Famous Fractals
Cantor Curtains
The Cantor Set can be formed by taking a line segment and continuously making a gap with a size of 1/3 in the middle. In addition to the Cantor Set, we can make similar fractal dusts with any size of the gap, ranging from 0 to 1. The smaller the gap size is, the higher the fractal dimension. We can show all of the dusts in one picture by stacking them one on top of the other. Such fractals are called Cantor Curtains. One of them can be formed by stacking the dusts, gradually increasing the gap size as we go down:

In this picture, the Cantor Set is shown in red. We can also form another curtain by gradually decreasing the fractal dimension as we go down. Although in this curtain the gap size will increase as well, it will not be gradual:
