Generate a Koch Star
Draw a Koch island fractal curve. 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 Star
- 1. Choose the iteration count. Set Iterations for how many times each side of the starting triangle sprouts a new bump. A 4-iteration Koch star already produces the classic 768-segment snowflake outline.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the star's outline. Since the shape grows outward from a triangle, keep the canvas roughly square for the cleanest result.
- 3. Pick colors and line width. Choose Line color, Background color and Line width depending on whether the image is for a printed handout, a slide or a decorative background.
- 4. Review the rendered snowflake. The tool draws the classic Koch island outline as an SVG, built from three sides each sprouting the same recursive bump. Save it once the detail level looks right.
When to use Generate a Koch Star
Generate a Koch Star draws the original Koch snowflake, one of the earliest and most widely taught fractal curves, built by repeatedly replacing the middle third of every line segment with two sides of a small triangle. It is the standard first fractal most students encounter.
- Introducing fractals in a first geometry lesson. The Koch snowflake is often the very first fractal students see, since the construction rule is easy to state and the resulting shape is immediately recognizable.
- Demonstrating infinite perimeter with finite area. A classic result is that the Koch snowflake has infinite perimeter but bounds a finite area. Rendering several iterations helps students see the perimeter growing while the area visibly stabilizes.
- Making a snowflake-themed design asset. The recognizable snowflake silhouette works well as a genuinely mathematical decoration for a winter holiday card, presentation slide or website background.
- Comparing against Koch snowflake variants. Render the standard Koch star alongside the anti-snowflake or quadratic Koch island to show a family of related constructions that all start from the same basic idea.
Examples
A 4-iteration Koch snowflake
Output
An SVG drawing of the classic Koch island with 768 segments.
About the Generate a Koch Star tool
Generate a Koch Star does its work locally, right in the browser. Draw a Koch island fractal curve. 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 Koch Star 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.