I am trying to find a way to calculate the Lyapunov exponents of the Mandelbrot set. There are some very nice diagrams that you can find on Flickr of a plot of the Lyapunov exponents of the Mandelbrot set, leading to a much higher detail in the structure of the set.
I would like to do this as well and have found the definition of the Lyapunov Exponent but I cannot find a good paper or documentation on how to calculate the Lyapunov Exponent for the M-Set. Especially the derivative of the function $z[n+1] = z^n + c$ with regards to the starting position $x_0$ is what I cannot figure out.
Do I have to use an approximation for this derivative? If yes, which one? If no, how can these exponents be calculated for the Mandelbrot set.
PS: I am a hobby mathematician, but mainly an engineer. A description in terms of an algorithm would greatly help. Thank you for your consideration.