I am wondering if anyone can help me to plot the [Cantor dust](http://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Cantor_dust.png/600px-Cantor_dust.png) on the plane in Mathematica. This is linked to the [Cantor set](http://en.wikipedia.org/wiki/Cantor_set).

Thanks a lot.

**EDIT**

I actually wanted to have something like this:

![enter image description here](https://i.stack.imgur.com/sLVqo.png)