Von Neumann neighborhood

Fig. 3.51 A few Snapshots of two-dimensional von-Neumann neighborhood totalistic rule X = l,2,3,4-> 1.

Fig. 3.61 Some snapshots of the evolution of a 5-neighbor von Neumann neighborhood percolating voting rule V3 the initial densities are (a) p = 0.35 < pc and (b) p = 0.50 = pc-...

Fig. 3.62 An example of overlapping convex-hulls in the 4-site (center-site excluded) von Neumann neighborhood voting rule with threshold = 2 see equation 3.77.

Consider the two-dimensional majority rule defined on the 4-neighbor von Neumann neighborhood ... 

Fig. 5.6. Some snapshots of the evolution of the 5-neighbor (von Neumann neighborhood) majority rule (p2d majority with threshold b = 2, The initial state is random with density po = 0.075.

The Greenberg-Hastings model [green78] uses the two-dimensional von-Neumann neighborhood and assumes that each site is populated by variables a that take on one of three values 0,1,2. It is important to have at least three values... 

Consider a two-dimensional array of sites, where each site oij 0,1,..., 7 and evolves according to the four-neighbor von Neumann neighborhood rule defined in table 11.1. Each of the eight states has a specific function to perform. The state... 

Figure 2.5. Cell neighborhoods (a) the von Neumann neighborhood, (b) the Moore neighborhood, and (c) the extended von Neumann neighborhood of cell A...

For typical simulations used in the study of aqueous and other liquid systems, several attributes are customarily recorded and used in comparative studies. These attributes used singly or in combination are useful for analyses of different phenomena (Examples of the use and significance of these attributes will be described in later examples). The commonly collected attributes for the liquid systems relate mainly to the states of bonding, i.e., the numbers of adjacent ingredients in the von Neumann neighborhood, of the ingredients. Their designations are as follows ... 

Some or all of the vertices in each fragment may be representative of a water molecule. The trace of each fragment may be mapped onto a two-dimensional grid (Figure 3.1c). This trace is equated with the mapping of a cellular automaton von Neumann neighborhood. The cellular automata transition rules operate randomly and asynchronously on the central cell, i, in each von... 

Figure 3.1. (a) Hexagonal array of water molecules in the solid state, (b) Tetrahedral arrangement of bound water molecules, (c) Trace of the tetrahedral arrangement if there are five bound water molecules on a surface. This mapping is equivalent to the von Neumann neighborhood... 

If the current state of a cell is ON, turn the cell OFF and turn ON a randomly selected cell in the von Neumann neighborhood. 

In this model, run on a square grid, each unit can adopt one of N states, 0, 1, 2, 3,..., (N - 1) states other than 0 are "excited states." The neighbors are those cells that share an edge with the target cell (a von Neumann neighborhood). The transition rules can be divided into two types first we have reaction rules ... 

Figure 5 The cellular automata neighborhoods associated with cell i. (a) The von Neumann neighborhood, (b) The Moore neighborhood, (c) The extended von Neumann neighborhood.

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