Generate a Cesaro Polyflake
Draw a Cesaro n-gon 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 Polyflake
- 1. Choose the base polygon and tear settings. Set Sides for the starting n-gon, Iterations for how many times each edge tears, and Angle for the tear's sharpness. More sides gives a rounder base shape before the spikes take over.
- 2. Decide which way the spikes point. Toggle Spikes inward to fold the tears into the polygon instead of outward, turning the flake into a star-like void pattern rather than a spiky outer boundary.
- 3. Size and style the drawing. Set Width (px), Height (px), Line color, Background color and Line width to fit the flake's silhouette and match wherever the image will be placed.
- 4. Review the rendered polyflake. The SVG shows every side of the n-gon torn into the same near-vertical spike pattern as the Cesaro curve. Save it once the shape and spike density look right.
When to use Generate a Cesaro Polyflake
Generate a Cesaro Polyflake applies the adjustable-angle Cesaro tear to every edge of a regular polygon instead of a single straight line. It is for anyone who wants a Koch-family flake with a sharper, more torn silhouette than the standard snowflake.
- Designing a distinctive flake logo. A hexagonal Cesaro flake at 85 degrees has a spikier, more aggressive outline than a standard Koch flake, which suits a logo that wants to feel sharp rather than soft.
- Exploring inward versus outward spikes. Toggling Spikes inward on the same hexagon produces an almost gear-like negative-space pattern instead of an outward star, useful for comparing both variants side by side in a paper.
- Building fractal geometry teaching material. Show a triangle, square and hexagon all torn with the same angle to demonstrate how the number of sides changes the flake's overall symmetry and spike count.
- Generating decorative SVG assets. A generative art piece needs an odd, spiky polygon outline as a base layer; export the SVG and layer other elements over the tear pattern in a design tool.
Examples
A hexagonal Cesàro flake at 85°
Output
An SVG drawing of a hexagon torn into 384 near-vertical spikes.
The classic Cesàro square
Output
Sides 4 with spikes inward: the traditional Cesàro square fractal.
About the Generate a Cesaro Polyflake tool
Generate a Cesaro Polyflake runs as plain JavaScript in your browser tab, with no server behind it. Draw a Cesaro n-gon 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 9 settings, including Iterations, Sides, Angle and Spikes inward, 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 Polyflake 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.