R中的2D运动模拟

Question

I need to make a simulation for this problem:

Two robots A and B are placed in 2D coordinate plane, A is placed on coordinates (0,0) and B is placed on (10,0). They can make step up, down, left or right with same probability. They start moving at the same time and I need to find after how many steps they will meet. If they make more than 15000 step it is considered that they are lost and will never meet. Robots have met if they are in the same square with side 1(Example coordinates (0,0)-(1,0); (0,0)-(0,0); (0,0)-(1,1))

Now i need to make both graphical simulation and count steps until they meet in R statistical software. I have some idea how to count steps, but I'm really stuck with the graphical simulation.

Answer 1

Maybe something like this helps? :

#basic plot
plot(NULL, ann = F, xlim = c(-10,20), ylim = c(-10,20))
abline(h = -10:20, col = grey(0.75), lty = 2)
abline(v = -10:20, col = grey(0.75), lty = 2)

#starting coordinates
A_coords = c(0,0)
B_coords = c(10,0)
text(A_coords[1], A_coords[2], "A", col = "red")
text(B_coords[1], B_coords[2], "B", col = "blue")

for(i in 1:15000)
 {
  Sys.sleep(1)

  text(A_coords[1], A_coords[2], "A", col = "white")
  text(B_coords[1], B_coords[2], "B", col = "white")
                                                       #used jonas's idea
  A <- A_coords + unlist(sample(list(c(0, 1), c(1, 0), c(-1, 0), c(0, -1)), 1)) 
  B <- B_coords + unlist(sample(list(c(0, 1), c(1, 0), c(-1, 0), c(0, -1)), 1))

  lines(c(A_coords[1], A[1]), c(A_coords[2], A[2]), col = "red")
  lines(c(B_coords[1], B[1]), c(B_coords[2], B[2]), col = "blue")

  A_coords <- A
  B_coords <- B

  text(A_coords[1], A_coords[2], "A", col = "red")
  text(B_coords[1], B_coords[2], "B", col = "blue")

  if(all(abs(A_coords - B_coords) <= 1)) break
 }

list(steps = i, A_coordinates = A_coords, B_coordinates = B_coords)

Answer 2

I'd try something like that:

plot_robots <- function(rob1, rob2){
  plot(1, xlim = c(-20, 20), ylim =c(-20, 20), type = "n", xaxs = "i", yaxs = "i")
  abline(h =-20:20, v = -20:20)
  points(c(rob1[1], rob2[1]), c(rob2[2], rob2[2]), pch = 21, cex = 2, bg = c("red", "blue"))
}

rob1 <- c(0, 0)
rob2 <- c(10, 0)

plot_robots(rob1, rob2)

for(i in 1:15000){
 rob1 <- rob1 + sample(list(c(0, 1), c(1, 0), c(-1, 0), c(0, -1)), 1)[[1]]
 rob2 <- rob2 + sample(list(c(0, 1), c(1, 0), c(-1, 0), c(0, -1)), 1)[[1]]
 plot_robots(rob1, rob2)
 Sys.sleep(.1)
}

It is not perfect but should give an idea... I don't think anybody has got the time to watch the robots until they meet. It will take ages...