How to plot non-linear decision boundaries with a grid in R?

Question

I find this particular graph in ISLR (Figure 2.13) or ESL very well done. I can\'t guess how the authors would have made this in R. I know how to get the orange and blue points

Answer 1

This was my silly attempt at approximation. Clearly the issues raised by @StephenKolassa are valid and not handled by this approximation.

myCurve1 = function (x)
  abs(x[[1]] * sin(x[[1]]) + x[[2]] * sin(x[[2]]))
myCurve2 = function (x)
  abs(x[[1]] * cos(x[[1]]) + x[[2]] * cos(x[[2]]))
myCurve3 = function (x)
  abs(x[[1]] * tan(x[[1]]) + x[[2]] * tan(x[[2]]))

tmp = function (myCurve, seed=99) {
  set.seed(seed)
  points = replicate(100, runif(2))
  colors = ifelse(apply(points, 2, myCurve) > 0.5, "orange", "blue")
  # Confound some
  swapInts = sample.int(length(colors), 6)
  for (i in swapInts) {
    if (colors[[i]] == "orange") {
      colors[[i]] = "blue"
    } else {
      colors[[i]] = "orange"
    }
  }
  gridPoints = seq(0, 1, 0.005)
  gridPoints = as.matrix(expand.grid(gridPoints, gridPoints))
  gridColors = vector("character", nrow(gridPoints))
  gridPch = vector("character", nrow(gridPoints))
  for (i in 1:nrow(gridPoints)) {
    val = myCurve(gridPoints[i, ])
    if (val > 0.505) {
      gridColors[[i]] = "orange"
      gridPch[[i]] = "."
    } else if (val < 0.495) {
      gridColors[[i]] = "blue"
      gridPch[[i]] = "."
    } else {
      gridColors[[i]] = "purple"
      gridPch[[i]] = "*"
    }
  }
  plot(x=gridPoints[ , 1], y=gridPoints[ , 2], col=gridColors, pch=gridPch)
  points(x=points[1, ], y=points[2, ], col=colors, lwd=2)
}

par(mfrow=c(1, 3))
tmp(myCurve1)
tmp(myCurve2)
tmp(myCurve3)