2^d$), depths above 10 create thousands of overlapping polygons that can impact canvas rendering performance.

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