The Vicsek fractal appears pretty banal at first glance but it finds applications as compact antennas in cellular phones. It is also known as a vicsek snowflake or a box fractal, though the latter term may also be an umbrella term for various fractals generated via iterative removal of boxes from a square or rectangular grid.
The basic idea behind constructing the Vicsek fractal is to take a square and apply the following operations:
- Divide the square into nine smaller squares using a
3×3
grid. - Keep the middle and the corner squares and remove the remaining ones.
- Repeat recursively for each of the squares till you reach the desired accuracy.
The version of the fractal thus achieved looks like a plus (➕) sign, while an alternative construction where the middle and corner squares are removed leads to a fractal rotated by 45 degrees.
For a chaos game implementation of the rotated form of the Vicsek fractal, we start with a square and take a point at its centre. We then pick a vertex or the centre of the square at random and jump 2/3 the distance to it from our previous point. This soon leads us to the Vicsek Fractal.