What is the Vicsek fractal?

It's a classic fractal built by dividing a square into a 3x3 grid of nine equal cells, keeping only the center cell and the four cells directly above, below, left, and right of it (five cells total), and discarding the four corner cells. That same keep-the-cross rule is then applied again inside each of the five surviving cells, recursively, producing a fractal cross pattern.

Why does the Depth control say "Depth" instead of "Iterations" like other fractal tools?

Both describe the same idea, how many times a rule is applied recursively, but for a grid-subdivision fractal like this one, "depth" better matches the mental model of subdividing a square deeper and deeper, rather than iterating a turtle-graphics drawing rule along a path.

How is this different from the turtle-graphics fractals elsewhere in this category?

Most fractals in this category are built by a turtle repeatedly drawing forward and turning based on a rule string, producing a connected line path. The Vicsek fractal here is built by recursive grid subdivision instead, at each level a square splits into a 3x3 grid and only five of the nine sub-squares survive, so the output is a set of filled squares rather than a stroked line.

Why is the maximum depth only 6?

Each level of recursion multiplies the surviving square count by 5, so by depth 6 there are already thousands of tiny squares. Beyond that the pattern becomes visually indistinguishable at typical screen resolution while the SVG output keeps growing, so the cap keeps renders and downloads fast.

Vicsek Fractal Generator - Classic Cross-Shaped Fractal Online

Overview

Introduction

Not every fractal comes from a turtle-graphics drawing rule. The Vicsek fractal is built by grid subdivision instead, splitting a square into nine equal cells and keeping only the cross-shaped arrangement of five, then repeating that inside each survivor.

Set a depth and the tool renders the resulting pattern as a set of filled SVG squares, downloadable as SVG or PNG.

What Is Generate a Vicsek Fractal?

A generator for the classic Vicsek fractal, a well-documented cross-shaped pattern produced by recursively subdividing a square into a 3x3 grid and keeping only the center and four edge-midpoint cells at every level.

Unlike the line-based curves elsewhere in this category, the output here is a set of filled squares, a solid cross-shaped pattern rather than an outline.

How Generate a Vicsek Fractal Works

The construction starts from one square. At each level of depth, every surviving square is divided into a 3x3 grid of nine equal sub-squares, and only five are kept, the center sub-square and the four sub-squares directly above, below, left, and right of it, the four corner sub-squares are discarded.

That same 3x3 subdivide-and-keep-the-cross step is then applied again inside each of the five surviving sub-squares, recursively, down to the requested depth, so the cross pattern repeats at every scale.

The final set of surviving squares is rendered as filled SVG rectangles rather than a stroked line path, and that same rectangle data feeds both the SVG and PNG downloads.

When To Use Generate a Vicsek Fractal

Use it when you want a solid, filled cross-shaped fractal pattern rather than an outlined curve, for design work, textures, or teaching recursive grid subdivision.

It's also a useful contrast to the turtle-graphics curves elsewhere in this category, for illustrating that fractals can be built from region subdivision just as well as from line-drawing rules.

Often used alongside Generate a Quadratic Cross Fractal, Generate a Levy C Curve and Generate a Triflake Curve.

Features

Advantages

Produces a recognizable, well-documented fractal pattern with a single depth control.
Filled squares render as a solid pattern, useful where a filled shape reads better than an outline.
Downloadable as scalable SVG or a flattened PNG.

Limitations

Capped at depth 6, since the 5-fold growth per level makes deeper subdivisions visually redundant while inflating file size.
Filled rectangles only, there is no stroked-outline-only mode for this particular fractal.

Examples

Depth 0

Input

Depth = 0

Output

A single filled square, no subdivision has happened yet.

At depth zero the recursive subdivision hasn't run, so the output is just the starting square.

Depth 4 (default)

Input

Depth = 4

Output

A dense, self-similar cross pattern made of hundreds of small filled squares.

Four rounds of the keep-the-cross subdivision rule have been applied, each one nested inside the surviving squares of the last.

Best Practices & Notes

Best Practices

Start at depth 1 or 2 to see the basic cross-of-five-squares pattern clearly before moving to the denser default of 4.
Use the SVG download if you plan to recolor or resize the filled squares in a vector editor, PNG for a quick raster embed.

Developer Notes

Unlike the L-system-based tools in this category, this fractal is built by direct recursive grid subdivision: at each level a square is split into a 3x3 grid and only cells where `row === 1 || col === 1` are kept (the center row and center column, five of nine cells), then the same subdivision is applied recursively inside each survivor down to the requested depth. Surviving squares are rendered as filled `rect` elements rather than a stroked path.

Generate a Vicsek Fractal Use Cases

Generating a solid cross-shaped fractal pattern for design or texture work
Teaching recursive grid subdivision as an alternative fractal construction method to turtle graphics
Producing a downloadable SVG asset of a classic, well-documented fractal

Common Mistakes

Expecting an outlined curve like the other fractal tools in this category, the Vicsek fractal here renders as filled squares, not a stroked line.
Assuming all nine grid cells at each level split further, only the five cross-shaped survivors (center plus the four edge-midpoints) are kept and recursed into, the four corners are dropped for good.

Tips

Compare this against Quadratic Cross Fractal to see two very different construction methods, grid subdivision here versus a turtle-graphics rule there, both converging on a cross-like silhouette.
Zoom into the downloaded SVG in a vector editor to inspect exactly which sub-squares survive at each depth level.

Generate a Vicsek Fractal