Domain Coloring
This description may lack mathematical explanation.In this text 'r' represent sqrt(x^2+y^2) .Domain coloring is a method of visualizing complex functions.On a complex plane each point has a real part and imaginary part . When a complex function is evaluated in a range of values its output value may or may not contain imaginary part.Complex numbers can also be represented in polar form( r and theta). The question arises how to draw r and theta of a complex function? To achieve this we can use RGB(red, blue and green) or HSV(hue, saturation and value).By using these color spaces we should be able to map r and theta of complex function to each component of these color spaces.For example how to represent theta in RGB or r in HSV. We select HSV colors .Theta of complex function is directly proportional to the Hue of image .And saturation and brightness are adjusted according to r of the complex function.This is open for experiment and gives a peculiar look to images.In some images real and imaginary values are used to vary the saturation this gives the lines going here and there.
If a complex function is raised to some power which itself is complex.Then resulting image has spirals .How they came I have no knowledge.This is not a standard way to visualize to visualize complex functions.When the complex function is polynomial poles and zeros appear in the image.I don't know whether these can be seen with trigonometric functions or other type of function.