London practise Platform - Wertel Oberfell and Matthias Bär have created Fractal Table, a 3D printed piece of furniture derived from a 3D fractal, that is, 'a rough or fragmented geometric form that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole' (according to Wikipedia). So fractals are a mathematical concept and, presumably, suited therefore to computational methods of fabrication. Here is a great result of what I postulate is the urge of all industrial designers when faced with 3D printing: exploiting the medium to make objects that have previously been mostly computational, or virtual. The designers claim that the table is "impossible to manufacture unless rapid prototyped" - a bold suggestion which I'm sure a worthy craftsmen will happily try to dispell! Either way, there is no denying that this is a effective marriage of concept and process, and a great example of how new processes can push designers into otherwise unexplored areas.
Image from EMSL
Image from IFF
Other fractal-craft projects of note are the Evil Mad Scientist Labs' Sierpinski Cookies ("make these by using a simple iterative algorithmic process of stretching out the dough and folding it over onto itself in a specific pattern"!) and Fimo Fractals. Finally, Dr Jeannine Mosely's Business Card Menger Sponge Project elegantly combines fractal geometry with 'metacycling' 66,000 business cards. Incidentally, this last project was exhibited by the Institute for Figuring who also happen to be crocheting a coral reef...
This all poses the question: What fractals can we create using laser cutting and Ponoko?