Generate a T-square Fractal
Draw a T-square 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 T-square Fractal
- 1. Set the iteration count. Choose Iterations for how many generations of smaller squares sprout from the corners of the previous ones. A 5-iteration T-square already shows the classic nested outline pattern.
- 2. Size the canvas. Set Width (px) and Height (px) to fit the nested square outlines, which grow inward and outward from the original square at each successive iteration.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to keep individual nested square outlines distinguishable at the iteration count you have chosen.
- 4. Review the rendered fractal. The tool draws the T-square fractal as nested square outlines in SVG form. Save it once the iteration count and level of nesting look right.
When to use Generate a T-square Fractal
Generate a T-square Fractal draws a pattern of half-sized squares sprouting recursively from the corners of a base square, named for the T-shaped negative space that appears in its construction. It is a straightforward example of corner-based recursive subdivision distinct from the center-removal approach of the Sierpinski carpet.
- Teaching corner-based recursive constructions. Unlike the Sierpinski carpet, which removes centers, the T-square fractal builds by adding smaller squares at corners, giving students a second recursive strategy to compare against removal-based fractals.
- Comparing to the Sierpinski square fractal. Both the T-square and Sierpinski square fractals grow from corners, and rendering them side by side highlights how a rotation parameter changes the resulting nested pattern.
- Designing a geometric tile or pattern. The T-square's nested outline structure works well as a repeating architectural or tile motif, generated at a chosen iteration count for the desired level of intricacy.
- Illustrating fractal dimension for a coursework example. The T-square fractal has a documented fractal dimension used in coursework on measuring self-similar complexity, supported by a rendered figure at a known iteration count.
Examples
A 5-iteration T-square fractal
Output
An SVG drawing of the T-square fractal as nested outlines.
About the Generate a T-square Fractal tool
Generate a T-square Fractal does its work locally, right in the browser. Draw a T-square fractal. 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 T-square Fractal 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.