neighbours {simecol}

Count Number of Neighbours on a Rectangular Grid.

Description

This is the base function for the simulation of deterministic and stochastic cellular automata on rectangular grids.

Usage

  neighbours(x, state = NULL, wdist = NULL, tol = 1e-4, bounds = 0)
  neighbors(x, state = NULL, wdist = NULL, tol = 1e-4, bounds = 0)

Arguments

x

Matrix. The cellular grid, in which each cell can have a specific state value, e.g. zero (dead cell) or one (living cell) or the age of an individual.

state

A value, whose existence is checked within the neighbourhood of each cell.

wdist

The neighbourhood weight matrix. It has to be a square matrix with an odd number of rows and columns).

tol

Tolerance value for the comparision of state with the state of each cell. If tol is a large value, then more than one state can be checked simultaneously.

bounds

A vector with either one or four values specifying the type of boundaries, where 0 means open boundaries and 1 torus-like boundaries. The values are specified in the order bottom, left, top, right.

Details

The performance of the function depends on the size of the matrices and the type of the boundaries, where open boundaries are faster than torus like boundaries. Function eightneighbours is even faster.

Value

A matrix with the same structure as x with the weighted sum of the neigbours with values between state - tol and state + tol.

See Also

seedfill, eightneighbours, conway

Examples

## ==================================================================
## Demonstration of the neighborhood function alone
## ==================================================================

## weight matrix for neighbourhood determination
wdist <- matrix(c(0.5,0.5,0.5,0.5,0.5,
                  0.5,1.0,1.0,1.0,0.5,
                  0.5,1.0,1.0,1.0,0.5,
                  0.5,1.0,1.0,1.0,0.5,
                  0.5,0.5,0.5,0.5,0.5), nrow=5)

## state matrix                  
n <- 20; m <- 20
x <- matrix(rep(0, m * n), nrow = n)

## set state of some cells to 1
x[10, 10] <- 1
x[1, 5]   <- 1
x[n, 15]  <- 1
x[5, 2]   <- 1
x[15, m]  <- 1
#x[n, 1]   <- 1 # corner

opar <- par(mfrow = c(2, 2))
## start population
image(x)
## open boundaries
image(matrix(neighbours(x, wdist = wdist, bounds = 0), nrow = n))
## torus (donut like)
image(matrix(neighbours(x, wdist = wdist, bounds = 1), nrow = n))
## cylinder (left and right boundaries connected)
image(matrix(neighbours(x, wdist = wdist, bounds = c(0, 1, 0, 1)), nrow = n))
par(opar) # reset graphics area                  
                  
## ==================================================================
## The following example demonstrates a "plain implementation" of a
## stochastic cellular automaton i.e. without the simecol structure.
##
## A simecol implementation of this can be found in
## the example directory of this package (file: stoch_ca.R).
## ==================================================================                  
mycolors <- function(n) {
  col <- c("wheat", "darkgreen")
  if (n>2) col <- c(col, heat.colors(n - 2))
  col
}

pj <- 0.99  # survival probability of juveniles
pa <- 0.99  # survival probability of adults
ps <- 0.1   # survival probability of senescent
ci <- 1.0   # "seeding constant"
adult <- 5  # age of adolescence
old   <- 10 # age of senescence

## Define a start population
n <- 80
m <- 80
x <- rep(0, m*n)

## stochastic seed
## x[round(runif(20,1,m*n))] <- adult
dim(x)<- c(n, m)

## rectangangular seed in the middle
x[38:42, 38:42] <- 5

## plot the start population
image(x, col = mycolors(2))

## -----------------------------------------------------------------------------
## Simulation loop (hint: increase loop count)
## -----------------------------------------------------------------------------
for (i in 1:10){

  ## rule 1: reproduction
  ## 1.1 which cells are adult? (only adults can generate)
  ad <- ifelse(x >= adult & x < old, x, 0)

  ## 1.2 how much (weighted) adult neighbours has each cell?
  nb <- neighbours(ad, wdist = wdist)

  ## 1.3 a proportion of the seeds develops juveniles
  ## simplified version, you can also use probabilities
  genprob <- nb * runif(nb) * ci
  xgen  <- ifelse(x == 0 & genprob >= 1, 1, 0)

  ## rule 2: growth and survival of juveniles
  xsurvj <- ifelse(x >= 1 & x < adult & runif(x) <= pj, x+1, 0)
  ## rule 2: growth and survival of adults
  xsurva <- ifelse(x >= adult & x < old & runif(x) <= pa, x+1, 0)
  ## rule 2: growth and survival of senescent
  xsurvs <- ifelse(x >= old & runif(x) <= ps, x+1, 0)

  ## make resulting grid of complete population
  x     <- xgen + xsurvj + xsurva + xsurvs

  ## plot resulting grid
  image(x, col = mycolors(max(x) + 1), add = TRUE)
  if (max(x) == 0) stop("extinction", call. = FALSE)
}

## modifications:  pa<-pj<-0.9

## additional statistics of population structure
## with table, hist, mean, sd, ...