Wednesday, February 29, 2012

Fractals - Vicsek

Vicsek fractal is also known as Vicsek snowflake or box fractal.
The basic square is decomposed into nine smaller squares in the 3-by-3 grid. The four squares at the corners and the middle square are left, the other squares being removed. The process is repeated recursively for each of the five remaining subsquares.
An alternative construction (shown below in the left image) is to remove the four corner squares and leave the middle square and the squares above, below, left and right of it. The two constructions produce identical limiting curves, but one is rotated by 45 degrees with respect to the other.
The Vicsek fractal is the set obtained at the limit of this procedure. The Hausdorff dimension of this fractal is log 5/log 3 ≈ 1.46497. (Source : Wikipedia)

Moving ahead ...
I created Viscek fractal using python module tkinter and its inbuilt canvas. A simple python 2.x code to visualize it is given below ...