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A continuous automaton can be described as a cellular automaton extended so the valid states a cell can take are not just discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, the real number range [0,1]. The cells however remain discretely separated from each other. One example is called computational verb cellular network (CVCN) [1][2] .,[3] of which the states of cells are in the region of [0,1].
A cellular automaton is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.
Such automata can be used to model certain physical reactions more closely, such as diffusion. One such diffusion model could conceivably consist of a transition function based on the average values of the neighbourhood of the cell. Many implementations of Finite Element Analysis can be thought of as continuous automata, though this degree of abstraction away from the physics of the problem is probably inappropriate.
Diffusion is the net movement of molecules or atoms from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in chemical potential of the diffusing species.
A neighbourhood, or neighborhood, is a geographically localised community within a larger city, town, suburb or rural area. Neighbourhoods are often social communities with considerable face-to-face interaction among members. Researchers have not agreed on an exact definition, but the following may serve as a starting point: "Neighbourhood is generally defined spatially as a specific geographic area and functionally as a set of social networks. Neighbourhoods, then, are the spatial units in which face-to-face social interactions occur—the personal settings and situations where residents seek to realise common values, socialise youth, and maintain effective social control."
Continuous spatial automata resemble continuous automata in having continuous values, but they also have a continuous set of locations rather than restricting the values to a discrete grid of cells.
Continuous spatial automata, unlike cellular automata, have a continuum of locations, while the state of a location still is any of a finite number of real numbers. Time can also be continuous, and in this case the state evolves according to differential equations.
Reference notes
↑ Yang, T. (March 2009). "Computational Verb Cellular Networks: Part I--A New Paradigm of Human Social Pattern Formation,". International Journal of Computational Cognition. Yang's Scientific Press. 7 (1): 1–34.
↑ Yang, T. (March 2009). "Computational Verb Cellular Networks: Part II--One-Dimensional Computational Verb Local Rules,". International Journal of Computational Cognition. Yang's Scientific Press. 7 (1): 35–51.
↑ Yang, T. (June 2009). "Computational Verb Cellular Networks: Part III--Solutions of One-Dimensional Computational Verb Cellular Networks,". International Journal of Computational Cognition. Yang's Scientific Press. 7 (2): 1–11.
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