Generate a Koch Polyflake
Draw a Koch 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 Koch Polyflake
- 1. Choose the base polygon and detail level. Set Sides for the starting n-gon and Iterations for how many times each side sprouts a Koch segment. A hexagon at moderate iterations already produces hundreds of segments.
- 2. Decide the spike direction. Toggle Spikes inward to fold the growth into the polygon rather than out of it, changing the flake from an outward star into an inward, gear-like shape.
- 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 your document or design.
- 4. Review the rendered flake. The SVG shows every side of the chosen polygon sprouting the standard 60-degree Koch bump. Save it once the shape and spike count look right.
When to use Generate a Koch Polyflake
Generate a Koch Polyflake applies the classic Koch bump to every edge of any regular polygon, not just a triangle. It generalizes the familiar Koch snowflake to squares, pentagons, hexagons and beyond, all using the standard 60-degree Koch rule.
- Extending the Koch snowflake beyond triangles. Students who know the Koch snowflake as a triangle-based fractal see here that the same bump rule applies to any n-gon, generalizing a familiar example into a whole family.
- Building a set of comparison figures. Render a triangle, square, and hexagon polyflake at the same iteration count side by side to show how the number of sides affects the resulting fractal's overall symmetry.
- Designing a decorative flake pattern. A hexagonal Koch flake makes a natural snowflake-style motif for winter-themed artwork, with the sides sprouting hundreds of Koch segments for fine detail.
- Exploring inward spike variants for art. Toggling Spikes inward on a pentagon or hexagon produces a star-like negative-space pattern, giving generative art projects an alternate look from the same base rule.
Examples
A hexagonal Koch flake
Output
An SVG drawing of a hexagon whose sides sprout 384 Koch segments.
A pentagon with inward spikes
Output
An SVG drawing of an inverted pentaflake-style outline.
About the Generate a Koch Polyflake tool
Generate a Koch Polyflake runs as plain JavaScript in your browser tab, with no server behind it. Draw a Koch 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 8 settings, including Iterations, Sides, Spikes inward and Width (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 Koch 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.