In my talk I shall discuss my collaboration with S. Stimac concerning attractors for Henon and Lozi maps, which have been studied since 1976, in connection with a system of differential equations modeling atmospheric convection, introduced by Edward Lorenz. These objects in the theory of dynamical systems serve as a fundamental example of a set of chaotic solutions of a deterministic, yet unpredictable system. We built fractal-like models, namely trees with dense set of branching points, that serve as good models for their topology and dynamics. There is an experimental, computer-based aspect of this study, that might help further develop the results in the future.