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Pythagoras tree generator

World's simplest math tool

Free online Pythagoras tree fractal generator. Just press a button and you'll get a Pythagoras fractal. There are no ads, popups or nonsense, just an awesome Pythagorean tree generator. Press a button – get a tree. Created by mathematicians for mathematicians.
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Iterations, Size, and Tilt
How many times to recursively draw tree branches?
Tree width.
Tree height.
Angle of rotation of the left square.
Pythagoras Tree Colors
Pythagoras tree background color.
Fill color for squares.
Color of the contour of the squares.
Tree Outline and Frame
Tree branches outline thickness.
Space between the frame and the Pythagoras tree.
Pythagoras tree generator tool What is a pythagoras tree generator?
This tool draws the Pythagoras tree fractal. The Pythagoras tree is created as follows - take a square, then adjacent to its top side draw two more squares at an angle so that the sides of all three squares form a right-angled triangle. If this triangle is isosceles, then the tree will grow symmetrically in both directions. If the triangle's base angles are different, then the Pythagorean tree will be tilted to the side of the smallest angle. In this tool you can set the tilt angle and see how the Pythagorean tree evolves with each step of iteration. You can colorize the branches, add a contour line around each branch, and set the background color. You can also set the distance that the tree will be drawn from the frame. Once you have generated the tree that you like you can resize it in your desired dimensions by entering width and height in pixels. Mathabulous!
Pythagoras tree generator examples Click to use
Symmetrical Pythagorean Tree
This example generates a symmetric Pythagoras tree using twelve generations. The outline of squares is not visible here because it's set to zero. The fractal uses only two colors – black for the background and blue for the tree. Notice that as the branches twist, overlap and intersect, this fractal starts to look very similar to Levy C curve.
Required options
These options will be used automatically if you select this example.
How many times to recursively draw tree branches?
Tree width.
Tree height.
Angle of rotation of the left square.
Pythagoras tree background color.
Fill color for squares.
Color of the contour of the squares.
Tree branches outline thickness.
Space between the frame and the Pythagoras tree.
Tilted Pythagoras Tree
In this example the angle of rotation of the left square is 30 degrees and right is 60 degrees. As a result left and right squares have different sizes and the whole tree is tilted to the left side. We also stretched the image horizontally by setting its size to 700x600px and set a black outline for squares with thickness of 2px.
Required options
These options will be used automatically if you select this example.
How many times to recursively draw tree branches?
Tree width.
Tree height.
Angle of rotation of the left square.
Pythagoras tree background color.
Fill color for squares.
Color of the contour of the squares.
Tree branches outline thickness.
Space between the frame and the Pythagoras tree.
Pro tips Master online math tools
You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!
https://onlinemathtools.com/generate-pythagoras-tree?&width=600&height=600&iterations=12&background-color=black&line-segment-color=&fill-color=%231395ff&line-width=&padding=10&angle=45
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