Complex numbers, beautiful surfaces and Mathematica

Posted February 9th, 2013 by admin & filed under Code, Graphics, Mathematica, Wolfram.

A few lines of code in Mathematica can produce beautiful images. Take as an example this simple but spectacular result of singularities in complex plane:

$f(x)=\Im\left(\frac{1}{\cos \left((x+i y)^4\right)}\right)$

Plot3D[Im[Sec[(x + I y)^4]], {x, -2, 2}, {y, -2, 2}, 
   Mesh -> None,  
   ClippingStyle -> None,  
   PlotStyle -> Directive[Orange, Opacity[.8], Specularity[White, 20]],  
   PlotPoints -> 50]