᠎᠎᠎          
51K

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!
we have a comic! comic for nerds
We have created our own comic! Check it out! New comics every week.
A link to this tool, including input, options and all chained tools.
Can't convert.
An error has occured.
Chain with...
Remove chain
Save as...
Copy to clipboard
Download
Export to Pastebin
Remove no tools?
This tool cannot be chained.
Iterations and Area
Iterate fractal this many times.
Fractal space width.
Fractal space height.
Thickness and Colors
Pen width for drawing the fractal's curve.
Pen color.
Fill fractal's background with this color.
Indents and Orientation
Indent around Morton's fractal. (Adds this many empty pixels to left, right, top, bottom sides.)
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.
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.
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.)
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.
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.)
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.
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.)
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
All fractal tools
Didn't find the tool you were looking for? Let us know what tool we are missing and we'll build it!
Draw a Dendrite Fractal
Quickly draw a custom McWorter dendrite fractal.
Draw a Canopy Fractal
Quickly draw a custom canopy tree fractal.
Draw a Flowsnake Fractal
Quickly draw a custom Gosper fractal.
Draw a Morton Fractal
Quickly draw a custom Z-order fractal.
Draw a Hilbert Fractal
Quickly draw a custom Hilbert fractal.
Draw a V-fractal
Quickly draw a custom binary v-fractal.
Draw a Peano Fractal
Quickly draw a custom Peano fractal.
Draw a Heighway Fractal
Quickly draw a custom Heighway dragon fractal.
Draw a Heighway Twins Fractal
Quickly draw a custom twin dragon Heighway fractal.
Draw a Triangle Dragon Fractal
Quickly draw a custom Heighway nonadragon fractal.
Draw a Koch Fractal
Quickly draw a custom Koch fractal.
Draw a Triflake Fractal
Quickly draw a custom triflake fractal.
Draw a Sierpinski Fractal
Quickly draw a custom Sierpinski triangle fractal.
Draw a Pentaflake Fractal
Quickly draw a custom Sierpinski pentagon fractal.
Draw a Hexaflake Fractal
Quickly draw a custom Sierpinski hexagon fractal.
Draw a Multiflake Fractal
Quickly draw a custom Sierpinski polygon fractal.
Draw a Moore Fractal
Quickly draw a custom Moore fractal.
Draw a Cantor Fractal
Quickly draw a custom Cantor comb fractal.
Draw a Dust Fractal
Quickly draw a custom Cantor dust fractal.
Draw a Levy Fractal
Quickly draw a custom Levy fractal curve.
Draw a Frosty Fractal
Quickly draw a custom ice fractal.
Draw a Pythagoras Fractal
Quickly draw a custom Pythagoras tree fractal.
Draw a T-square Fractal
Quickly draw a custom t-square fractal.
Draw a Hausdorff 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 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 Cantor String
Encode the Cantor set 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.
Sierpinski Pyramid
Generate a Sierpinski tetrahedron (tetrix) fractal.
Cantor's Cube
Generate a Cantor's cube fractal.
Menger Sponge
Generate a Sierpinski-Menger fractal.
Jerusalem Cube
Generate a Jerusalem cube fractal.
Mosely Snowflake
Generate a Jeaninne Mosely fractal.
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.
Mandelbulb Fractal
Generate a Mandelbulb fractal.
Mandelbox Fractal
Generate a Mandelbox fractal.
Buddhabrot Fractal
Generate a Buddhabrot fractal.
Burning Ship Fractal
Generate a Burning Ship fractal.
Toothpick Fractal
Generate a toothpick sequence fractal.
Ulam-Warburton Fractal
Generate an Ulam-Warburton fractal curve.
ASCII Fractal
Generate an ASCII fractal.
ANSI Fractal
Generate an ANSI fractal.
Unicode Fractal
Generate a Unicode fractal.
Emoji Fractal
Generate an emoji fractal.
Braille Fractal
Generate a braille code fractal.
Audio Fractal
Generate a fractal in audio form.
Draw a Pseudofractal
Create a fractal that looks like one but isn't a fractal.
Convert Text to a Fractal
Generate a fractal from any text.
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.
Iterate an ICAF
Run infinite compositions of analytic functions.
Generate a Fractal Landscape
Create a surface that mimics a natural terrain.
Generate a Brownian Surface
Create a fractal surface via Brownian motion.
Generate a Self-similar Image
Apply fractal algorithms on your image and make it self-similar.
Find Fractal Patterns in Images
Find fractal patterns in any given image.
Find Fractal Patterns in Text
Find fractal patterns in any given text.
Find Fractal Patterns in Numbers
Find fractal patterns in any given number.
Fill a Plane with Fractals
Tessellate a plane with fractals.
Run a Cellular Automaton
Run a cellular automaton with custom rules.
Play Game of Life
Play Conway's Game of Life on an infinite grid.
Created with love by
51K
@browserling
We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling we love to make developers' lives easier, so we created this collection of online fractal tools. Unlike many other tools, we made our tools free, without ads, and with the simplest possible user interface. Our online fractal tools are actually powered by our programming tools that we created over the last couple of years. Check them out!
Secret message
If you love our tools, then we love you, too! Use coupon code FRACTALLING to get a discount at Browserling.
Privacy Policy we don't log data!
All conversions and calculations are done in your browser using JavaScript. We don't send a single bit about your input data to our servers. There is no server-side processing at all. We use Google Analytics and StatCounter for site usage analytics. Your IP address is saved on our web server, but it's not associated with any personally identifiable information. We don't use cookies and don't store session information in cookies. We use your browser's local storage to save tools' input. It stays on your computer.
Terms of Service the legal stuff
By using Online Fractal Tools you agree to our Terms of Service. TLDR: You don't need an account to use our tools. All tools are free of charge and you can use them as much as you want. You can't do illegal or shady things with our tools. We may block your access to tools, if we find out you're doing something bad. We're not liable for your actions and we offer no warranty. We may revise our terms at any time.