How to Draw a Circle with color changing gradually?

I would like to draw a circle with color changing gradually due to value, in which each point in circle area has the value which is defined by a function of variables are radius and rotation angle.

The image enclosed thank you!

Answer 1

[Punit]

http://www.mathworks.com/help/matlab/creating_plots/contour-plot-in-polar-coordinates.html

check this

[Hoang Phuc Ho]

thank you, but if i define the value of each point in the circle area by a matrix of values (because the function is not explicit) , how can i solve in this situation