2D Vicsek Fractal

The 2D Vicsek Fractal starts with a square. That square is divided into a 3 x 3 grid, but instead of keeping all nine smaller squares, only five of them survive. In the classic saltire version those are the center square and the four corners. In the cross version, the center square is kept together with the four edge squares.

That makes it a close relative of the Sierpinski Carpet, which uses the same 3 x 3 subdivision but keeps eight squares instead of five. It is also connected to the N-Flake: the square member of that family turns into the Vicsek construction as soon as a centered square is kept together with the outer copies.

Because the whole fractal is built from repeated squares, it also feels related to the T-Square Fractal, even though the recursion rule is different. Its three-dimensional cousin, the 3D Vicsek Fractal, applies the same idea to cubes instead of squares. The version here lets you switch between the saltire and cross arrangements so you can see how a small change in the pattern leads to a noticeably different rhythm.