"Bald Eagle" <cre### [at] netscapenet> wrote:
> Over the last 2 days, I've fallen down the mathematical pattern rabbit hole, and
> have been experimenting with all manner of what can be done with a simple
> pigment {function {}}
> statement.
>

Two older ones for your collection. Thing I found on the web years ago:

---%<------%<---
// Persistence of Vision Ray Tracer Scene Description File
// File: contour.pov
// Vers: 3.5
// Desc: contour plots Idea: Eric Weeks
// http://www.physics.emory.edu/~weeks/ideas/tplot.html
// Date: 2003
// Auth: Ingo Janssen

#version 3.5;

#include "gradients.inc"
//https://news.povray.org/povray.binaries.scene-files/message/%3CXnsA9D7C1F3776F3seed7%40news.povray.org%3E/#%3CXnsA9D7
C1F3776F3seed7%40news.povray.org%3E

global_settings {assumed_gamma 1.0}
camera {location <0,0,-25> look_at 0}

#declare Contour = function(x,y,z,A,B,C,D,E,F,I,J,K,L) {
  E*sin(A*sin(I*x)+ B*cos(J*y))+F*cos(C*cos(K*x)+D*sin(L*y))
}

#declare A =1;
#declare B =1;
#declare C =1;
#declare D =1;
#declare E =1;
#declare F =1;

#declare I =1;
#declare J =1;
#declare K =1;
#declare L =1;

#declare Test  = function(Pf){
   (G_smoothstep(Pf,0.1,0.15)-G_smoothstep(Pf,0.15,0.2))
  +(G_smoothstep(Pf,0.4,0.6)-G_smoothstep(Pf,0.7,.9))
};

plane {
  -z, 0
  pigment {
    function{Contour(x,y,z,A,B,C,D,E,F,I,J,K,L)}

    //function{G_Blinn_Wyvill(Contour(x,y,z,A,B,C,D,E,F,I,J,K,L))}

    //function{Test(Contour(x,y,z,A,B,C,D,E,F,I,J,K,L))}

    //function{abs(Contour(x,y,z,A,B,C,D,E,F,I,J,K,L))}

    //sine_wave
    colour_map {
      [0 rgb 0]
      [1 rgb 1]
    }
  }
  finish {ambient 1}
}
---%<------%<---

---%<------%<---
// POV-Ray 3.7
// Ingo
// found on a Japanese site
// +w1280 +h480 +a0.05 +am3 +ac0.90 +r3
#version 3.7;
global_settings{assumed_gamma 1}
#default{ finish{ambient 0 diffuse 1}}
camera {
  orthographic
  location <0,0,1>
  look_at 0
  right x*image_width/image_height
}
#declare PHI = 1.61803399;

// Shuhei Kawachi
// A>0
#declare ShuheiKawachi = function (x,y,z,A,B){
  ((cos(x)*cos(y)+cos((sqrt(A)*x-y)/B)*
  cos((x+sqrt(A)*y)/B)+cos((sqrt(A)*x+y)/B)*
  cos((x-sqrt(A)*y)/B)))/3///6 + 0.5
}


plane{ <0,0,-1>, 0
  texture {
    pigment {
      //function{(ShuheiKawachi(x,y,z,pi,1.5))}
      function{abs(ShuheiKawachi(x,y,z,pi,1.5))}
      sine_wave
      scale 0.02
    }
    finish {ambient 1 diffuse 0}
  }
}
---%<------%<---

ingo

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