Is this a standard named construction?

No, this is our own generalization of the classic Cantor set's underlying rule. The classic set divides each segment into 3 equal parts and keeps the outer 2, discarding the middle. This variant instead divides into 5 equal parts and keeps 3 of them, the 1st, 3rd, and 5th fifths, discarding the 2nd and 4th.

How does 3-of-5 change the pattern compared to the classic 2-of-3?

Every segment now splits into 3 children per iteration instead of 2, so the segment count grows faster with depth, 3^depth instead of 2^depth. Each child is also smaller relative to its parent (one-fifth instead of one-third), so at the same depth this variant produces a visibly denser field of smaller, more numerous surviving segments.

Does this variant keep more or less total length than the classic set?

Slightly less per iteration: this variant keeps 3/5 (60%) of each segment's length per step, versus the classic set's 2/3 (about 66.7%). What stands out visually isn't extra length, it's the extra branching, three children instead of two means many more, shorter segments survive at any given depth.

What does the Depth setting control?

Depth (0 to 6) sets how many times the keep-3-of-5 split repeats. The maximum is lower than the classic set's depth-8 cap because segment count grows faster here (3^depth versus 2^depth), so fewer iterations already produce a dense row.

Generalized Cantor Set Generator - Keep-3-of-5 Variant SVG

Overview

Introduction

The classic Cantor set is really a special case of a more general idea: divide a segment into equal parts, keep some of them, and repeat. This tool explores a different point in that family.

Instead of the classic rule of dividing into 3 equal parts and keeping 2, this generator divides each segment into 5 equal parts and keeps 3 of them, the 1st, 3rd, and 5th fifths, producing three children per segment at every iteration instead of two.

What Is Generate a Generalized Cantor Set?

A generator for our own generalization of the classic Cantor set's keep-ratio rule, drawn the same way as the standard construction, one stacked row per iteration, but with each segment splitting into three children instead of two.

This is not a single fixed textbook object, it's a demonstration of how the classic middle-thirds idea extends to other divide-and-keep ratios.

How Generate a Generalized Cantor Set Works

Row 0 starts as a single unbroken segment. At every subsequent row, each surviving segment is conceptually divided into 5 equal fifths, and the 1st, 3rd, and 5th fifths are kept as new child segments while the 2nd and 4th fifths are discarded.

Because 3 children survive from every parent segment each iteration, the segment count triples every row, reaching 3^depth segments in the final row rather than the classic set's 2^depth.

Each surviving child is one-fifth the length of its parent, smaller relative to its parent than the classic set's one-third children, so the rows fill with more numerous, individually shorter segments as depth increases.

When To Use Generate a Generalized Cantor Set

Use it to illustrate that the Cantor set's core idea, self-similar removal at every scale, generalizes beyond the specific 3-parts-keep-2 rule to other divide-and-keep ratios and branch counts.

It's a useful visual contrast to the Asymmetric Cantor Set Generator: that tool changes the split's symmetry while keeping two children per segment, this one changes the branch count itself.

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

Features

Advantages

Demonstrates a genuinely different kind of variation from an uneven split, changing the number of surviving children per iteration rather than just their relative sizes.
Produces a visibly denser, more finely divided pattern at a given depth than the classic 2-child construction.
Exports as clean vector SVG or a flattened PNG, matching the other Cantor set tools in this category.

Limitations

This is our own generalization, not a single standard named object, so it won't appear under this exact name in a textbook.
Depth is capped at 6, lower than the classic set's 8, because the segment count grows faster (3^depth) and already produces a dense, hard-to-read row at higher depths.

Examples

Depth 0

Input

Depth = 0

Output

A single unbroken horizontal segment spanning the full width.

At depth 0, no division has happened yet.

Depth 3

Input

Depth = 3

Output

Four stacked rows, with the bottom row containing 27 segments (3^3), visibly denser than the classic Cantor Set Generator's 8 segments (2^3) at the same depth.

Each iteration produces 3 children per segment instead of 2, so segment count grows as 3^depth rather than 2^depth.

Best Practices & Notes

Best Practices

Compare it directly against the classic Cantor Set Generator at the same depth to see how the extra branch per segment changes the density of the result.
Keep depth at 4 or below for the clearest view of individual segments, since 3^depth segments become very numerous quickly.

Developer Notes

Implemented via the shared `cantorRows` row-stacking helper with a custom split function that returns `[start, length/5]`, `[start + 2*length/5, length/5]`, and `[start + 4*length/5, length/5]`, keeping the 1st, 3rd, and 5th fifths of each segment (60% of its length) split across three equal children instead of the classic set's two children from thirds.

Generate a Generalized Cantor Set Use Cases

Illustrating that the Cantor set's construction rule generalizes to other divide-and-keep ratios and branch counts
Producing a denser, more finely subdivided fractal-like pattern than the classic 2-child construction at a comparable depth
Side-by-side comparison against the classic and asymmetric Cantor set variants

Common Mistakes

Expecting this to keep more total length than the classic set, it actually keeps slightly less per iteration (60% versus about 66.7%), the density increase comes from more branches, not more surviving length.
Setting depth too high and losing the ability to distinguish individual segments, since 3^depth segments crowd the row quickly.

Tips

Try the Smith-Volterra-Cantor Set Generator next to see a construction aimed at keeping more total length rather than more branches.
Download as SVG to inspect the exact segment layout of a given depth at high zoom.

Generate a Generalized Cantor Set