Generate a Sierpinski Curve
Draw a Sierpinski closed plane 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 Sierpinski Curve
- 1. Set the iteration count. Choose Iterations for how finely the closed loop fills its region. A 3-iteration Sierpinski curve already covers its plane region densely while forming a single closed path.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the closed loop's fill pattern, keeping the canvas square to match the curve's symmetric coverage.
- 3. Pick colors and line width. Choose Line color, Background color and Line width depending on whether you want the individual loop windings visible or a smoother overall filled appearance.
- 4. Review the rendered curve. The tool draws the closed Sierpinski space-filling curve as an SVG, a single loop that covers a plane region without lifting the pen. Save it once the fill density looks right.
When to use Generate a Sierpinski Curve
Generate a Sierpinski Curve draws a closed, self-similar space-filling curve related to the Sierpinski triangle family, distinct from both the filled carpet and the open arrowhead curve. It is for exploring closed-loop space-filling constructions beyond the more commonly taught Hilbert and Moore curves.
- Expanding beyond Hilbert-family space-filling curves. Most space-filling curve coursework focuses on Hilbert and Peano curves built on square grids. This curve shows the same closed-loop filling idea applied to a triangular subdivision instead.
- Comparing closed and open Sierpinski constructions. Render this closed curve next to the open Sierpinski arrowhead curve to show students the difference between a space-filling loop and a boundary-tracing path within the same fractal family.
- Producing an unusual generative art texture. The dense, triangular fill pattern of this curve gives a different visual texture from square-grid space-filling curves, useful as a distinctive background layer in generative art.
- Illustrating advanced fractal curve topics in a paper. A paper surveying the range of space-filling curve constructions can include this less common triangular variant alongside the standard Hilbert and Peano examples.
Examples
A 3-iteration Sierpinski curve
Output
An SVG drawing of the closed Sierpinski space-filling curve.
About the Generate a Sierpinski Curve tool
Generate a Sierpinski Curve runs as plain JavaScript in your browser tab, with no server behind it. Draw a Sierpinski closed plane fractal. Whatever you put in stays on your device from start to finish.
The tool is part of EditSafely's Math Tools section, 234 single-purpose utilities built around the same idea: open the page, get the result, keep your data to yourself.
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.
That local-first design has practical benefits beyond privacy. The tool keeps working on a flaky connection once the page has loaded, results are instant because nothing round-trips to a server, and it is safe to use with confidential material.
Frequently asked questions
Does Generate a Sierpinski Curve 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.