Create an image from a rosette function.

rosette.R

library(ggplot2)
library(data.table)

## Implement ideas from creating symmetry
## chapter 7

f <- function(z,a,m,n) a*(z^m*Conj(z)^n)

# Set resolution
N=2000

# Set domain
lim=seq(-1,1,l=N)*.7

# Create points as a dataset
d <- as.data.table(expand.grid(x=lim, y=lim))

# Create z = x + iy
d[, z:=x+1i*y]

# Calculate fz to plot.
# Alter the 'a' parameters to get different pictures that maintain the symmetry.
d[, fz := f(z,a=2i+2,5,0)+
          f(z,a=1i+1,0,5)+
          f(z,a=1,6,1)+
          f(z,a=1,1,6)+
          f(z,a=1,4,-6)+
          f(z,a=1,-6,4)
]

# Map hue, saturation and value to fz however you want
d[, s:=((Arg(fz)+pi)%%(2*pi))/(2*pi)]
d[, h:=.7]
d[, v:=log(Mod(fz))%%1]

# Now plot and save
g<-ggplot(d[is.finite(v)==TRUE],aes(x,y)) + 
  geom_raster(aes(fill=hsv(h,.9*s,v))) + scale_fill_identity() + theme_void() + coord_fixed()
ggsave("test1.jpg",g,dpi="retina", width=2000,height=2000, units = "px")