simecol (version 0.6-6)

neighbours: Count Number of Neighbours in a Rectangular Cellular Grid.

Description

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

Usage

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

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.

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.

Value

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

Details

See example for details.

See Also

seedfill, eightneighbours, conway

Examples

## ==================================================================
## 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
}

# 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)

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)
  dim(ad) <- c(n,m)

  ## 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
  dim(x)  <-c(n,m)

  ## 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, ...