Is this the standard textbook Cantor set?

No. This is our own asymmetric variant of the classic construction. The standard Cantor set removes an even middle third, keeping two equal one-third pieces; this tool instead keeps an uneven 30% on one side and 50% on the other, removing a 20% gap that sits off-center rather than in the exact middle.

Why keep 30% and 50% instead of an even split?

It's a deliberate variation to show what happens when the classic construction's symmetry is broken. Because the two surviving pieces are different sizes (30% and 50% of the parent), the rows stop looking mirror-symmetric and instead develop a visibly lopsided, denser-on-one-side pattern as depth increases.

Does more total length survive than the classic Cantor set at the same depth?

Yes. This variant keeps 80% of each segment's length per iteration (30% + 50%) versus the classic set's roughly 66.7% (two-thirds), so at any given depth noticeably more total length remains visible here than in the standard middle-thirds construction.

What does the Depth setting control?

Depth (0 to 8) sets how many times the 30%/50% split repeats, drawn as one stacked row per iteration from the untouched starting segment down to the chosen depth.

Asymmetric Cantor Set Generator

Overview

Introduction

The classic Cantor set removes an even middle third from every segment, leaving a perfectly symmetric pattern at every scale. This tool asks what happens if that symmetry is broken.

Instead of two equal one-third pieces, this asymmetric variant keeps the first 30% of each segment and the last 50%, discarding a 20% gap that sits off-center rather than dead in the middle.

What Is Generate an Asymmetric Cantor Set?

A generator for our own asymmetric variant of the classic middle-thirds Cantor set, drawn as one stacked row per iteration just like the standard construction, but with an uneven 30%/50% keep ratio instead of an even split.

This is not a textbook-standard named construction, it's a deliberate variation built to illustrate how breaking the classic set's left-right symmetry changes the resulting pattern.

How Generate an Asymmetric Cantor Set Works

Row 0 starts as a single unbroken segment. At every subsequent row, each surviving segment is split into two children: one covering the first 30% of its parent's length, the other covering the last 50%, with the 20% gap in between removed.

Because the two children are different sizes, the resulting pattern loses the left-right mirror symmetry of the classic Cantor set: the 50%-side sub-segments shrink more slowly across iterations than the 30%-side ones, so the pattern visibly skews denser toward one side as depth increases.

As with the classic construction, every segment still splits into exactly two children each iteration, so segment count still doubles per row (2^depth in the final row), only the sizes of those children differ from the even case.

When To Use Generate an Asymmetric Cantor Set

Use it to demonstrate, side by side with the classic Cantor Set Generator, how the specific 1/3-1/3-1/3 split isn't essential to producing a self-similar, sparse fractal-like set, any uneven keep ratio below 100% produces analogous behavior.

It's also a useful visual for exploring how symmetry (or its absence) in a recursive removal rule shows up in the resulting pattern.

Often used alongside Generate a Cantor Set, Generate a Generalized Cantor Set and Generate a Smith-Volterra-Cantor Set.

Features

Advantages

Visibly demonstrates that Cantor-set-style constructions don't require an even middle-third split to produce a self-similar, sparse pattern.
Retains noticeably more total length at a given depth than the classic set, since 80% is kept per iteration versus roughly 66.7%.
Exports as clean vector SVG or a flattened PNG, matching the other Cantor set tools in this category.

Limitations

This is our own variant, not a standard named construction from a textbook or reference, so it won't appear under this exact name in academic sources.
Depth is capped at 8 for renderability, matching the classic Cantor Set Generator's limit.

Examples

Depth 0

Input

Depth = 0

Output

A single unbroken horizontal segment spanning the full width.

At depth 0, no removal has happened yet.

Depth 4

Input

Depth = 4

Output

Five stacked rows, visibly less thinned-out than the classic Cantor Set Generator at the same depth, and noticeably lopsided rather than mirror-symmetric.

Each iteration keeps 80% of a segment's length split unevenly (30%/50%), so more length survives per row than the classic set's even 66.7% keep ratio.

Best Practices & Notes

Best Practices

Compare it directly against the Cantor Set Generator at the same depth to see how the uneven split changes both the symmetry and the total surviving length.
Use a mid-range depth (4 to 6) to see the asymmetric skew clearly, without the rows becoming too thin to read.

Developer Notes

Implemented via the shared `cantorRows` row-stacking helper with a custom split function that returns `[start, length * 0.3]` and `[start + length * 0.5, length * 0.5]`, keeping 80% of each segment's length per iteration split unevenly rather than the classic set's even two-thirds split into equal pieces.

Generate an Asymmetric Cantor Set Use Cases

Demonstrating that the Cantor set's self-similar structure doesn't depend on an even middle-third split
Side-by-side visual comparison against the classic Cantor Set Generator
Illustrating how symmetry-breaking in a recursive rule changes the resulting pattern

Common Mistakes

Assuming this is the standard Cantor set under a different name, it's a deliberately asymmetric variant we built, not a textbook construction.
Expecting the rows to look mirror-symmetric like the classic set, the 30%/50% split means each row skews visibly toward one side.

Tips

Try the Generalized Cantor Set Generator next to see a different kind of variation, more branches per iteration rather than an uneven split.
Download as SVG to inspect the exact segment boundaries at high zoom.

Generate an Asymmetric Cantor Set