Cellular Automata and Artificial Life.ppt

Cellular Automata and Artificial Life Cellular Automata (元胞自动机) Each Unit Is an Automata Connectivity: Each Automata Is Linked With Its Neighborhood An example of Cellular Automata every unit has a value: a, b, c and d. An example of Cellular Automata An example of Cellular Automata An example of Cellular Automata See the pictures of the dynamics of these rules. Text book: Gerard Weisbuch, Complex Systems Dynamics, an introduction to automata networks, Addison-Wesley Publishing Company, Inc. USA. P25-P27 Strong attractors Rule 250: all 1 Rule 128: all configurations with at least one 0 converge toward the attractor containing only 0’s, ( exception of configuration of all 1’s ) Short-period attractors Rule 108 and 178: periods of 1 or 2. long-period attractors Rule 90 and 126: too long to be easily observable. One dimensional cellular automata with three inputs One dimension ( two dimensions ) With three inputs ( with more than 3 inputs) Neighbors: 3, 5, … The nearest neighbors One dimensional cellular automata with two inputs One dimensional cellular automata with two inputs Two-dimensional Cellular Automata The first cellular automata proposed by von Neumann were on the nodes of a two-dimensional square grid. Have a relatively ancient history, from von Neumann’s self-reproducing automata of the 1940’s to Conway’s “game of life”. 2D Cellular Automata 2D Cellular Automata Homogeneous: The state change rules are in principle the same for all of the automata in the lattice. (inhomogeneous) Parallel iteration mode; The connectivity structure is related to the symmetries of the lattice. Two kinds of neighborhood Von Neumann neighmorhood (left) k=5 Moore neighborhood (right) k=9 2D threshold automata Threshold t: -1 = t = k+1 New State = 1 iff S = t. S: the sum of the states of the neighbors If T is small or large Weak thresholds ( T = 0 or is close to 0 ) favor the growth of zones of automata in state 1. Strong thresholds ( T is close to k ) favor the gro