Would you like to find a polynomial whose Julia set looks like a cat? a car? a triangle? This talk will tell you how to construct such a polynomial. I proved that any Jordan curve in the plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Some types of more complicated shapes can be approximated by the basins of attraction of rational maps. I will discuss these results and show pictures of neat Julia sets.