#version 3.8;
global_settings {assumed_gamma 1}
#declare E = 0.0001;
//#include "ArrayMacros.inc"
#include "functions.inc"
#include "math.inc"
//#include "rand.inc"


#declare Zoom = 10;
camera {
	orthographic
	location <0, 0, -50>
	right x*image_width/Zoom
	up y*image_height/Zoom
	look_at <0, 0, 0>
	rotate y*0
}



camera {
	location <0, 0, -200>
	right     x*image_width/image_height
	up y
	look_at <0, 0, 0>
	
}


light_source {<50, 50, -50> rgb 1}
light_source {<-50, 50, -50> rgb 1}

sky_sphere {pigment {rgb 1}}


#declare Distance = function (X, Y, Z) {sqrt (X*X+Y*Y+Z*Z)}
#declare fmod = function (Value, Modulo) {select (Value, 1 - mod (abs (Value), Modulo), mod (abs (Value), Modulo))}  // this gives a mod function that remains consistant across the origin
#declare Sqr = function (N) {N*N}

#declare ArmSpacing = 0.004;
#declare LineThickness = 0.0004;

#declare Aspect = image_width/image_height;
#declare U = function {x/image_width*Aspect}
#declare V = function {y/image_height}

#declare Angle = function {atan2 (V(x,y,z), U(x,y,z))}
#declare l = function {Distance (U(x,y,z), V(x,y,z), 0)}

#declare Offset = function {l(x,y,z) + ArmSpacing * (Angle(x,y,z)/(tau))}
#declare circles = function {fmod (Offset(x,y,z), ArmSpacing)}

#declare FracTurn = function {abs (l(x,y,z)/ArmSpacing - Angle(x,y,z)/(tau))}
#declare ArcLength = function (b, _Theta) {b/2 * (_Theta * sqrt (1 + _Theta*_Theta) + ln (_Theta + sqrt (1 + _Theta*_Theta)))}

//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness, 0, 1)}
//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness, 0, 0.0+FracTurn(x, y, z))}
//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness,  (ArcLength (l(x,y,z) + ArmSpacing, Angle (x, y, z)-pi)), 0 )}
//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness,  ArcLength ((l(x,y,z)/ArmSpacing+Angle (x, y, z))/10, Angle (x, y, z)-pi), 0 )}
#declare f_Spiral = function {select (circles (x,y,z) - LineThickness,  1-(ArcLength (Offset(x,y,z)*10, Angle (x, y, z)-tau)), 0 )}
//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness, 20*Offset(x, y, z), 1)} // varying thickness
//#declare f_Spiral = function {select (circles (x,y,z) - LineThickness*50*Offset(x, y, z), 20*Offset(x, y, z), 0)} // varying thickness

/*
#define COLOR_RATE 0.1
#define COLOR_RATE2 0.001
#define COLOR_CONST 0.1
float rate = mod(COLOR_RATE+(iTime*COLOR_RATE2), 2.0*PI);
float r = fract(spiral_degrees*rate);
float g = fract(spiral_degrees*(rate+COLOR_CONST));
float b = fract(spiral_degrees*(rate+COLOR_CONST+COLOR_CONST));
*/


#declare Pattern = function {f_Spiral(x, y, z)}
#declare TSpiral = 
	texture {
		pigment {
	        average
	        pigment_map {
	            [
	                function { Pattern (x, y, z) }
	                color_map {
	                    [ 0 red 0 ]
	                    [ 1 red 3 ]
	                }
	            ]
	            [
	                function { Pattern (x, y, z) }
	                color_map {
	                    [ 0 green 0 ]
	                    [ 1 green 3 ]
	                }
	            ]
	            [
	                function { Pattern (x, y, z)}
	                color_map {
	                    [ 0 blue 0 ]
	                    [ 1 blue 3 ]
	                }
	            ]

			} // end pigment map
		} // end pigment
	} // end layered texture

#declare Spiral = pigment {function {f_Spiral(x,y,z)}}
plane {z, 0 texture {TSpiral finish {diffuse 1}}}

// float offset=abs(o.x)+abs(o.y)+(angle/(2.*PI))*dis;	// square spiral
// float offset=(log(l)+(angle/(2.*PI))*dis);	// log spiral
// float offset=(log(l)/log(e*5.)+(angle/(2.*PI))*dis);	// wider log spiral