Famous Fractals   

Star Fractal

Although a "Star Fractal" is a name given to a whole series of fractal, they all got their names from their most famous representative. The Star Fractal is formed by taking a 5-corner star and connecting stars that are 3 times smaller to every corner:

If you do the same to every one of the smaller stars and continue it infinitely, you will get the Star Fractal:

LENGTH

It is possible to find the total length of all the lines in the Star Fractal. If you check the total length of all stars at the first several iterations, you will find that the lengths is increasing with every iteration. The sum of an increasing sequence of numbers is always infinite. This means that the Star Fractal is infinite in length.