Generate a Cesaro Fractal
Draw a Cesaro 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 Cesaro Fractal
- 1. Set iterations and tear angle. Choose Iterations for how many times each segment gets torn, and Angle for how sharply it folds. Angles near 90 degrees produce tall spikes; smaller angles keep the curve closer to a straight line.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the spike pattern you are producing. High iteration counts at steep angles need more vertical room since the spikes stack densely.
- 3. Style the line. Pick Line color, Background color and Line width. A thin line at high contrast shows individual spikes clearly; a thicker line reads better when the image is shrunk down for a thumbnail.
- 4. Review the rendered curve. The tool draws a single line torn into thousands of near-vertical spikes as an SVG. Zoom in to inspect individual folds, or save the full image for print.
When to use Generate a Cesaro Fractal
Generate a Cesaro Fractal renders the Cesaro curve, a variant of the Koch construction where the angle of each tear is adjustable instead of fixed at 60 degrees. It exists to show how a single parameter change turns a smooth-ish curve into a jagged, torn-looking one.
- Teaching parameterized fractals. You want students to see the same recursive rule produce very different pictures just by moving the Angle slider, connecting the abstract L-system rule to a concrete visual outcome.
- Generating textured backgrounds. A torn, spiky line at a steep angle makes an unusual background texture for a poster or album cover, distinct from the smoother Koch snowflake most people have already seen.
- Comparing to the classic Koch curve. Set the angle to 60 degrees to reproduce a standard Koch curve, then adjust it to see how far you can push the tear before the curve becomes visually chaotic.
- Producing a print-ready fractal figure. A dissertation appendix on iterated function systems needs a labeled figure of a torn curve at a specific iteration count; the SVG output stays crisp at any print resolution.
Examples
A 5-iteration Cesàro curve at 85°
Output
An SVG drawing of a line torn into 1024 near-vertical Koch spikes.
The same curve at 60°
Output
An SVG drawing of the classic Koch curve.
About the Generate a Cesaro Fractal tool
Generate a Cesaro Fractal runs as plain JavaScript in your browser tab, with no server behind it. Draw a Cesaro 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 7 settings, including Iterations, Angle, Width (px) and Height (px), and the result refreshes the moment you change one. 2 worked examples further down the page show exactly what the tool produces for real inputs.
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 Cesaro Fractal 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.