We have considered here an outline of our Automata Network Algorithm for construction of fractal objects, The algorithm is a natural evolution of our previous Neural Network Algorithm but the former is simpler and more efficient because there is no need to calculate and store synaptic weights. So we have the possibilities to calculate fractal attractors with the help of automata networks or by neural computations. As very interesting perspective we mentioned the intention to apply the formalism of Evolving Algebras for describing our algorithm. This is a subject for some future investigations.