A gallery of Chua attractors. Part IV

The literature on Chua Oscillator includes more than a thousand papers, describing an astonishing variety of chaotic behavior. Gallery of Chua attractors, Part IV presents a collection of 101, previously unknown attractors, generated by a generalization of Chua circuit with a smooth nonlinear function. The gallery is the result of an extensive exploration of the parameter space for Chua cubic system, in which we used PCA and Hausdorf Distances to guide us. During this exploration we sensed the beauty of the chaotic patterns and recorded this beauty for the nonlinear community. The attractors we describe here represent only a small proportion of those we discovered during our exploration of phase space: much intensive research remains to be done. However, the very number of attractors we found suggests it might be possible not only to detect the morphogenetic processes which determine the points in phase space ("catastrophe points") where a family of attractors disappears and another one comes to life, but to identify more general "laws of morphogenesis" governing the behavior of these systems. In this paper, we outline five such rules.