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## generate a snow flake by recursion
## author: Taiyun Wei <taiyun.wei@cos.name>
recur.snow <- function(k, col = 'blue') {
plot(0, 0, xlim = c(0, 1), ylim = c(-sqrt(3)/6, sqrt(3)/2),
asp = 1, type = 'n', ann = FALSE, axes = FALSE)
plotkoch <- function(x1, y1, x2, y2, n) {
if (n > 1) {
plotkoch(x1, y1, (2 * x1 + x2)/3, (2 * y1 + y2)/3, n - 1)
plotkoch((2 * x1 + x2)/3, (2 * y1 + y2)/3,
(x1 + x2)/2 - (y1 - y2) * sqrt(3)/6,
(y1 + y2)/2 - (x2 - x1) * sqrt(3)/6, n - 1)
plotkoch((x1 + x2)/2 - (y1 - y2) * sqrt(3)/6,
(y1 + y2)/2 - (x2 - x1) * sqrt(3)/6, (2 * x2 + x1)/3,
(2 * y2 + y1)/3, n - 1)
plotkoch((2 * x2 + x1)/3, (2 * y2 + y1)/3, x2, y2, n - 1)
}
else {
x = c(x1, (2 * x1 + x2)/3, (x1 + x2)/2 - (y1 - y2) * sqrt(3)/6, (2 * x2 + x1)/3, x2)
y = c(y1, (2 * y1 + y2)/3, (y1 + y2)/2 - (x2 - x1) * sqrt(3)/6, (2 * y2 + y1)/3, y2)
lines(x, y, type = 'l', col = col)
}
}
plotkoch(0, 0, 1, 0, k)
plotkoch(0.5, sqrt(3)/2, 0, 0, k)
plotkoch(1, 0, 0.5, sqrt(3)/2, k)
}
## example
for (i in 1:5) {
recur.snow(i, col = i)
Sys.sleep(1)
}
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