Vicsek fractal

It has applications including as compact antennas, particularly in cellular phones.

Box fractal also refers to various iterated fractals created by a square or rectangular grid with various boxes removed or absent and, at each iteration, those present and/or those absent have the previous image scaled down and drawn within them.

The Sierpinski triangle may be approximated by a 2 × 2 box fractal with one corner removed.

The Sierpinski carpet is a 3 × 3 box fractal with the middle square removed.

The Vicsek fractal is the set obtained at the limit of this procedure.

The two constructions produce identical limiting curves, but one is rotated by 45 degrees with respect to the other.

The Vicsek fractal has the surprising property that it has zero area yet an infinite perimeter, due to its non-integer dimension.

The boundary of the Vicsek fractal is the Type 1 quadratic Koch curve.

Similarly to the two-dimensional Vicsek fractal, this figure has zero volume.

There exist an infinite number of cross sections which yield the two-dimensional Vicsek fractal.