# Hilbert fractal

## World's simplest fractal tool

This utility lets you draw custom and colorful Hilbert fractals. You can customize Hilbert fractal's width and height, fractal curve's color and width, as well as the background color. You can also set its orientation and change the number of recursive iterations. As the Hilbert fractal is space-filling, then given enough iterations, this fractal will eventually fill entire space. Fractabulous!

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Hilbert fractal tool
What is a hilbert fractal?

This online browser-based tool illustrates Hilbert fractals. It's useful if you want to create your own personal Hilbert fractal. The Hilbert fractal is actually a variant of the space-filling Peano fractal and it grows exponentially with each iteration size. The space-filling property means that given enough iterations, it will always fill the entire given space without ever crossing itself. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Hilbert fractal examples
Click to use

Fourth-order Hilbert Fractal

In this example, we set the iterations count to 4 and that created a 4th-order Hilbert fractal. We love colors so we also chose cardinal pink as the background color and Paris daisy yellow as curve color.

**Required options**

Fractal width.

Fractal height.

Recursive depth of the fractal.

Fractal curve color.

Fractal curve width.

Background color.

Padding around the fractal.
(In pixels.)

A Vertical Hilbert Curve

In this example, we're drawing a Hilbert curve in a 500x800 space. As the height is larger than width, it creates a vertical Hilbert fractal curve.

**Required options**

Fractal width.

Fractal height.

Recursive depth of the fractal.

Fractal curve color.

Fractal curve width.

Background color.

Padding around the fractal.
(In pixels.)

A Hilbert Maze

In this example, we've set the recursion depth to 6. We've chosen a green color for the curve and it makes this example look like a maze. We call it a Hilbert Maze. (Fun stuff: If you change the depth to 7, then the fractal will fill entire space. Try it!)

**Required options**

Fractal width.

Fractal height.

Recursive depth of the fractal.

Fractal curve color.

Fractal curve width.

Background color.

Padding around the fractal.
(In pixels.)

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-hilbert-fractal?&width=500&height=500&iterations=4&background-color=%238a0863&line-segment-color=%23fff373&line-width=4&padding=15&direction=down

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Coming soon
These fractal tools are on the way

Generate a Hilbert Sequence

Walk the Hilbert fractal and enumerate its coordinates.

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Walk the Peano fractal and enumerate its coordinates.

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Walk the Moore fractal and enumerate its coordinates.

Generate a Cantor String

Encode the Cantor set as a string.

Generate a Hilbert String

Encode the Hilbert fractal as a string.

Generate a Peano String

Encode the Peano fractal as a string.

Generate a Moore String

Encode the Moore fractal as a string.

Generate a Dragon String

Encode the Heighway Dragon as a string.

Generate a Sierpinski String

Encode the Sierpinski fractal as a string.

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Generate a Barnsley's tree fractal.

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Generate a Barnsley's fern fractal.

Binary Fractal Tree

Generate a binary tree fractal.

Ternary Fractal Tree

Generate a ternary tree fractal.

Dragon Fractal Tree

Generate a dragon tree fractal.

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Generate a de Rham curve.

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Generate a Takagi-Landsberg fractal curve.

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Generate a Peano pentagon fractal curve.

Tridendrite Fractal

Generate a tridendrite fractal curve.

McWorter's Pentigree

Generate a Pentigree fractal curve.

McWorter's Lucky Seven

Generate a lucky seven fractal curve.

Eisenstein Fractions

Generate an Eisenstein fractions fractal curve.

Bagula Double V

Generate a Bagula double five fractal curve.

Julia Set

Generate a Julia fractal set.

Mandelbrot Set

Generate a Mandelbrot fractal set.

Toothpick Fractal

Generate a toothpick sequence fractal.

Ulam-Warburton Fractal

Generate an Ulam-Warburton fractal curve.

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