Generate a Quadratic Cross Fractal
Draw a quadric cross 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 Quadratic Cross Fractal
- 1. Set the iteration count. Choose Iterations for how many times the plus-sign shape grows finer detail. A 3-iteration cross already produces around 1,500 segments in the fractal boundary.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the cross shape, which grows outward symmetrically in four directions from a central plus sign.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to keep the fine right-angle detail near the arms of the cross legible at your chosen canvas size.
- 4. Review the rendered cross. The tool grows a plus sign into a dense, right-angled fractal boundary as an SVG. Save it once the iteration count and detail level match what you need.
When to use Generate a Quadratic Cross Fractal
Generate a Quadratic Cross Fractal grows a plus-sign shape into a fractal boundary using repeated right-angle subdivisions, related to the quadratic Koch family of curves. It is for exploring how a simple symmetric starting shape develops fine, self-similar detail along its edges.
- Teaching quadratic Koch curve variants. The quadratic cross uses the same 90-degree subdivision family as the quadratic Koch island, and comparing them shows how starting shape affects the resulting fractal boundary.
- Designing a symmetric decorative motif. The plus-sign symmetry of this fractal makes it a natural choice for a symmetric badge, icon or tile pattern that wants mathematically precise fine detail along its edges.
- Illustrating boundary complexity growth. Rendering the cross at increasing iteration counts shows students how quickly the segment count grows, from a simple plus sign to over a thousand segments after just three steps.
- Building a comparison set of quadratic fractals. Place the quadratic cross alongside the quadratic Koch island in a paper or presentation to show two different starting shapes under the same right-angle subdivision rule.
Examples
A 3-iteration quadric cross
Output
An SVG drawing of a plus sign grown into a 1500-segment fractal cross.
About the Generate a Quadratic Cross Fractal tool
Generate a Quadratic Cross Fractal runs as plain JavaScript in your browser tab, with no server behind it. Draw a quadric cross 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 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.
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 Quadratic Cross 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.