With J: the Hodge Podge Machine the General Idea of the Hodgepodge Rules the Hodgepodge Rules in J

Cellular automata are collections of cells arranged in some manner such that each cell contains a value that is updated from generation to generation according to a local rule. The Game of Life [1-5,7,15] is perhaps the best known cellular automaton. It is based upon a rectangular arrangement of cells that are either 0 or 1, along with simple rules of evolution: if a cell is 0 and has exactly 3 immediate neighbors then it becomes a 1; if a cell is 0 and has exactly 2 or 3 immediate neighbors that are 1, then the cell remains 1; otherwise, the cell becomes or remains 0. The Game of Life is incredibly intriguing, giving rise to complex behavior that is visually stimulating, mathematically interesting and, moreover, it is known to be capable of universal computation. Despite the fact that at a basic level it was designed to model alive and dead cells, it is primarily a toy model in the sense that it does not model any physical behavior well. In this note we describe the Hodge Podge machine which was developed to model an oscillating chemical reaction. One of the earliest oscillating chemical reactions described is the Belousov-Zhabotinski reaction. There is an interesting discussion of the history of this reaction in [14]. It seems that Belousov observed a reaction that oscillated dozens of times between being yellow and clear until finally reaching equilibrium after about an hour. Belousov was basically unsuccessful in his attempt to publish this chemical reaction which is sometimes viewed as a tragic rejection of a report of an unknown phenomenon [10,14]. Zhabotinski was successful in further researching the reaction and publishing that work. Since then, oscillating chemical reactions have become well known. Gerhardt and H. Schuster [6], coined the term Hodge Podge Machine and introduced that automaton to model an oscillating chemical reaction. We will use a slight modifications of their automaton to facilitate using general scripts [12] designed for use with Fractals, Visualization and J [11] and the Image3 Addon [13]. In particular, these scripts implement automata where cells take values between 0 and 1. We will see a great number of different sorts of selforganizing and oscillating behavior, including dramatic spiral waves that evolve from random configurations. Other references that put this automaton and reaction into a scientific context include [8-9].