A fractal is fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole. The term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning broken or fractured. A mathematical fractal is based on a recursive equation. There are several examples of fractals, which are defined as portraying exact self-similarity, quasi self-similarity, or statistical self-similarity. While fractals are a mathematical construct, they are also found in nature.

2D line-division type fractals are easy to create on the MakerBot. Recursive algorithms can neatly define the act of repeatedly inserting a sequence in between copies of itself to generate the Coch Curve and other related shapes.

3D fractals, like the Serpinski sponge, aren't as easy to create. The Serpinski sponge in particular has overhangs that will make it poorly suited for printing on a non-support printer, and although the self-similar nature of fractals may make it plausible to make 3D fractals which by construction do not need supports, the added complexity of the formulas, coupled with their lack of innate suitability to the plotting method will cause some trouble.