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Peano fractal

World's simplest fractal tool

This utility lets you draw custom and colorful Peano fractals. You can customize Peano fractal's color, width, height, as well as its form – regular form, which creates the original space-filling fractal and diamond form, which creates a neat-looking diamond shape fractal. You can also set the recursive iteration count for drawing the fractal. Fun fact – Peano fractal is the first fractal ever discovered in 1890. Fractabulous!
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Peano Fractal's Form
If you select this, then the fractal will fill the entire image.
If you select this, then the fractal will have a neat diamond-like shape.
Make fractal curve's corners rounded.
Recursion, Size and Colors
Recursive depth of the fractal.
Fractal width.
Fractal height.
Fractal background color.
Fractal curve's color.
Curve, Padding and Orientation
Fractal curve's thickness.
Padding around the fractal.
Peano fractal's orientation.
Peano fractal tool What is a peano fractal?
This online browser-based tool lets you create your own personal Peano fractal. It's also useful for illustrating and learning how the Peano fractal works. The Peano fractal is very similar to Hilbert fractal. Both fractals are space-filling and evolve exponentially with every recursive step. If recursion is set high enough, the fractal will occupy the whole space and its curve length will approach infinity. An infinite curve in a finite space! Mind boggling and cool at the same time, or as we love to say – fractabulous!
Peano fractal examples Click to use
Peano Diamond
In this image, we've drawn a diamond-shaped Peano fractal with smooth corners. Here the fractal's space is a 400- by 400-pixel square, the curve width is 4 pixels and padding is 5 pixels. The background is golden fizz yellow and the fractal itself is Persian blue.
In this image, we've drawn a diamond-shaped Peano fractal with smooth corners. Here the fractal's space is a 400- by 400-pixel square, the curve width is 4 pixels and padding is 5 pixels. The background is golden fizz yellow and the fractal itself is Persian blue.
Required options
These options will be used automatically if you select this example.
If you select this, then the fractal will have a neat diamond-like shape.
Make fractal curve's corners rounded.
Recursive depth of the fractal.
Fractal width.
Fractal height.
Fractal background color.
Fractal curve's color.
Fractal curve's thickness.
Padding around the fractal.
Peano fractal's orientation.
A Vertical Peano Fractal
This illustration is an example of a vertical Peano fractal. We've created this fractal by drawing it on a 350x500 canvas and setting iterations count to 3. We've also chosen to make Peano line's corners smooth and set the drawing direction to "up".
This illustration is an example of a vertical Peano fractal. We've created this fractal by drawing it on a 350x500 canvas and setting iterations count to 3. We've also chosen to make Peano line's corners smooth and set the drawing direction to "up".
Required options
These options will be used automatically if you select this example.
If you select this, then the fractal will fill the entire image.
Make fractal curve's corners rounded.
Recursive depth of the fractal.
Fractal width.
Fractal height.
Fractal background color.
Fractal curve's color.
Fractal curve's thickness.
Padding around the fractal.
Peano fractal's orientation.
Space-filling Peano Curve
This image is an example of a space-filling Peano fractal. It uses a cornflower blue color for the background and white for the fractal line. As you can see, with only 4 iterations it has almost filled the entire space. If you increase iterations to 5, then you'll get a white image as the curve is white color and it will occupy the entire image.
This image is an example of a space-filling Peano fractal. It uses a cornflower blue color for the background and white for the fractal line. As you can see, with only 4 iterations it has almost filled the entire space. If you increase iterations to 5, then you'll get a white image as the curve is white color and it will occupy the entire image.
Required options
These options will be used automatically if you select this example.
If you select this, then the fractal will fill the entire image.
Make fractal curve's corners rounded.
Recursive depth of the fractal.
Fractal width.
Fractal height.
Fractal background color.
Fractal curve's color.
Fractal curve's thickness.
Padding around the fractal.
Peano fractal's orientation.
Pro tips Master online fractal 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://onlinefractaltools.com/draw-peano-fractal?&width=400&height=400&iterations=3&background-color=%23fff836&line-segment-color=%23221ab0&line-width=4&padding=5&direction=right&rhombus-form=true&rounded-corners=true
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Walk the Hilbert fractal and enumerate its coordinates.
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Encode the Cantor set as a string.
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Generate a Barnsley's fern fractal.
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Generate a ternary tree fractal.
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Generate a dragon tree fractal.
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Generate a de Rham curve.
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Generate a toothpick sequence fractal.
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Generate an Ulam-Warburton fractal curve.