Abstract
The issue of spatial diffusion and pattern division of traditional cellular automata (CA) has drawn widespread attention and generated extensive work by scholars. However, there are many deficiencies in traditional configurations of CA neighborhoods, which reduce simulation accuracy. The effect of improved methods of traditional configurations of CA neighborhoods is not obvious, and its interoperability is not strong. Therefore, this paper firstly puts forward the concept of the circular neighborhood of CA constrained by the space metric method based on map algebra, and compares the spatial division pattern and anisotropy of different types of neighborhoods in detail. Then, the CA’s weighted diffusion model is discussed to delineate urban spheres of influence in Henan Province. Finally, Weibo data is used to justify a reasonable delineation of urban spheres of influence and can correctly reflect the state of regional development, further proving that improved cellular automata in algorithms and applications have great significance.
Highlights
Cellular automata (CA) is a dynamical model which makes discrete evaluations in time according to some local rules in cellular space which consist of discrete cells possessing a finite number of states [1]
When the point set of raster space P is 2 or greater, “waves” similar to real waves in nature, which means a continuous, extensional process from the inside out according to the existing template and beginning at the generator, start to diffuse around each generator and intersect at some time, which forms a pattern with a certain feature, so we can define the spatial process and spatial pattern of CA diffusion as follows: Definition 2.: there is a two-dimensional raster of space L (m × m) and m × m Cells
Choice of cellular neighborhood configuration has a significant impact on space division structure
Summary
Cellular automata (CA) is a dynamical model which makes discrete evaluations in time according to some local rules in cellular space which consist of discrete cells possessing a finite number of states [1]. The definition of neighborhood, including the size and shape of a neighborhood, plays a pivotal role in the state change of cells, the expression of the validity of the rules and formation of spatial pattern. The range of neighborhoods in this system is mainly the von Neumman neighborhood and Moore neighborhood surrounding the center cell, or the four neighborhoods that remain after removing the four corner-direction cells from the 3 × 3 adjacent domains [4,5] This kind of neighborhood is homogeneous; that is, the distribution, size and shape of cellular neighborhoods are the same [6]. This paper puts forward the concept of circular neighborhoods of CA constrained by space metrics based on map algebra though comprehensive and quantitative analysis of a standard neighborhood’s diffusion with different-weight and its effect on the formation of spatial pattern. The Weibo data would be used to justify a reasonable delineation of urban spheres of influence and could correctly reflect the state of regional development
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