We introduce a versatile method for finding prime numbers that display surprisingly intricate visual patterns— hypothetically, any desired pattern is possible, with only mild distortion. We use this method to locate several examples of large prime numbers that are, in and of themselves, self-referential works of art.

The images on this page are created using the standard iterative series of the Mandelbrot, that is, iterate the function zn+1 = zn2 + z0 where z0 is each point in the image plane (complex plane). However, instead of recording the behavior of the series at each point z0 we now consider only those points that escape to infinity and we create a density plot of the terms in the series. The result then is a 2D density plot of the trajectories that escape to infinity. The following shows the buddhabrot for that part of the complex plane that is interesting.

Beautiful illustrations.