Description Usage Arguments Details Value Author(s) References Examples

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.

1 2 | ```
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.

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 38 39 40 41 42 43 | ```
## 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)
``` |

```
```

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