The best thing I could find was an academic paper called "Generalized Scheme For Fractal Based Digital Signature (GFDS)" which proposes a digital signature scheme based on Mandelbrot and Julia fractal
Fascinating stuff!! here are some excerpts: " It is possible to have digital signature scheme based on fractal due to the strong connection between the Mandelbrot and Julia fractal sets. The link between the two fractal sets is used for the conversion of the private key to a public key"
"This paper has shown the possibility of using Fractal sets (Mandelbrot and Julia function sets) in Cryptographic keys exchange protocol. The Fractal based key exchange protocol is made possible because of the intrinsic connection between the Mandelbrot and Julia Fractal sets"