Generate an Asymmetric Cantor Set
Draw an asymmetric Cantor set. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate an Asymmetric Cantor Set
- 1. Set the number of levels. Use the Levels slider to choose how many times each interval splits unevenly. Higher levels reveal how the left half and right quarter drift apart in size over time.
- 2. Size the canvas. Set Width (px) and Height (px) so the unevenly sized segments stay visible at every level, since the asymmetric split produces a less regular pattern than the classic Cantor set.
- 3. Pick colors and line width. Choose Line color, Background color and Line width to keep each level's bars distinguishable, especially useful for spotting the asymmetry between kept segments.
- 4. Review the rendered set. The SVG shows the Cantor set keeping the left half and right quarter of each interval at every level, drawn as one row of bars per level. Save it once the pattern looks right.
When to use Generate an Asymmetric Cantor Set
Generate an Asymmetric Cantor Set builds a Cantor-like construction that keeps unequal fractions on each side of every interval, unlike the classic Cantor set which splits symmetrically into equal thirds. It shows what happens when the removal rule loses its left-right symmetry.
- Teaching that Cantor sets do not require symmetry. Most introductions to the Cantor set use the symmetric middle-thirds rule. This shows students that keeping unequal fractions on each side still produces a valid, self-similar fractal.
- Comparing symmetric and asymmetric constructions. Rendering this next to the standard Cantor set at the same level count highlights how losing left-right symmetry changes the visual regularity of the resulting dust pattern.
- Exploring self-similarity with unequal scaling ratios. Since the left and right kept fractions differ, this fractal has two different self-similarity ratios instead of one, a useful stepping stone toward more general multifractal constructions.
- Producing a supporting figure for a fractal geometry paper. A paper discussing self-similar sets with unequal scaling factors can reference this asymmetric construction as a concrete, simple example before moving to more complex cases.
Examples
A 6-level asymmetric Cantor set
Output
An SVG drawing of the Cantor set that keeps the left half and right quarter of each interval.
About the Generate an Asymmetric Cantor Set tool
Generate an Asymmetric Cantor Set is a free online tool that works entirely inside your web browser. Draw an asymmetric Cantor set. 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
Does Generate an Asymmetric Cantor Set 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.