Fractal easter eggs
Using certain types of irrational numbers, mathematicians have been able to hide hidden secrets (easter eggs) inside fractals. These appear at an arbitrary point at some arbitrary zoom level and are not repeated (or at least not completely) anywhere else in the fractal. Although they were created when the fractals were first created, most fractal easter eggs were not discovered until they could be found with computer software such as GNU Xaos.
These easter eggs are aberations from the normal repeating fractal pattern in that they do not always repeat, or do not always repeat clearly. It is a convention to hide easter eggs in fractals at coordinates involving the number sequence 7-3-5.
The simplistic nature of the Cantor Set makes hiding a complex easter egg in the formula difficult, and restricted the complexity of the easter egg to the absolute bare minimum, but there is one known easter egg in the Cantor Set. Staying with the lefthand line segment, go seven levels down, then take the right segment on that level, go three layers down with the left segment, then take the right on that level and go seven layers down. The line segment on the right at this position in the Candor Set is bent a few degrees.
Similar to the Cantor Set egg, the easter egg in the Skerpenski Triangle appears by taking the lower left triangle seven levels deep, then switching to the top triangle on that level, taking the lower right triangle within that three levels deep, then switching to the top triangle on that level, then taking the lower left triangle five layers deep. The triangle reached at this level has a small square area sticking out perpendicular to it's upper right edge. This does not repeat.
At a certain point in the Mandlebrot set, Benoit Mandlebrot hid a outline of a picture of Kevin Bacon's face. The corresponding Julia set looks more like Nicholas Cage.
Opting for more of a sci-fi direction, the Sierpinski Carpet contains a hidden picture of Bender from Futurama.