Complex Domain Coloring

September 30, 2014
By

(This article was first published on Ripples, and kindly contributed to R-bloggers)

Why don’t you stop doodling and start writing serious posts in your blog? (Cecilia, my beautiful wife)

Choose a function, apply it to a set of complex numbers, paint  the result using the HSV technique and be ready to be impressed because images can be absolutely amazing. You only need ggplot2 package and your imagination. This is what happens when function is f(x)=(1+i)log(sin((x3-1)/x)):
ComplexDomainColoring

To learn more about complex domain coloring, you can go here. If you want to try your own functions, you can find the code below. I will try to write a serious post next time but meanwhile, long live doodles!

require(ggplot2)
f = function(x) (1+1i)*log(sin((x^3-1)/x))
z=as.vector(outer(seq(-5, 5, by =.01),1i*seq(-5, 5, by =.01),'+'))
z=data.frame(x=Re(z),
y=Im(z),
h=(Arg(f(z))<0)*1+Arg(f(z))/(2*pi),
s=(1+sin(2*pi*log(1+Mod(f(z)))))/2,
v=(1+cos(2*pi*log(1+Mod(f(z)))))/2)
z=z[is.finite(apply(z,1,sum)),]
opt=theme(legend.position="none",
panel.background = element_blank(),
panel.grid = element_blank(),
axis.ticks=element_blank(),
axis.title=element_blank(),
axis.text =element_blank())
ggplot(data=z, aes(x=x, y=y)) + geom_tile(fill=hsv(z$h,z$s,z$v))+ opt

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