Polar rose

It’s fascinating to see how simple mathematical transformations look like in different coordinate systems.  ”Polar rose” is the name of a mathematical curve – described by the polar equation:

Below is a small code to draw it in R using the ggplot2 package:

require(ggplot2)

#data points
p <- data.frame(t=seq(-2*pi, 2*pi, 0.1))

#1.. drawing polar rose
c <- ggplot(p, aes(x=t, y=cos(3*t)))
c + geom_line(colour="red", size=1.5) + coord_polar()

#2.. another one with sine
c <- ggplot(p, aes(x=t, y=2*sin(4*t)))
c + geom_line(colour="red", size=1.5) + coord_polar()

…and the output

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