Pythagoras Tree Generator

Pythagoras Tree Generator - Create Pythagorean Fractal Art

Generate stunning Pythagoras tree fractals with our free online generator. The Pythagoras tree is a plane fractal constructed from squares, named after the ancient Greek mathematician Pythagoras. Starting with a single square, two smaller squares are attached to its top side at angles that form a right triangle, creating a branching tree pattern that grows exponentially more complex with each iteration. The result is a beautiful, self-similar fractal that resembles a leafy tree.

What is a Pythagoras Tree?

The Pythagoras tree, first drawn by Dutch mathematics teacher Albert E. Bosman in 1942, is constructed by recursively attaching squares to the sides of right triangles. Beginning with a base square, a right triangle is drawn on top, and two smaller squares are attached to its legs. The process repeats on each new square, creating a fractal tree. At iteration 0, it's a single square. By iteration 7 or 8, the tree becomes a dense, intricate fractal pattern with remarkable beauty.

Frequently Asked Questions

How many iterations can I generate?

You can generate up to 12 iterations of the Pythagoras tree. Each iteration doubles the number of squares, so higher iterations produce increasingly detailed and complex tree structures. Higher iterations may take longer to render.

Can I change the branching angle?

Yes, you can adjust the branching angle of the right triangle used in the construction. Different angles produce dramatically different tree shapes — from narrow, tall trees to wide, bushy ones. The classic Pythagoras tree uses a 45-degree angle.

Can I customize the colors?

Yes, you can customize the fill colors, stroke colors, and use gradient effects to create beautiful, colorful tree designs. Many users create vibrant fractal art by applying color gradients based on iteration depth.

What can I use Pythagoras tree images for?

Pythagoras tree images are popular as decorative art, educational materials for teaching fractal geometry and recursion, website backgrounds, and print-on-demand products like posters and canvas prints.

Can I download the tree as a vector graphic?

Yes, you can download the Pythagoras tree as a PNG image or SVG vector file. SVG output preserves all details at any scale and is perfect for printing or further editing in vector graphics software.

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Pythagoras Tree Generator