# Complex Domain Coloring

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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

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