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Twin dragon curve

World's simplest fractal tool

This utility lets you draw colorful and stylish Heighway twin fractals. The options below will help you customize your fractal – you can set fractal's iteration stage, dimensions, orientation, and colors for each twin dragon individually. Make sure to select opposite colors for the twins to get a fabulous looking fractal. Fun fact – you can join infinitely many Heighway dragons together back-to-back, back-to-belly, or belly-to-belly and tile the entire space. Fractabulous!
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Recursion and Dimensions
Final iteration stage. (Stop recursion at this level.)
Canvas width
Canvas height
Width of line segment used to draw the fractal.
Twin Heighway Palettes
Fractal's background color.
First dragon's color.
Second dragon's color.
Padding and Orientation
Number of pixels between the fractal and canvas.
Heighway twin dragon orientation.
Twin dragon curve tool What is a twin dragon curve?
This online browser-based tool allows you to draw your own unique twin dragon fractal. The twin dragon fractal is often casually called the Heighway twins. The scientists, Chandler Davis and Donald Knuth, who discovered this fractal attributed it to Heighway because of its resemblance and connection to the regular Heighway fractal. As it turns out, the Heighway twins are Siamese dragons conjoined belly to belly. When iterated for many stages, the dragon heads start from a single one point, diverge into bodies and converge again, ending with both tails touching at another point. The larger the iteration depth, the tighter together the dragon lines are drawn until finally lines are so close together that they fill the twins' bodies completely. Heighway twins is one of many fractals that can be tiled – if you take a copy of this fractal, you can conjoin it with the previous copy. You can repeat this process multiple times until the whole area is filled with dragons. Mind boggling and awesome at the same time, or as we love to say – fractabulous!
Twin dragon curve examples Click to use
Filled Heighway Twins
In this example, we increase the iteration stage to 16 and set the curve drawing width to 2 pixels. These conditions are sufficient for the curves to be drawn so close together that they completely fill the bounds of both Siamese dragons. As a result, we get two filled Heighway twin dragons, one filled with cyan color and the other filled with lime color.
In this example, we increase the iteration stage to 16 and set the curve drawing width to 2 pixels. These conditions are sufficient for the curves to be drawn so close together that they completely fill the bounds of both Siamese dragons. As a result, we get two filled Heighway twin dragons, one filled with cyan color and the other filled with lime color.
Required options
These options will be used automatically if you select this example.
Final iteration stage. (Stop recursion at this level.)
Canvas width
Canvas height
Width of line segment used to draw the fractal.
Fractal's background color.
First dragon's color.
Second dragon's color.
Number of pixels between the fractal and canvas.
Heighway twin dragon orientation.
Detailed Twin Dragons
This example gives a detailed view of twin Heighway fractal. By setting the recursion level to 11 iterations, we can see how this fractal is made of individual line segments that form a mesh of interconnected rectangles. We've chosen complementary colors for the drawing to make it maximally attractive. It uses a governor-bay color for the first dragon, thunderbird color for the second dragon, and anakiwa color for the background. It sets the line segment width to 7 pixels and canvas space to 800x1000 pixels.
This example gives a detailed view of twin Heighway fractal. By setting the recursion level to 11 iterations, we can see how this fractal is made of individual line segments that form a mesh of interconnected rectangles. We've chosen complementary colors for the drawing to make it maximally attractive. It uses a governor-bay color for the first dragon, thunderbird color for the second dragon, and anakiwa color for the background. It sets the line segment width to 7 pixels and canvas space to 800x1000 pixels.
Required options
These options will be used automatically if you select this example.
Final iteration stage. (Stop recursion at this level.)
Canvas width
Canvas height
Width of line segment used to draw the fractal.
Fractal's background color.
First dragon's color.
Second dragon's color.
Number of pixels between the fractal and canvas.
Heighway twin dragon orientation.
Twin Dragon Island
In this example, we create a twin dragon island fractal. This fractal is constructed by using just one color (cloud-burst blue) to fill the contours of the twins and a high iteration count (18 iterations). The dragon curve is just one pixel thick but by the time it's iterated 18 times, it's twisted and looped so many times that this tiny line completely fills the dragon bounds. This fractal island is also often called the Heighway island fractal.
In this example, we create a twin dragon island fractal. This fractal is constructed by using just one color (cloud-burst blue) to fill the contours of the twins and a high iteration count (18 iterations). The dragon curve is just one pixel thick but by the time it's iterated 18 times, it's twisted and looped so many times that this tiny line completely fills the dragon bounds. This fractal island is also often called the Heighway island fractal.
Required options
These options will be used automatically if you select this example.
Final iteration stage. (Stop recursion at this level.)
Canvas width
Canvas height
Width of line segment used to draw the fractal.
Fractal's background color.
First dragon's color.
Second dragon's color.
Number of pixels between the fractal and canvas.
Heighway twin dragon 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-twin-heighway-fractal?&width=700&height=600&iterations=16&background-color=%2307026b&dragon-1-color=%2305d1ff&dragon-2-color=%23c4ff00&line-width=2&padding=10&direction=right
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