fractalcurve: Fractal Curves

Description Usage Arguments Details Value Author(s) References Examples

View source: R/fractalcurve.R

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

1
2
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.

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.

Value

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

Author(s)

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.

References

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

Examples

 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)

Example output



pracma documentation built on Dec. 11, 2021, 9:57 a.m.