# Z-fractal

## World's simplest fractal tool

This utility lets you draw custom and colorful Morton z-fractals. You can explore the fractal's behavior by recursively iterating it as many times as you want and changing its size in the options. You can also customize the thickness and color of the drawing pen, as well as adjust the color of the background. Fun fact – with each iteration, the number of z letters in the fractal quadruples. Created by fractal fans from team Browserling. Fractabulous!

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Z-fractal tool
What is a z-fractal?

This online browser-based tool allows you to create a custom Morton fractal. The Morton fractal, named after Guy Macdonald Morton (G.M.Morton), was first investigated in 1966. The Morton fractal is also called the z-fractal because it consists of a sequence of connected letters z, which fills the entire space. It's often used in data algorithms as it maps multidimensional data to one dimension while preserving locality of the data points. Ingenious and mind blowing at the same time, or as we love to say – fractabulous!

Z-fractal examples
Click to use

Four Iterations of Morton Fractal

In this example, we create a 4th-order z-order curve on a square canvas of 800x800 pixels. To do this, we use a 4-pixel pen and draw a white line on a catalino-blue background.

**Required options**

Iterate fractal this many times.

Fractal space width.

Fractal space height.

Pen width for drawing the
fractal's curve.

Pen color.

Fill fractal's background
with this color.

Indent around Morton's fractal.
(Adds this many empty pixels
to left, right, top, bottom sides.)

Norton's Fractal

In this example, we set the orientation for Morton fractal to vertical. As a result, all letters z are flipped on the side. This fractal is also called Norton fractal curve (a pun on Morton's name) because all z's are now n's.

**Required options**

Iterate fractal this many times.

Fractal space width.

Fractal space height.

Pen width for drawing the
fractal's curve.

Pen color.

Fill fractal's background
with this color.

Indent around Morton's fractal.
(Adds this many empty pixels
to left, right, top, bottom sides.)

Rectangular Morton Fractal

This example uses a rectangular space with a size of 800 by 1200 pixels to draw a z-order fractal. It calls the drawing algorithm recursively five times, which means there are 256 letters "z". (In general there are 4^(n-1) "z" letters for recursive depth "n".)

**Required options**

Iterate fractal this many times.

Fractal space width.

Fractal space height.

Pen width for drawing the
fractal's curve.

Pen color.

Fill fractal's background
with this color.

Indent around Morton's fractal.
(Adds this many empty pixels
to left, right, top, bottom sides.)

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-morton-fractal?&iterations=4&width=800&height=800&line-width=4&line-segment-color=white&background-color=%23082585&padding=15&direction=horizontal

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Coming soon
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Walk the Hilbert fractal and enumerate its coordinates.

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Walk the Moore fractal and enumerate its coordinates.

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Encode the Hilbert fractal as a string.

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Encode the Peano fractal as a string.

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Encode the Cantor set as a string.

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Encode the Heighway Dragon as a string.

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Encode the Sierpinski fractal as a string.

Sierpinski Pyramid

Generate a Sierpinski tetrahedron (tetrix) fractal.

Cantor's Cube

Generate a Cantor's cube fractal.

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Generate a Sierpinski-Menger fractal.

Jerusalem Cube

Generate a Jerusalem cube fractal.

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Generate a Jeaninne Mosely fractal.

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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.

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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.

Mandelbulb Fractal

Generate a Mandelbulb fractal.

Mandelbox Fractal

Generate a Mandelbox fractal.

Toothpick Fractal

Generate a toothpick sequence fractal.

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Generate an Ulam-Warburton fractal curve.

ASCII Fractal

Generate an ASCII fractal.

ANSI Fractal

Generate an ANSI fractal.

Unicode Fractal

Generate a Unicode fractal.

Braille Fractal

Generate a braille code fractal.

Draw a Pseudofractal

Create a fractal that looks like one but isn't a fractal.

Convert a String to a Fractal

Generate a fractal from a string.

Convert a Number to a Fractal

Generate a fractal from a number.

Merge Two Fractals

Join any two fractals together.

Draw a Random Fractal

Create a completely random fractal.

Iterate an IFS

Set up an arbitrary IFS system and iterate it.

Run IFS on an Image

Recursively transform an image using IFS rules.

Generate a Self-similar Image

Apply fractal algorithms on your image and make it self-similar.

Find Fractal Patterns in Text

Find fractal patterns in any given text.

Find Fractal Patterns in Numbers

Find fractal patterns in any given number.

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