On probabilistic Mandelbrot maps

In this work, we propose a definition for a probabilistic Mandelbrot map in order to extend and support the study initiated by Argyris et al. [Argyris J, Andreadis I, Karakasidis Th. On perturbations of the Mandelbrot map. Chaos, Solitons and Fractals 2000;11:1131-1136.] with regard to the numerical stability of the Mandelbrot and Julia set of the Mandelbrot map when subjected to noise.