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During the last decade, fractal processes and chaotic systems were widely studied in many areas of research. Chaotic systems are highly dependent on initial conditions. Small changes in initial conditions can generate widely diverging or converging outcomes for both bifurcation or attraction in chaotic systems. In this work, we present a new method on how to generate a new family of chaotic attractors by combining these with a network of fractal processes. The proposed approach in this article is based upon the construction of a new system of fractal processes.