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Consider an evolving abstract one-dimensional world in which each landowner has two neighboring landowners. During each discrete period of time, each landowner can use its land in one of two ways (blue or red, corresponding to 0 and 1). And during each period of time, the landowner receives a score depending on the combination of the landowner's choice of how to use its land and its nearest neighbors' choices of how to use their land. It might, for example, be best if a blue use were surrounded by one red use and be worst if a red use were surrounded by two blue uses. If the landowner changes the way it uses its land from the immediately prior iteration, it also incurs a "transition cost", which is subtracted from that score. Landowners then simultaneously "optimize" in a somewhat shortsighted fashion. They decide on their next turn to choose the use of land which, with transition costs taken into account, will yield them the highest score, assuming their neighbors keep their behavior the same. This Demonstration permits exploration of such a system by creating an elementary cellular automaton (outer totalistic) that emulates this behavior. You choose the scores accorded each configuration of landowner and neighbors. You also choose how much it costs each landowner to change its land use (a "transition cost"). You also choose the initial configuration of land use. You can choose "seed mode", in which you start with some small user-selected "seed" against a user-selected uniform "seed background". Or you choose "random mode" and can choose a random initial configuration. Finally, you choose whether property that has been "zoned" to a certain initial configuration is permitted to evolve based on simultaneous private optimization. The Demonstration responds by computing the elementary cellular automaton whose behavior mimics that of the optimizing landowners. It also computes a "zoned initial configuration" consisting of repeated land use blocks of length eight. These blocks of "zoned" land use are calculated to score relatively highly given the scoring rules—at least before interactions with neighboring blocks at the "seams" are taken into acount. They are thus the sort of arrangements that might be selected by a governing body with limited computational abilities but that was interested in total wealth maximization. The Demonstration further responds with array plots for both the unzoned and zoned regimes that show the evolution of uses to which each landowner puts its land and the scores it receives as a result of that use and any transitions between uses. The bottom two plots show the history of total scores under the unzoned and zoned regimes.
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