Generate a Smith-Volterra-Cantor Set
Draw an ε-Cantor set 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 Smith-Volterra-Cantor Set
- 1. Set the number of levels. Use the Levels slider to choose how many removal steps run. At step n, the middle interval removed has length 1/4^n, shrinking much faster than the classic Cantor set's middle thirds.
- 2. Size the canvas. Set Width (px) and Height (px) so the shrinking gaps stay visible even at higher levels, where the removed intervals become extremely small compared to what remains.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to keep each level's bars distinguishable, particularly useful when explaining how little is actually removed overall.
- 4. Review the rendered set. The SVG shows the fat Cantor set, one row of bars per level, with progressively shrinking gaps. Save it once the level count matches what you are illustrating.
When to use Generate a Smith-Volterra-Cantor Set
Generate a Smith-Volterra-Cantor Set draws the fat Cantor set, a construction that removes intervals shrinking as 1/4^n at each step rather than a fixed third, resulting in a set with positive measure despite having no interior. It is a key counterexample in real analysis.
- Teaching sets with positive measure but empty interior. The fat Cantor set is the standard counterexample showing that a nowhere-dense set can still have positive Lebesgue measure, unlike the classic Cantor set which has measure zero.
- Comparing removal rates across Cantor-like sets. Rendering this alongside the classic Cantor set at the same level count shows visually why removing intervals that shrink as 1/4^n leaves so much more of the line intact.
- Supporting a real analysis course assignment. An assignment asking students to compute the total measure removed at each step benefits from a rendered figure showing exactly how the gaps shrink level by level.
- Illustrating subtleties in topology versus measure theory. This set is a go-to example for showing that topological smallness, being nowhere dense, and measure-theoretic smallness, having measure zero, are genuinely different concepts.
Examples
A 6-level Smith-Volterra-Cantor set
Output
An SVG drawing of the fat Cantor set that removes a middle interval of length 1/4^n at step n.
About the Generate a Smith-Volterra-Cantor Set tool
Generate a Smith-Volterra-Cantor Set is a free online tool that works entirely inside your web browser. Draw an ε-Cantor set fractal. Because the processing happens on your own device, nothing you enter is uploaded, logged or stored anywhere.
This page is one of 234 Math utilities on EditSafely. Each one does a single job well, and all of them follow the same rule: your input stays on your machine.
You can shape the output with 6 settings, including Levels, 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.
Because nothing leaves your device, the tool is suitable for sensitive content such as internal documents, credentials or customer data. It also responds instantly, since every keystroke is handled on your own machine rather than by a remote API.
Frequently asked questions
Is Generate a Smith-Volterra-Cantor Set 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.