Fulbright Tour, Japan, 2005, Lecture 1 Ralph Abraham, University of California at Santa Cruz Title: The Chaos Revolution, Part 2 Abstract: We consider mathematics as a network of three subcultures: pure, applied, and computational. The latter is a new branch. The chaos revolution is part of the new subculture of computational and experimental methods. In this talk, we review the tremendous evolution of chaos mathematics since its first florescence in 1975. The prehistory, Part 1 of this sequence, is the subject of the book, "The Chaos Avant-garde" edited by Prof. Yoshike Ueda and myself. We will be talking about chaos, complexity, complex systems, bifurcations, emergence, neural networks, and so on. Exemplary cases: Cellular Automata (CAs) Cellular Dynamata (CDs), Toral Logistic lattice Fractal Attractors, Electric Sheep Landscape Dynamics, Veblen Model