Fractal

Some years ago, my folks bought Daughter #1 this magnetic board, complete with hundreds of little coloured discs. It has lain unused for quite some time, but this evening has given me a little distraction from work, and an emergency blip.

For those that need to know, the design is known as Sierpinski's Triangle (or Sieve, or Gasket)

p.s. If you like a brainteaser, how many white dots are there in the design?
(You can work it out without counting them individually)