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Dragon fractal

World's simplest fractal tool

This utility lets you draw custom and colorful Heighway fractals. You can adjust the size of the fractal, the number of its iterations, and pick the colors for the background and curve line. You can also specify the fractals's thickness, padding, and set the direction of the dragon's head. Cool fact – the dragon fractal can be created from nothing but a strip of paper! Can you figure out how to do it? (Hint: observe how the fractal changes when you increase iterations from one and up.) Fractabulous!
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Recursion and Area
Iterative depth of the fractal.
Fractal width.
Fractal height.
Line and Fill Colors
Heighway dragon line color.
Heighway dragon line width.
Heighway dragon fill color.
Indents and Direction
Drawing indent (in pixels).
Dragon's head direction.
Dragon fractal tool What is a dragon fractal?
This online browser-based tool allows you to draw a personalized dragon fractal. It's also sometimes called Harter-Heighway dragon or simply Heighway dragon. This name comes from physicists John Heighway and William Harter. The dragon fractal is an example of a self-similar curve. The fractal consists of one continuous line and it never intersects. This fractal is one of the few fractals that can be folded from a strip of paper iteratively. To do this, first bend the paper strip at a 90-degree angle, then bend it in half and rotate it 45 degrees, then repeat this same procedure again. The size of each dragon formed this way in every next iteration is √2 smaller than the previous one. Mind boggling and cool at the same time, or as we love to say – fractabulous!
Dragon fractal examples Click to use
Detailed Dragon Fractal
This example draws a detailed Heighway dragon fractal of depth twelve. It uses the ultramarine color for the line, sets it 4 pixels thick and uses an area of 600 by 900 pixels to paint it.
This example draws a detailed Heighway dragon fractal of depth twelve. It uses the ultramarine color for the line, sets it 4 pixels thick and uses an area of 600 by 900 pixels to paint it.
Required options
These options will be used automatically if you select this example.
Iterative depth of the fractal.
Fractal width.
Fractal height.
Heighway dragon line color.
Heighway dragon line width.
Heighway dragon fill color.
Drawing indent (in pixels).
Dragon's head direction.
Line-filled Heighway Dragon
In this example, we generate the Heighway fractal at the 15th iteration step. We're using 3 pixels for line thickness and because the lines are drawn very close together, they fill the shape of the fractal. We use a golden-fizz color for the line and resolution-blue color for the background.
In this example, we generate the Heighway fractal at the 15th iteration step. We're using 3 pixels for line thickness and because the lines are drawn very close together, they fill the shape of the fractal. We use a golden-fizz color for the line and resolution-blue color for the background.
Required options
These options will be used automatically if you select this example.
Iterative depth of the fractal.
Fractal width.
Fractal height.
Heighway dragon line color.
Heighway dragon line width.
Heighway dragon fill color.
Drawing indent (in pixels).
Dragon's head direction.
Bright Heighway Fractal
This example creates a bright-pink dragon fractal on a yellow background. It runs the fractal algorithm for 17 steps and paints it on an 800- by 1200-pixel canvas with indentation of 15 pixels around the canvas edges.
This example creates a bright-pink dragon fractal on a yellow background. It runs the fractal algorithm for 17 steps and paints it on an 800- by 1200-pixel canvas with indentation of 15 pixels around the canvas edges.
Required options
These options will be used automatically if you select this example.
Iterative depth of the fractal.
Fractal width.
Fractal height.
Heighway dragon line color.
Heighway dragon line width.
Heighway dragon fill color.
Drawing indent (in pixels).
Dragon's head direction.
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-heighway-fractal?&width=600&height=900&iterations=13&background-color=%23befeff&line-segment-color=%230a0e91&line-width=4&padding=10&direction=down
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