nb_kernel: Define the neighborhood used in a stochastic cellular...

In alexgenin/chouca: A Stochastic Cellular Automaton Engine

Define the neighborhood used in a stochastic cellular automaton

Description

This function builds standard neighborhood kernels for use in a cellular automaton

Usage

nb_kernel(type, distance)

Arguments

type	The type of neighborhood kernel, either "von_neumann", "moore", or "circular"
distance	The distance (sometimes called "order") that the neighborhood should span. A value of 1 for example will only consider neighbors directly adjacent to a focal cell, and a value of 3 will consider neighbors that are up to three cells away from a focal cell.

Details

A key concept in a stochastic cellular automaton is the neighborhood, which defines which cells are used to compute q_i, the proportion of cells around a focal cell in state i.

Typical neighborhoods include the Moore and Von Neumann neighborhoods of order 1, which means that q will be computed using the 8 cells all around a focal cell, or only its 4 nearest neighbors, respectively. These types of neighborhoods can be extended to larger distances, i.e. considering neighbors that are not only adjacent to a cell, but at a given integer distance distance. See Examples section to visualize different types of neighborhoods.

Examples

# Classic moore and von_neumann neighborhoods
print( nb_kernel("moore", 1) )

print( nb_kernel("von_neumann", 1) )

# Moore kernel of order 2
ker <- nb_kernel("moore", 2)
image(ker)

# Different kernel types and distances 
opar <- par(no.readonly = TRUE)
par(mfcol = c(3, 5)) 
lapply(c(1, 3, 6, 9, 12), function(distance) { 
 image( nb_kernel("von_neumann", distance) )
 title(sprintf("Von Neumann kernel, distance %s", distance))
 image( nb_kernel("moore", distance) )
 title(sprintf("Moore kernel, distance %s", distance))
 image( nb_kernel("circular", distance) )
 title(sprintf("Circular kernel, distance %s", distance))
})

par(opar)

# Circular kernel with a given distance
opar <- par(no.readonly = TRUE)
par(mfrow = c(3, 3)) 
lapply(seq(1, 9*2, by = 2), function(distance) { 
 image( nb_kernel("circular", distance) )
 title(sprintf("Circular kernel, distance %s", distance))
})
par(opar)

alexgenin/chouca documentation built on Aug. 28, 2024, 5:22 a.m.