I am sorry to be this blunt but this is really utter and complete nonsense. The phrase that the mandelbrot set can't be represented in a lookup table is as such true but that is because nothing that you do with finite precision numbers can represent the mandelbrot set because it essentially is an inifinte object. The function f(x) = x^2 + c as an RNN can also not compute the mandelbrot set if the numbers it uses are of finite precision. That is exactly the same limitation that the lookup table also faces so there is no fundamental difference between the two.