Generate a Levy C Curve
Draw a self-similar Levy C 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 Levy C Curve
- 1. Choose the iteration count. Set Iterations for how many times each segment folds at a right angle. Around 10 iterations produces a dense, self-overlapping C-shaped curve typical of published examples.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the curve's characteristic C shape, which can fold back on itself and overlap significantly at higher iteration counts.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to keep overlapping folds readable, especially important since the Levy curve crosses itself frequently at higher iterations.
- 4. Review the rendered curve. The tool draws the Levy C curve as a self-similar folded line in SVG form. Save it once the fold density and overlap pattern look the way you expect.
When to use Generate a Levy C Curve
Generate a Levy C Curve draws the Levy C curve, a fractal built by repeatedly replacing each segment with two shorter segments folded at 90 degrees. It is notable for self-overlapping folds that produce a dense, C-shaped silhouette unlike the non-overlapping Koch or dragon curves.
- Teaching self-intersecting fractal curves. Unlike the Koch curve or Hilbert curve, the Levy C curve overlaps itself as it grows, making it a useful counterexample when discussing which fractals avoid self-intersection.
- Comparing dragon-family fractal folding rules. The Levy C curve's right-angle fold rule is closely related to the dragon curve's folding pattern, and rendering both side by side highlights the similarities and differences.
- Producing a dense textured background. At 10 or more iterations, the Levy C curve's overlapping folds create a naturally dense, web-like texture suited to abstract background art.
- Illustrating fractal dimension in coursework. The Levy C curve has a well-documented fractal dimension used in coursework on measuring curve complexity, and a rendered figure at a known iteration count supports that discussion.
Examples
A 10-iteration Levy C curve
Output
An SVG drawing of the Levy C curve fractal.
About the Generate a Levy C Curve tool
Generate a Levy C Curve does its work locally, right in the browser. Draw a self-similar Levy C 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
Is Generate a Levy C Curve free to use?
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?
Everything happens locally. Your browser downloads the tool's code once, then does all the processing itself; nothing you enter is transmitted, stored or logged. You can even go offline after the page loads and it will still work.
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?
No. The tool works in any modern browser on desktop, tablet or phone. There is no account to create, no extension to add and no software to install.
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.