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I understand that certain mathematical sets produce fractals. Are there fractals defined by sets with more than 2 variables? Is that possible?

Alex
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Yes, they do. Most fractal constructions can be taken into three dimensions. One of the easiest to visualize is to make a 3D version of the Sierpinski carpet.

Take a cube, cut it into $3 \times 3 \times 3$ subcubes, checkerboard color them with the corners black, and remove all the white ones. Now partition the subcubes you kept and keep going. The result is enter image description here

Ross Millikan
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  • Also http://upload.wikimedia.org/wikipedia/commons/b/b4/Sierpinski_pyramid.png. – lhf Sep 23 '14 at 01:15