Fractal Fern
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I’m gonna share a short code snippet that I thought was interesting. This post is inspired by one of my engineering computation classes at Rice. The program initializes a pair of coordinates ‘z’ and iteratively updates z by matrix multiplication based on some random number generation criteria. After each successive coordinate update, the new ‘z’ is plotted.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | library(ggplot2)
z <- matrix(c(0, 0), nrow = 2)
x <- c()
y <- c()
for (i in 1:40000) {
r <- runif(1)
if (r < .01) {
z <- matrix(c(0, 0, 0, .16), nrow = 2, byrow = T) %*% z
}
else if (r < .86) {
z <- matrix(c(.85, .04, -.04, .85), nrow = 2, byrow = T) %*% z + c(0, 1.6)
}
else if (r < .93) {
z <- matrix(c(0.2, -.26, .23, .22), nrow = 2, byrow = T) %*% z + c(0, 1.6)
}
else {
z <- matrix(c(-.15, .28, .26, .24), nrow = 2, byrow = T) %*% z + c(0, .44)
}
x[i] <- z[1]
y[i] <- z[2]
}
qplot(x, y, size = I(.5)) + theme_bw() + opts(axis.line = element_blank(),
axis.text.x = element_blank(), axis.text.y = element_blank(),
axis.ticks = element_blank(), axis.title.x = element_blank(),
axis.title.y = element_blank()) + scale_x_continuous(breaks = NULL) +
scale_y_continuous(breaks = NULL) + ggtitle("Fractal Fern")
|
Pretty.
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