Generate a Quadratic Koch Island
Draw a quadratic Koch flake. 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 Quadratic Koch Island
- 1. Set the iteration count. Choose Iterations for how many times each side of the square grows a right-angled bump. A 3-iteration island already produces roughly 500 segments along its coastline.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the square coastline. Higher iteration counts pack in finer right-angle detail, so leave enough room to keep individual segments visible.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to make the square, right-angled segments distinct from the smoother triangular Koch bumps of the original snowflake.
- 4. Review the rendered island. The tool draws a square coastline built entirely from right-angled segments, known as the Minkowski sausage, as an SVG. Save it once the detail level looks right.
When to use Generate a Quadratic Koch Island
Generate a Quadratic Koch Island draws the Minkowski sausage, a variant of the Koch snowflake that uses 90-degree right-angle bumps on a square instead of the standard 60-degree triangular bumps on a triangle. It shows how changing the subdivision angle produces a distinctly different coastline texture.
- Comparing angular fractal families. Placing the quadratic Koch island next to the standard Koch snowflake highlights how a right-angle subdivision rule produces a blockier, more geometric coastline than the triangular bumps.
- Teaching the Minkowski sausage by name. The quadratic Koch island is commonly referred to by its historical name, the Minkowski sausage, and rendering it helps connect that name to the actual right-angled fractal shape.
- Designing a blocky, architectural fractal motif. The square, right-angled segments of this fractal give it a more architectural, pixel-art feel than the rounder Koch snowflake, suited to a design that wants sharp, orthogonal lines.
- Illustrating coastline complexity with a square base. Fractal dimension discussions sometimes use the Minkowski sausage as a second example alongside the Koch curve, since its dimension differs due to the different subdivision angle.
Examples
A 3-iteration quadratic Koch island
Output
An SVG drawing of a square coastline built from 500 right-angled segments.
About the Generate a Quadratic Koch Island tool
Generate a Quadratic Koch Island does its work locally, right in the browser. Draw a quadratic Koch flake. 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 Quadratic Koch Island 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.