# 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!

announcement
check out our new project!

We just created something new for all science fans – SCIURLS – a neat science news aggragator. Check it out!

A link to this tool, including input, options and all chained tools.

Can't convert.

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

All fractal tools

Quickly draw a custom McWorter dendrite fractal.

Quickly draw a custom canopy tree fractal.

Quickly draw a custom Gosper fractal.

Quickly draw a custom Z-order fractal.

Quickly draw a custom Hilbert fractal.

Quickly draw a custom binary v-fractal.

Quickly draw a custom Peano fractal.

Quickly draw a custom Heighway dragon fractal.

Quickly draw a custom twin dragon Heighway fractal.

Quickly draw a custom Heighway nonadragon fractal.

Quickly draw a custom Koch fractal.

Quickly draw a custom Sierpinski triangle fractal.

Quickly draw a custom Sierpinski pentagon fractal.

Quickly draw a custom Sierpinski hexagon fractal.

Quickly draw a custom Sierpinski polygon fractal.

Quickly draw a custom Moore fractal.

Quickly draw a custom Cantor comb fractal.

Quickly draw a custom Cantor dust fractal.

Quickly draw a custom Levy fractal curve.

Quickly draw a custom ice fractal.

Quickly draw a custom t-square fractal.

Quickly draw a custom Hausdorff tree fractal.

Coming soon
These fractal tools are on the way

Generate a Hilbert Sequence

Walk the Hilbert fractal and enumerate its coordinates.

Generate a Peano Sequence

Walk the Peano fractal and enumerate its coordinates.

Generate a Moore Sequence

Walk the Moore fractal and enumerate its coordinates.

Generate a Cantor String

Encode the Cantor set as a string.

Mandelbrot Tree

Generate a Mandelbrot tree fractal.

Barnsey's Tree

Generate a Barnsley's tree fractal.

Barnsey's Fern

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.

De Rham Fractal

Generate a de Rham curve.

Takagi Fractal

Generate a Takagi-Landsberg fractal curve.

Peano Pentagon

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.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!