Is this the same thing as the Sierpinski carpet?

No. The carpet splits each cell into a 3x3 grid and removes the single center cell. This tool splits each cell into a 2x2 grid instead and removes one quadrant, which produces an L-shaped recursion rather than a centered one. It's our own square-based variant built for this category, not the classical carpet construction.

Which quadrant gets dropped?

The same relative quadrant is dropped at every level and in every sub-cell, so the fractal is self-similar in one consistent direction, producing the L-shaped silhouette rather than a symmetric, centered hole pattern.

What does the Depth input control?

Depth sets how many times the 2x2-minus-one-quadrant split repeats, from 0 to 8. At depth 0 you get one solid square. Each added level quarters every surviving square and removes one quadrant from each, recursively.

Why does this tool allow a much higher Depth than the carpet-based tools?

Each level only splits a cell into 4 pieces instead of 9, so the sub-cell count grows more slowly and stays legible at greater depth, that's why this tool's Depth range extends up to 8 instead of 4.

Sierpinski Square Generator - L-shaped Fractal SVG

Overview

Introduction

Most Sierpinski-style square fractals are built on the carpet's 3x3-minus-center rule. This tool takes a different, simpler approach, split each square into just 4 quadrants and drop one of them, repeated recursively.

The result is a self-similar, L-shaped fractal rather than the carpet's centered, symmetric hole pattern, and it's our own square-based variant rather than a reproduction of the classical carpet.

What Is Generate a Sierpinski Square?

A recursive square fractal generator that subdivides each surviving square into a 2x2 grid of quadrants and removes one specific quadrant at every level.

It shares the same recursive spirit as the Sierpinski carpet, subdivide and remove, but with a different grid size and removal pattern, producing a visually distinct L-shaped silhouette instead of the carpet's centered lattice.

How Generate a Sierpinski Square Works

Starting from a single square, the tool splits it into a 2x2 grid of four equal quadrants and discards one fixed quadrant, keeping the other three.

Each of the three surviving quadrants is then recursively split the same way, into 4 sub-quadrants with one dropped, down to the chosen Depth.

Because the same quadrant position is dropped at every level and every scale, the overall silhouette accumulates into an L-shaped, self-similar outline rather than a centered hole pattern.

When To Use Generate a Sierpinski Square

Use it when you want a square-grid fractal with an asymmetric, L-shaped character, for generative art, geometric backgrounds, or teaching recursive subdivision with a simpler 2x2 rule than the carpet's 3x3.

If you specifically need the classical, centered Sierpinski carpet pattern, use a carpet generator instead, this tool's quadrant-drop rule produces a different shape.

Often used alongside Generate a Sierpinski Maze, Generate a Sierpinski Hexagon and Generate a Sierpinski Pentagon.

Features

Advantages

Simple 2x2 subdivision rule that's easy to follow visually, even at higher depth.
Supports Depth up to 8, well beyond the 3x3-grid tools, since each level only quarters the surviving squares.
Filled-square rendering makes the recursive structure easy to read at a glance.

Limitations

Not the classical Sierpinski carpet, if you need that exact centered construction, this L-shaped variant isn't a substitute.
The self-similarity is directional (always the same quadrant dropped), so the fractal isn't rotationally symmetric the way the carpet is.

Examples

Depth 5 square fractal

Input

Depth: 5

Output

A dense, self-similar L-shaped arrangement of small filled squares, five levels of quadrant-dropping recursion deep.

Every surviving quadrant from depth 4 is quartered again with one quadrant removed, repeated recursively.

Best Practices & Notes

Best Practices

Start around Depth 3-4 to see the L-shaped structure clearly before pushing toward the higher end of the range.
Use the SVG export if you plan to recolor the filled squares or extract them as separate shapes later.

Developer Notes

The geometry reuses the shared `subdivideGrid` helper with `gridSize = 2` and a `keep(row, col)` predicate that drops one fixed quadrant (row 0, col 1), unlike the carpet/maze tools which pass `gridSize = 3` and drop only the center cell. Because the sub-cell count only grows by a factor of 3 per level (3 kept of 4) rather than 8 of 9, `boundsCheck` allows Depth up to 8 here instead of 4.

Generate a Sierpinski Square Use Cases

Generative art and geometric background patterns with an asymmetric fractal silhouette
Teaching recursive subdivision using a simpler 2x2 rule before introducing the carpet's 3x3 rule
Comparing subdivision strategies against the carpet-based Sierpinski Maze Generator

Common Mistakes

Assuming this produces the same shape as the classic Sierpinski carpet, the 2x2 quadrant-drop rule gives a different, L-shaped result.
Setting Depth too high too quickly, the squares shrink fast and the structure can become hard to distinguish visually past depth 6 or 7 at typical viewing sizes.

Tips

Compare this tool against Sierpinski Maze Generator at the same conceptual depth to see how a 2x2 versus 3x3 subdivision rule changes the resulting silhouette.
Lower the Depth if you're exporting for a small thumbnail, the finest detail only matters at larger render sizes.

Generate a Sierpinski Square