Generate a Heighway Triangle
Draw a Heighway triangle fractal. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate a Heighway Triangle
- 1. Set the iteration count. Choose Iterations to control how many right-triangle steps the chain contains. Around 10 iterations gives a recognizable, dense outline of the Heighway dragon shape.
- 2. Size the drawing. Set Width (px) and Height (px) so the full chain of steps fits without cropping. More iterations pack in finer right-angle detail, needing extra canvas room to stay legible.
- 3. Choose colors and line width. Pick Line color, Background color and Line width based on whether you want a clean, high-contrast diagram or a softer texture for a background image.
- 4. Review the rendered triangle chain. The tool traces the Heighway dragon as a chain of right-triangle steps rather than the usual folded-square outline. Save it once the level of detail matches your needs.
When to use Generate a Heighway Triangle
Generate a Heighway Triangle renders the same dragon fractal that underlies the classic dragon curve, but constructed from a chain of right triangles rather than folded line segments. It gives a different visual entry point into the same underlying self-similar structure.
- Showing an alternate dragon curve construction. Students who have already seen the standard folded dragon curve benefit from seeing the same fractal built a different way, reinforcing that multiple constructions can produce related shapes.
- Teaching right-triangle recursive subdivision. The Heighway triangle construction repeatedly splits a right triangle into two smaller right triangles, a recursion pattern that shows up elsewhere in computational geometry.
- Comparing fractal geometry variants in a paper. A paper on dragon-curve-family fractals wants a labeled figure of the right-triangle variant alongside the standard dragon curve at a matched iteration count.
- Producing a geometric art piece. The stepped, angular look of the right-triangle chain gives a more architectural feel than the smoother dragon curve, useful for a design that wants sharp, blocky lines.
Examples
A 10-iteration Heighway triangle
Output
An SVG drawing of the Heighway dragon traced as a chain of right-triangle steps.
About the Generate a Heighway Triangle tool
Generate a Heighway Triangle does its work locally, right in the browser. Draw a Heighway triangle fractal. There is no upload step, no queue and no account, and your data never travels over the network.
It belongs to the Math Tools collection on EditSafely, a set of 234 small, focused Math utilities that share the same instant, private workspace.
You can shape the output with 6 settings, including Iterations, Width (px), Height (px) and Line color, and the result refreshes the moment you change one. A worked example further down the page shows exactly what the tool produces for a real input.
Running locally also makes the tool fast and dependable: results appear as you type or drop a file, there is no server outage that can take it down mid-task, and confidential data can be processed without a second thought.
Frequently asked questions
Does Generate a Heighway Triangle cost anything?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
No data leaves your device. The whole tool is JavaScript that runs inside your browser tab, so there is no upload, no server-side processing and no log of what you did. If you disconnect from the internet after the page loads, it keeps working.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
Nothing to install and no account needed. Open the page in any up-to-date browser, including on a phone or tablet, and the tool is ready.
Can I save what the tool produces?
Yes. Use the download or copy controls in the output panel to keep the rendered result once it looks the way you want.