pracma (version 1.9.9)

fractalcurve: Fractal Curves

Description

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.

Usage

fractalcurve(n, which = c("hilbert", "sierpinski", "snowflake", "dragon", "triangle", "arrowhead", "flowsnake", "molecule"))

Arguments

n

integer, the `order' of the curve

which

character string, which curve to cumpute.

Value

Returns a list with x, y the x- resp. y-coordinates of the generated points describing the fractal curve.

Details

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.

References

Peitgen, H.O., H. Juergens, and D. Saupe (1993). Fractals for the Classroom. Springer-Verlag Berlin Heidelberg.

Examples

## 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)