February 10, 2013
Conformal Map Viewer
Have you ever wanted a visualization tool for complex functions?
The starting function "(z)" is the identity function, and shows how the tool colors the complex plane, with a ring at |z| = 1 and a small circle at |z| < 1/16, and 1/16th unit colored checkers on the rest of the plane. There is also a colored circle shown towards infinity, at |z| > 16. Colors are turquoise in the positive direction, red in the negative, gold-green in the "+i" direction, and they get darker as you go out towards infinity. The tool draws a quick fuzzy preview; wait a minute for it to complete the computation for a clear antialiased rendering. Lots of other functions can be typed into the box. For example, notice that |z|*e^(i*arg(z)) is the same as z.
Try visualizing the complex values in z^2, sin(z), e^z, log(z), sech(z), arctan(z), z^3-1, sin(z^3-1)/z, Jacobi elliptical functions sn(z,0.3), the Gamma function gamma(z), or a polynomial to squeeze a circle into a square 0.926(z+7.3857e-2 z^5+4.5458e-3 z^9).
Or try this: iter(z+z'^2,z,12). Recognize it?Posted by David at February 10, 2013 01:54 AM
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