Yesterday, when playing with the kids, I found Mr. Pythagoras unexpectedly in their room. For a fraction of a second, I wondered why the Lego fence would fit perfectly across. Then, I saw that I had produced an instance of the 3-4-5 triangle.
It seems completely natural that going from 2d to 3d adds a new dimension of awesomeness to fractals. Accordingly, it is quite a shame that until very recently, I was not aware of the magnificent Mandelbulb. If this is a new world for you, too, go and explore the wonders of 3d fractals using tools like Mandelbulb 3d.