Hat number 3 in R

hat3.R

x <- function(k, t) {

  c(     -sin(4*pi*k/1000) + sin(t)*sin(t/3)/5,
     -0.5*sin(8*pi*k/1000) + cos(t)/2
  )
}

y <- function(k, t) {
  c(     -cos(2*pi*k/1000) + cos(t)*cos(t/3)/2,
     -0.5*cos(4*pi*k/1000) + sin(t)/3
  )
}

# max_x <- -Inf
# min_x <-  Inf
# max_y <- -Inf
# min_y <- Inf

png(file = "hat3-%03d.png", width = 120, height = 120)
par(bg = "black")
par(mar = rep(0,4))
for (t in seq(0, 6*pi, length.out = 200)) {
  plot.new()
  plot.window(c(-1.2,1.2),c(-1.2,1.5))
  for (i in 0:999) {
      # max_x <- max(max_x,x(i,t))
      # min_x <- min(min_x,x(i,t))
      # max_y <- max(max_x,x(i,t))
      # min_y <- min(min_x,x(i,t))
      lines(x(i,t), y(i,t), col = alpha(rgb(1,1,1), 0.3))
  }
}
dev.off()
system("convert -delay 1 hat3-*.png hat3.gif")
file.remove(list.files(pattern="hat3-.*.png"))