This movie shows all the Littlewood polynomials of degree 25 with a positive constant term (L(z) = 1 ± z ± z^2 ± z^3 ... ± z^25) evaluated at a point in the complex plane that changes over time; that point is shown in the inset, against a backdrop of all the roots (within a certain disk) of the same Littlewood polynomials.

More information, and a Java applet that lets you explore these sets for yourself, at gregegan.net/SCIENCE/Littlewood/Littlewood.html