Fractal Curves
Generates the following fractal curves: Dragon Curve, Gosper Flowsnake Curve, Hexagon Molecule Curve, Hilbert Curve, Koch Snowflake Curve, Sierpinski Arrowhead Curve, Sierpinski (Cross) Curve, Sierpinski Triangle Curve.
fractalcurve(n, which = c("hilbert", "sierpinski", "snowflake",
"dragon", "triangle", "arrowhead", "flowsnake", "molecule"))n |
integer, the ‘order’ of the curve |
which |
character string, which curve to cumpute. |
The Hilbert curve is a continuous curve in the plane with 4^N points.
The Sierpinski (cross) curve is a closed curve in the plane with 4^(N+1)+1 points.
His arrowhead curve is a continuous curve in the plane with 3^N+1 points, and his triangle curve is a closed curve in the plane with 2*3^N+2 points.
The Koch snowflake curve is a closed curve in the plane with 3*2^N+1 points.
The dragon curve is a continuous curve in the plane with 2^(N+1) points.
The flowsnake curve is a continuous curve in the plane with 7^N+1 points.
The hexagon molecule curve is a closed curve in the plane with 6*3^N+1 points.
Returns a list with x, y the x- resp. y-coordinates of the
generated points describing the fractal curve.
Copyright (c) 2011 Jonas Lundgren for the Matlab toolbox fractal
curves available on MatlabCentral under BSD license;
here re-implemented in R with explicit allowance from the author.
Peitgen, H.O., H. Juergens, and D. Saupe (1993). Fractals for the Classroom. Springer-Verlag Berlin Heidelberg.
## The Hilbert curve transforms a 2-dim. function into a time series.
z <- fractalcurve(4, which = "hilbert")
## Not run:
f1 <- function(x, y) x^2 + y^2
plot(f1(z$x, z$y), type = 'l', col = "darkblue", lwd = 2,
ylim = c(-1, 2), main = "Functions transformed by Hilbert curves")
f2 <- function(x, y) x^2 - y^2
lines(f2(z$x, z$y), col = "darkgreen", lwd = 2)
f3 <- function(x, y) x^2 * y^2
lines(f3(z$x, z$y), col = "darkred", lwd = 2)
grid()
## End(Not run)
## Not run:
## Show some more fractal surves
n <- 8
opar <- par(mfrow=c(2,2), mar=c(2,2,1,1))
z <- fractalcurve(n, which="dragon")
x <- z$x; y <- z$y
plot(x, y, type='l', col="darkgrey", lwd=2)
title("Dragon Curve")
z <- fractalcurve(n, which="molecule")
x <- z$x; y <- z$y
plot(x, y, type='l', col="darkblue")
title("Molecule Curve")
z <- fractalcurve(n, which="arrowhead")
x <- z$x; y <- z$y
plot(x, y, type='l', col="darkgreen")
title("Arrowhead Curve")
z <- fractalcurve(n, which="snowflake")
x <- z$x; y <- z$y
plot(x, y, type='l', col="darkred", lwd=2)
title("Snowflake Curve")
par(opar)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.