A Monte Carlo simulation of random walks in flatland, to see how long it takes an agent (p) to visit every unit in flatland at least once

flatland-randomwalk.R

# A random-walk in flat-land.  Note that the world is a circle.

maxworld <- 1000  # Flatland is maxworld units long
p <- integer(maxworld/2)  # place p on the unit halfway between 0 and maxworld
 
dist <- c()  # dist: the distribution of "times it took to complete each iter(ation) of the randmo walk"

for(loop in 1:1000){  # Run the siumulation of random walks 1000 times
  world <- rep(0, maxworld)  # Set up the world, as maxworld-long unvisited units
  keep_going <- T  # keep_going determined whether a random walk simulation continues
  iter <- 0  # iter is a count of the number of the number of time p moved around flatland before every unit in flatland was visited at least once
  while(keep_going == T){  # Move p around flatland until every unit has been visited at least once
    iter <- iter + 1  # Count the number of time p moved
    p <- ifelse (runif(1, -1, 1)<0, p-1, p+1)  # p's movement is a random walk
    p <- ifelse(p > maxworld, 1, p)  # Make sure p moves in a circle around the world
    p <- ifelse(p < 1, maxworld, p)  # Make sure p moives in a circle around the world 
    world[p] <- world[p] + 1  # count the number of time p visited each unit in the world
    
    if(sum(world==0) == 0){  # If every unit in the world has been visited
      keep_going <- F}  # set keep-going to false, so the whiule loop fails.
  }
  dist <- c(dist, iter)  # add the number of moves made in this random-walk and add it to the vector of random walks
}

# Plot the distribution of random-walks
plot(dist, xlab = "Iterations to Completion")