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POV-Ray-complex-functions

POV-Ray v3.7 include file for working with complex functions

List of available complex operators

Images created with the examples:

j = Sqrt(-1)
Z = re + im*j
Re(Z) = re
Im(Z) = im
|Z| = Sqrt(re^2 + im^2)

Isosurface with domain colors of a complex function

F(Z) = 1/(Z5 - 2)2

x-axis y-axis z-axis
re |F(Z)| im

Source code
Image - Isosurface - Five poles

Mesh with domain colors of a complex function

F(Z) = 1/(Z5 - 2)2

x-axis y-axis z-axis
re |F(Z)| im

Source code
Image - Mesh - Five poles - Magn

Mesh with domain colors of a complex function

F(Z) = 1/(Z5 - 2)2

x-axis y-axis z-axis
re Re(F(Z)) im

Source code
Image - Mesh - Five poles - Real

Mesh with domain colors of a complex function

F(Z) = 1/(Z5 - 2)2

x-axis y-axis z-axis
re Im(F(Z)) im

Source code
Image - Mesh - Five poles - Imag

Mesh with domain colors of a complex function

F(Z) = (Z2 + 1)/(Z2 - 1)

x-axis y-axis z-axis
re |F(Z)| im

Source code
Image - Mesh - Two zeros & Two poles

Mesh with domain colors of a complex function

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis y-axis z-axis
re Ln(|F(Z)|) im

Source code
Image - Mesh - Hue stripes & Magnitude height

Plane with domain colors of a complex function (Ln magnitude scale)

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis z-axis
re im

Source code
Image - Plane - Hue ramps & Magnitude ramps

Plane with domain colors of a complex function (Ln magnitude scale)

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis z-axis
re im

Source code
Image - Plane - Hue ramps & Magnitude stripes

Plane with domain colors of a complex function (Ln magnitude scale)

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis z-axis
re im

Source code
Image - Plane - Hue stripes & Magnitude ramps

Plane with domain colors of a complex function (Ln magnitude scale)

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis z-axis
re im

Source code
Image - Plane - Hue stripes & Magnitude stripes

Mesh with domain colors of magnitude of a complex function

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis y-axis z-axis
re |F(Z)| im

Source code
Image - Mesh - Hue stripes & Magnitude height

Mesh with domain colors of real part of a complex function

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis y-axis z-axis
re Re(F(Z)) im

Source code
Image - Mesh - Hue stripes & Real height

Mesh with domain colors of imaginary part of a complex function

F(Z) = (-Z3 + Z2*j + 1)/(Z - 1 + j)2

x-axis y-axis z-axis
re Im(F(Z)) im

Source code
Image - Mesh - Hue stripes & Imag height

Plane with domain colors of the 7th iterate of a complex function (Ln magnitude scale)

G(Z) = (1 + j)*Sin(Z)

F(Z) = G7(Z) = G(G(G(G(G(G(G(Z)))))))

x-axis z-axis
re im

Source code
Image - Plane - Iterated function