/*
 * First we declare a pattern function. crackle form x suits our needs
 * pretty well, from the POV docs:
 * "Another commonly-used form is <1,0,0>, corresponding to the distance 
 *  to the closest point, which produces a pattern that looks roughly like
 *  a random collection of intersecting spheres or cells."
*/

#declare f_crackle_form =
	function { pattern { crackle form <1,0,0> } }


/*
 * To get that linear 0 -> 1 curve a bit more interesting, declare
 * a "crater-shaped" spline function through which to put the pattern. 
 * A bit of tweaking will probably make it look better.
*/

#declare f_crater_spline =
	function {
		spline {
			cubic_spline	
			0.0, 0.4*x   // From the center...
			0.01, 0.3*x
			0.03, 0*x
			0.12, 0.1*x
			0.24, 0.2*x
			0.3, 1*x
			0.4, 0.9*x
			0.6, 0.7*x
			1.0, 0.5*x   // ...outwards.
		}
	}


/*
 * Next we create the actual crater field pattern. It is basically 
 * a 1/f fractal pattern, similar in principle to how granite or 
 * f_ridged_mf work internally. It adds together several layers of 
 * the crackle pattern, varying the frequency (scale) and amplitude.
*/

/*
 * First, declare some variables to parametrize the pattern creation.
*/

/*
 * The octaves, ie. the number of fractal layers to use.
*/

#declare O = 6;

/*
 * The "lambda" or "lacunarity" value. The multiplier used to
 * determine the frequency/amplitude "gap" between octaves.
*/

#declare L = 2;  


/*
 * Build the pattern with a #while loop.
*/

#declare f_craters =
	function {

		#declare I = 0;
		#declare M = 1;

		/* 
 		 * The 1-exp(-x) function is just used to keep the value
 		 * below 1 (its limit in infinity is 1). I don't think it is
	   * actually needed if the function is not used in a pigment,
	   * but... Again, this needs more experimenting.
		*/

		1-exp(-(
			
			#while(I < O)
				#declare M = L * M;
				
				+ 
				f_crater_spline(
					f_crackle_form(x * M, y * M + I, z * M)
				).x / M
				
				#declare I = I + 1;
			#end

		))
	}


/*
 * Here's the final function to be used with a height field
 * or an isosurface.
*/

#declare Craters =
	function {
		pattern  {
			function { f_craters(x,y,z) }
			
			/*
	     * Apply some turbulence. Could use some tweaking.
	    */
			
			scale 100
			warp { turbulence 0.4 }
			scale 1/100
		}
	}