Cellular Automata and Self Organized Criticality
نویسنده
چکیده
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simpliied models for many phenomenaseen in nature. Among other things, they provide insight into self-organized critical-ity, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. 1 Self-organized Criticality Self-organized criticality is a concept aimed at describing a class of dynamical systems which naturally drive themselves to a state where interesting physics occurs on all scales 1. The idea provides a possible \explanation" of the omnipresent multi-scale structures throughout the natural world, ranging from the fractal structure of mountains, to the power law spectra of earthquake sizes 2. Recent applications include such diverse topics as punctuated evolution 3 and traac ow 4. The concept has even been invoked to explain the unpredictable nature of economic systems, i.e. why you can't beat the stock market 5. The prototypical example is a sandpile. On slowly adding grains of sand to an empty table, a pile will grow until its slope becomes critical and avalanches start spilling over the sides. If the slope becomes too large, a large catastrophic avalanche is likely, and the slope will reduce. If the slope is too small, then the sand will accumulate to make the pile steeper. Ultimately one should obtain avalanches of all sizes, with the prediction of the size for the next avalanche being impossible without actually running the experiment. Self-organized criticality nicely compliments the concept of chaos. In the latter, dynamical systems with a few degrees of freedom, say three or more, can display highly complex behavior, including fractal structures. With self-organized criticality, we start instead with systems of many degrees of freedom, and nd a few general common features. Another attractive feature of this topic is the ease with which computer models can be implemented and the elegance of the resulting graphics. Most of the gures in this chapter were produced using my publicly available set of programs \xtoys" 6. The original Bak, Tang, Wiesenfeld paper 1 presented a simple model wherein each site in a two dimensional lattice has a state represented by a 1
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تاریخ انتشار 1996