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 options

Iterations and Area

Iterations Iterate fractal this many times.

Width Fractal space width.

Height Fractal space height.

Thickness and Colors

Line Width Pen width for drawing the fractal's curve.

Line color Pen color.

Background color Fill fractal's background with this color.

Indents and Orientation

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

Select Orientation Morton fractal's orientation.

What is a z-fractal?

learn more about this tool

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

These options will be used automatically if you select this example.

Iterations Iterate fractal this many times.

Width Fractal space width.

Height Fractal space height.

Line Width Pen width for drawing the fractal's curve.

Line color Pen color.

Background color Fill fractal's background with this color.

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

Select Orientation Morton fractal's orientation.

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.

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

Required options

These options will be used automatically if you select this example.

Iterations Iterate fractal this many times.

Width Fractal space width.

Height Fractal space height.

Line Width Pen width for drawing the fractal's curve.

Line color Pen color.

Background color Fill fractal's background with this color.

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

Select Orientation Morton fractal's orientation.

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".)

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

Required options

These options will be used automatically if you select this example.

Iterations Iterate fractal this many times.

Width Fractal space width.

Height Fractal space height.

Line Width Pen width for drawing the fractal's curve.

Line color Pen color.

Background color Fill fractal's background with this color.

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

Select Orientation Morton 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-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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