# Complex Domain Coloring

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)):

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

## 2 thoughts on “Complex Domain Coloring”

1. Jon says:

Just as an asside, why HSV/HSL vice CIELAB?

1. Easy enough to convert from one to the other. De gustibus, etc. BTW, I enjoy a similar task: pick some complex polynomial and color the complex plane according to the root each point converges to via Newton-Raphson.