Distributes n=3 plant species across k=12 x m=12 grid cells, in a way that no individual has another individual of it’s own species in its 4-cell (von Neumann: up, down, left, right) neighborhood. This script originated from a question posted on http://theoreticalecology.wordpress.com/2014/01/14/sampling-design-combinatorics/ , solution posted b…

samplingDesign3SpeciesWithNoEqualNeigbors.r

# plot layout
x=12
y=12
# number of diff samples
n=3

# plot A, which holds
A=array(NA,c(x,y))
# repeat 1 through n as many times as subplots are in A
s=rep(1:n, x*y/n)

# stop after kmax iterations in the while loop
kmax=10000

# loop over supplots in A
for (i in 1:x) {
  for (j in 1:y) {
    # if a suitable subplot was found
    found=FALSE
    
    # number of remaining suplots
    ns=length(s)
    # counter to break possible infinite while loop
    k=0
    while (!found) {
      k=k+1
      if (k>kmax) break
      # choose a sample from remaining subplots
      A[i,j] = sample(s,1)
      # assume it suits
      found=TRUE
      # if it doesn’t reset
      if (i>1 && A[i,j] == A[i-1,j]) found=FALSE
      if (j>1 && A[i,j] == A[i,j-1]) found=FALSE
    }
    # warn if equal subplots are next to each other
    if (found==FALSE) warning("*** layout not possible, ran out of possible subplots! ***")
    
    # break if the last subplot is gone
    if (length(s)==1) break
    # first remove all equal subplots,
    s=s[! s %in% A[i,j]]
    # the append one less to the remaining subplots
    s=append(s,rep(A[i,j],ns-length(s)-1))
  }
}


# text and image output
print(A)
for (i in 1:n) print(paste(i, ": ", length(A[A==i]),sep=""))
image(A)