Copyright 2008 S.Monnier
Here are some invaders (see the previous image) with order 4 rotation symmetry. There is one invader of the first generation (the big dark sqares), 100 invaders of the second generation (they are 10 times smaller), and finally 10000 invaders of the third generation (again 10 times smaller), for a total of 10101 invaders. As there are only 2^16 = 65536 types of invaders with this symmetry and that in this image they are picked randomly, it is almost certain (see the birthday problem) that some invaders show up twice in the image. Try to find them...
Of course there are more generations of invaders, but they are invisible at this resolution.
The image was rendered without antialiasing, at size 1000x1000 so that each invader of third generation occupies exactly 8x8 pixels.