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This week I reimplemented part of Conic Sections 1 model from NetLogo. In the model turtles seek to to be in target distance from center.

My code takes only one center point, so only circles can be obtained. Apart from turtle location plot given in NetLogo implementation I added:
1. plot showing maximal difference between turtle distance and target distance;
2. decreasing turtle step size.
Here is the plot showing final simulation state, but it is also nice to watch the simulation run:

Below is the code generating the simulation:
# n: number of turtles
# p.x, p.y: location of center
# range: turtles have random position from [0,range]
#        and will move in random angle a
# step: how fast turtles move
# target: target distance from center
# time: simulation time
init <- function(n, p.x, p.y, range, step, target, time) {
sim <- list(
turtles = data.frame(x = runif(n, max = range),
y = runif(n, max = range),
a = runif(n, max = 2 * pi)),
p.x = p.x, p.y = p.y, step = step, target = target,
time = time, max.dist = rep(NA, time))

# Calculate turtle distance from center
sim$turtles$dist <- sqrt((sim$turtles$x - p.x) ^ 2 +
(sim$turtles$y - p.y) ^ 2)
return(sim)
}

step <- function(sim) {
x <- sim$turtles$x
y <- sim$turtles$y

# Remember last distance and save current distance
o.dist <- sim$turtles$dist
n.dist <- sqrt((x - sim$p.x) ^ 2 + (y - sim$p.y) ^ 2)
sim$turtles$dist <- n.dist

# For turtles that are too far and are moving out
# or too close and are moving in randomly change direction
w.dist <- ((n.dist < o.dist) & (n.dist < sim$target)) | ((n.dist > o.dist) & (n.dist > sim$target))
sim$turtles$a[w.dist] <- runif(sum(w.dist), max = 2 * pi)

sim$turtles$x <- x + sin(sim$turtles$a) * sim$step sim$turtles$y <- y + cos(sim$turtles$a) * sim$step
return(sim)
}

do.plot <- function(sim) {
rng <- quantile(c(sim$turtles$x, sim$turtles$y),
c(0.05, 0.95))
rng <- round(rng, -1) + c(-10, 10)
par(mai = rep(0.5, 4), mfrow = c(1, 2))
plot(sim$turtles$x, sim$turtles$y, pch = ".",
xlim = rng, ylim = rng, xlab = "", ylab = "",
main = "Turtle location")
points(sim$p.x, sim$p.y, col = "red", pch = 20, cex = 2)
plot(sim$max.dist, type = "l", ylim = c(0, max(sim$max.dist, na.rm = TRUE) + 5),
xlab = "", ylab = "", main = "Max difference from target")
}

run <- function(sim) {
for (i in 1:sim$time) { sim <- step(sim) sim$step <- sim$step * 127 / 128 sim$max.dist[i] <- max(sim$turtles$dist) - sim\$target
do.plot(sim)
}
}

sim <- init(4096, 128, 128, 256, 2, 128, 512)
set.seed(0)
run(sim)