In fact my computer drew the triangle exactly that way. After 50,000 iterations or so it's already starting to appear. It might be a lot sooner than that, but a PC can do something like this about 1,000,000 times a second. There is an amazing connection between the Sierpi ski triangle and another famous mathematical triangle - Pascal's triangle. Click here to find out more.
Random iteration is a very good way of constructing fractals.
To get really high quality images you need to iterate about 5 million times, for a screen image, and maybe 30,000,000 for a printed image. You may be surprised to learn that there is a good chance you know how to calculate these transformations. All you have to do is remember the matrix multiplication you probably learned at school. A contracting transformation is one where the matrix always brings points closer together. The computer remembers how often it has plotted a point in the pixel being plotted and colours it accordingly.