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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 math nerds from team Browserling.

᠎᠎᠎          Tool Options

Tree Class

Angle of rotation at each
level stays the same.
Left and right rectangles change
rotation angle at each level.
Left and right rectangles change
rotation angle every two levels.
Left and right rectangles change
rotation angle every time.
Random rotation angle is selected
for each level.
Random rotation angle is selected
for all rectangles.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.

Iterations, Size, and Tilt

How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.

Pythagoras Tree Colors

Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

What is a pythagoras tree generator?

This tool draws the Pythagoras tree fractal. The Pythagoras tree is created as follows – take a rectangle (or a square), then adjacent to its top side draw two more rectangles at an angle so that the sides of all three rectangles 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 the iteration. You can apply a gradient color the branches, add a contour line around each box, and set the background gradient. You can also set the distance that the tree will be drawn from the frame. Additionally, you can generate several different tree types – coniferous tree type, semi-coniferous tree type, alternating, and a random tree. Once you have generated the tree that you like, you can resize it to your desired dimensions by entering width and height in pixels. Mathabulous!


Pythagoras tree generator examples

Click to try

Symmetrical Pythagorean Tree

This example generates a symmetric Pythagoras tree using twelve generations. It uses a square as the base figure. The outlines of recursively drawn squares are not visible here because it's set to zero. The fractal uses four colors to define two gradients. The first gradient is applied to the background and uses tolopea to black colors. The second is a smooth transition in the tree growth direction from a dodger-blue to spring-green color. Notice that as the branches twist, overlap and intersect, this fractal starts to look very similar to the Levy C curve.

Required options
These options will be used automatically if you select this example.
Angle of rotation at each
level stays the same.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Regular Tree from Rectangles

In this example, we set the width of the initial rectangle to 100 pixels and height to 400 pixels. This base figure has a ratio of 4:1 and as a result, we grow a Pythagorean tree that's thin and tall. The rotation angle is 40 degrees, which makes the tree tilt to the right. We use an indigo to jaguar color gradient for the background and yellow to chartreuse color gradient from the Pythagoras tree, drawing it from the trunk to twigs.

Required options
These options will be used automatically if you select this example.
Angle of rotation at each
level stays the same.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Coniferous Pythagorean Tree

In this example, we draw a coniferous Pythagoras tree, with individual segment gradient. In this type of tree, the angle of rotation alternates at every level. On the first level, the left square rotates 60 degrees, and on the second level, the right square rotates 60 degrees, and so on. We set the rectangular shape of the image (800x1000px) and generate 15 iterations, without using a border around squares.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle at each level.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Semi-Coniferous Pythagorean Tree

This example draws a semi-coniferous type of tree. This type alternates the rotation angle every two levels. On the first and second levels, the left square rotates by 50 degrees, and on the third and fourth by 90-50 = 40 degrees. The angles change up to the 11th iteration level this way. We fill the tree with a gradient from the roots to leaves and draw a limeade color line around branches.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle every two levels.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Realistic Pythagorean Tree

In this example, we generate a tree that looks very realistic, like you see in nature. This is achieved by selecting the semi-coniferous tree type option (where alpha and beta angles swap every two levels), setting the alpha angle to 34 degrees (beta is automatically set to 56 degrees), and using a non-square base rectangle. The height of each rectangle is 3 times greater than its width. This aspect ratio makes this Pythagoras tree look very realistic and all branches bend very smoothly. We also chose to use a gradient only for the background here and draw 14 iterative levels.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle every two levels.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Alternating Pythagorean Tree

This example draws an alternating type of tree. In this case, every pair of squares exchange base corner angles. Here we set the rotation angle to 58 degrees, which then turns to 32 degrees for the next pair of squares, then to 58 again, then 32, and so on. Also, in this example, we're using an interesting combination of colors for the tree – we don't use gradients and set the same color for the background and squares, and another for the contour. As a result, we get a transparent-looking tree.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle every time.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Extraordinary Pythagorean Tree

Believe or not, this is also a Pythagorean tree. You've got to agree that it has a very unusual appearance. The reason it's so weird is that the width of each rectangle is 5 times greater than its height. It's drawn using the alternating-angles method with the initial rotation angle of 50 degrees. It uses white fill color for all rectangles, Monza to flirt color gradient for the background and dark red color for the contour.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle every time.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Randomize Rotation Angles on Every Tree Level

In this example, we introduce some randomness in our Pythagoras trees. This example generates a Pythagoras tree that uses a random angle for every tree level. Note that one angle is randomly selected for every recursion level and it doesn't change on that level. For example, on the fifth level all triangles will have the same angle but fourth and sixth levels will have different angles. Every time you click on the example, you'll get something new because of randomization. Also, you can just press the Draw a Pythagoras Tree button to get a new, random Pythagoras tree.

Required options
These options will be used automatically if you select this example.
Random rotation angle is selected
for each level.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Randomize all Rotation Angles

This example uses a different tree randomization method. Here the rotation angles are randomly selected for each pair of squares. The branches each time tilt in different directions, creating a chaotic tree shape. An interesting feature of this tree is its disappearance at the tips. As we've set only the lower color of the tree's gradient, its upper part becomes transparent, and only the white outline shows the shape of twigs and twiglets.

Required options
These options will be used automatically if you select this example.
Random rotation angle is selected
for all rectangles.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Symmetrize Pythagoras Tree

This example uses the additional symmetrize function. This function gradually increases (or decreases) the angle to 45°. In our example, the tree starts at 10° and we generate 10 iterations of the tree. To achieve symmetry this angle has to be increased to 45°. To do it, at every iteration the angle increases by 3.5°. We can quickly calculate that by generating 10 levels we get 3.5° × 10 = 35° plus the initial 10° makes it 45°.

Required options
These options will be used automatically if you select this example.
Left and right rectangles change
rotation angle at each level.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Tilted Pythagoras Tree

In this example, the angle of rotation of the left square is 30 degrees and the 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 a thickness of 2px.

Required options
These options will be used automatically if you select this example.
Angle of rotation at each
level stays the same.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

Random Rectangles

This example turns on the randomize rectangle sizes function. It does the obvious thing – the size of each rectangle gets randomized. Note that only the height can be randomized because the width is automatically computed so that every pair of rectangles formed a right triangle. In our case, the height is a random number from 1 to 200 (because we set the base rectangle's height to 200). This example is similar to the first example where we're drawing a regular Pythagorean tree with a base angle of 45 degrees but symmetry is lost here because of height randomization.

Required options
These options will be used automatically if you select this example.
Angle of rotation at each
level stays the same.
At each level, the rotation angle
increases or decreases so that
it reaches 45 degrees in the last iteration.
Size of each rectangle is chosen
arbitrarily.
How many times to recursively
draw tree branches?
Tree width.
Tree height.
Base rectangle width.
Base rectangle height.
Angle of rotation of the left
rectangle.
Tree branches outline thickness.
Space between the frame and
the Pythagoras tree.
Starting direction of movement.
Tree background from color.
Tree background to color.
Rectangles fill from color.
Rectangles fill to color.
Color of the contour of the
rectangles.

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://onlinetools.com/math/generate-pythagoras-tree?width=600&height=600&base-width=100&base-height=100&iterations=12&gradient-in-tree-direction=true&background-from-color=%2523110152&background-to-color=black&fill-from-color=%25231395ff&fill-to-color=%252303ff5b&line-segment-color=&line-width=&padding=10&angle=45&direction=up&regular-tree=true&symmetrize-tree=false&randomize-rectangle-sizes=false

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Convert a vector in one format to another format.

Transpose a Vector

Convert a row-vector to column-vector.

Duplicate a Vector

Create multiple copies of the same vector.

Increment a Vector

Increment vector components.

Decrement a Vector

Increment vector components.

Rotate a Vector

Rotate a vector by any angle.

Scale a Vector

Shrink or enlarge a vector by a constant factor.

Calculate Vector Angle

Find the angle that's formed between two vectors.

Set Vector Angle

Create pairs of vectors with a specific angle.

Normalize a Vector

Create a unit vector of length one from any given vector.

Generate a Random Vector

Create one or more random vectors of any length.

Generate a Custom Vector

Create custom vectors with specific components.

Generate a Dense Vector

Create a vector with very few zero components.

Generate a Sparse Vector

Create a vector with many zero components.

Generate a Null Vector

Create a vector all components equal to zero.

Generate a Ones Vector

Create a vector all components equal to one.

Generate a Unit Vector

Create one or more random vectors of length one.

Generate Opposite Vectors

Create pairs of antiparallel vectors.

Generate Parallel Vectors

Create pairs of parallel vectors.

Generate Perpendicular Vectors

Create pairs of perpendicular vectors.

Generate Orthogonal Vectors

Create pairs of orthogonal vectors.

Generate Orthonormal Vectors

Create pairs of perpendicular unit vectors of length one.

Find Vector Norm

Calculate L₁, L₂, L₃, L₄, L₅, and other vector norms.

Find Vector Length

Calculate the length of a vector.

Set Vector Length

Create vectors with a specific length.

Find Vector Dot Product

Calculate the scalar product of two vectors.

Set Vector Dot Product

Find two vectors with a specific scalar product value.

Find Vector Cross Product

Calculate the cross product of two vectors.

Set Vector Cross Product

Find two vectors with a specific cross product value.

Find Scalar Triple Product

Calculate the mixed product of three vectors.

Find Vector Triple Product

Calculate the vector triple product (back of the cab).

Find Scalar Quadruple Product

Calculate the scalar quadruple product of four vectors.

Find Vector Quadruple Product

Calculate the vector product of four vectors.

Mix Vectors

Mix the components of multiple vectors.

Join Vectors

Concatenate two or more vectors.

Add Vectors

Find the sum of two or more vectors.

Multiply Vectors

Multiply two or more vectors.

Multiply Vector by Constant

Multiply all vector components by a scalar value.

Find Vector Component Sum

Find the sum of all vector components.

Find Vector Component Product

Find the product of all vector components.

Find Vector Dimensions

Find the number of components in a vector.

Calculate Sine

Calculate the sine of an angle.

Visualize Sine

Draw the sine function.

Calculate Arcsine

Calculate the arcsine of an angle.

Visualize Arcsine

Draw the arcsine function.

Calculate Cosine

Calculate the cosine of an angle.

Visualize Cosine

Draw the cosine function.

Calculate Arccosine

Calculate the arccosine of an angle.

Visualize Arccosine

Draw the arccosine function.

Calculate Tangent

Calculate the tangent of an angle.

Visualize Tangent

Draw the tangent function.

Calculate Cotangent

Calculate the cotangent of an angle.

Visualize Cotangent

Draw the cotangent function.

Calculate Cosecant

Calculate the cosecant of an angle.

Visualize Cosecant

Draw the cosecant function.

Calculate Secant

Calculate the secant of an angle.

Visualize Secant

Draw the secant function.

Draw All Trigonometric Functions

Visualize all trigonometric functions at once.

Draw an Archimedean Spiral

Generate an Archimedean spiral curve.

Draw an Euler Spiral

Generate a Cornu spiral curve (polynomial spiral).

Draw a Fibonacci Spiral

Generate a Fibonacci spiral curve.

Draw a Theodorus Spiral

Generate a square root spiral.

Draw a Fermat Spiral

Generate a parabolic spiral curve.

Draw Fibonacci Rectangles

Generate a drawing of Fibonacci rectangles.

Draw a Fibonacci Seed Head

Generate a Fibonacci flower head.

Draw a Padovan Fractal

Generate a Padovan equiliteral triangles fractal.

Draw a Apollonian Gasket

Generate an Apollonian gasket fractal.

Draw a Mandelbrot Fractal

Generate a Mandelbrot fractal.

Draw a Julia Fractal

Generate a Julia fractal.

Draw a Rauzy Fractal

Generate a Rauzy fractal.

Draw Blancmange Fractal Curve

Generate a Blancmange fractal.

Draw Weierstrass Function

Generate a Weierstrass fractal.

Draw Minkowski Question-mark Curve

Generate a Minkowski Question-mark fractal.

Draw Thomae's Function

Generate a Thomae's function (also known as popcorn or raindrop function).

Draw Dirichlet's Function

Generate a Dirichlet's function.

Draw a Gabriel's Horn

Draw a geometric figure with infinite surface area and finite volume.

Convert Words to Numbers

Convert numbers as English text to actual digits.

Convert Numbers to Words

Convert numbers to written English text.

Convert Decimal Notation to Scientific Notation

Convert numbers written in decimal form to scientific form.

Convert Scientific Notation to Decimal Notation

Convert numbers written in scientific form to decimal form.

Round Numbers Up

Apply ceil operation to numbers.

Round Numbers Down

Apply floor operation to numbers.

Analyze Numbers

Count how many times each number appears.

Rewrite a Number as a Sum

Create a sum that adds up to the given number.

Rewrite a Number as a Product

Create a product that multiplies up to the given number.

Generate a Multiplication Table

Draw an n×m multiplication table.

Generate an Addition Table

Draw an n×m addition table.

Generate a Division Table

Draw an n×m division table.

Generate a Modular Arithmetic Table

Draw an n×m modular arithmetic table for any modulus.

Draw a Pie Chart

Draw a pie chart and show relative sizes of data.

Draw a Bar Chart

Draw a bar chart and visualize data.

Draw a Column Chart

Draw a column chart and visualize data.

Draw a Line Chart

Draw a line chart and visualize data.

Draw an Area Chart

Draw an area chart and visualize data.

Visualize Percentage

Draw a chart that shows percentage.

Tile a Plane

Fill a plane by convex regular polygons.

Flip a Coin

Toss a coin and get head or tails.

Roll a Dice

Throw a dice and get a number on its side.

Generate a Maze

Draw a maze of any size and complexity.


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