MandelbrotSet/MoonShadowPostscript

%! Postscript code to draw the Mandelbrot Set.
% Shove this in a file called mandelbrot.ps or something,
% and use a postscript viewer like Ghostview.
% It takes a while. 
% Adjustable stuff -----------------------------------------------------

/x_start -2 def				% Initial x value (real part)
/y_start -2 def				% Initial y value (imaginary)
/x_end 2 def				% Final x value (real part)
/y_end 2 def				% Final y value (imaginary)
/max 250 def     			% Maximum number of iterations
/quality 1.0 def            % Rendering quality, 1.0 = 100% .. 0.5=50% .. 0.1 = 10%

% General procedures -----------------------------------------------------
/inch {72 mul} def
/minimum {% Return the lesser of two top stack values
	/b exch def
	/a exch def
	a b le {a} {b} ifelse
} def
/maximum {% Return the greater of two top stack values
	/b exch def
	/a exch def
	a b gt {a} {b} ifelse
} def

% Scaling things for the page
/page_width 8.5 inch def
/page_height 11 inch def
page_width 2 div page_height 2 div translate	% Set origin at center of page

/x_domain x_end x_start sub def		% Domain of x numbers
/x_range page_width .9 mul def		% Horizontal space on page, w/ margins
/x_scale x_range x_domain div def	% Maximum x scaling factor
/y_domain y_end y_start sub def		% Domain of y numbers
/y_range page_height .9 mul def		% Vertical space on page, w/ margins
/y_scale y_range y_domain div def	% Maximum y scaling factor
/page_scale x_scale y_scale minimum def	% Final scaling factor	

page_scale dup scale % Set proper scale

x_domain 2 div x_start add neg	% x distance from image center to origin
y_domain 2 div y_start add neg	% y distance from image center to origin
translate			% move origin so image is centered on page

/xstep x_domain x_range div quality div def
/ystep y_domain y_range div quality div def

/xsize xstep 1.5 mul def % x size of pixel
/ysize ystep 1.5 mul def % y size of pixel

/square {
dup mul
} bind def

/double {
dup add
} bind def

/box {% Draw filled rectangle, size slightly larger than w x h, with (x,y) at bottom left
                        % w h x y
2 index 2 div add       % w h x (y+h/2)
moveto                  % w h 
setlinewidth            % w
0 rlineto stroke
} bind def

% Plot points in Mandelbrot set
x_end xstep x_start {
	y_end ystep y_start {
                  % lx . . ly
		max       % lx . . ly count
		4 index   % lx . . ly count x
		2 index   % lx . . ly count x y 
		{
                            % args: x y

		    2 copy 2 copy         % x y x y x y
		    sub                   % x y x y x-y
		    3 1 roll add          % x y x-y x+y
		    mul                   % x y x*x-y*y
		    7 index add           % x y x*x-y*y+x
		    3 1 roll mul double   % x*x-y*y+x 2xy
		    3 index add           % x' y'
	    		    
		    2 copy 2 copy         % x y x y x y
		    sub                   % x y x y x-y
		    3 1 roll add          % x y x-y x+y
		    mul                   % x y x*x-y*y
		    7 index add           % x y x*x-y*y+x
		    3 1 roll mul double   % x*x-y*y+x 2xy
		    3 index add           % x' y'
	    		    
		    2 copy 2 copy         % x y x y x y
		    sub                   % x y x y x-y
		    3 1 roll add          % x y x-y x+y
		    mul                   % x y x*x-y*y
		    7 index add           % x y x*x-y*y+x
		    3 1 roll mul double   % x*x-y*y+x 2xy
		    3 index add           % x' y'
	    		    
		    % check exit condition
		    2 copy square         % x y x y*y
		    exch square           % x y y*y x*x
		    2 copy add 4 ge {     % copy y*y+x*x and check if we can bail out
		         pop pop pop pop            % kill locals
		         max div setgray            % set colour
		         xsize ysize 5 index 3 index box
		         exit
		    } if
		    sub neg               % x y x*x-y*y
		    7 index add           % x y x*x-y*y+x
		    3 1 roll mul double   % x*x-y*y+x 2xy
		    3 index add           % x' y'

			3 -1 roll             % get counter
			4 sub                 % update counter
			dup 4 lt {
			    pop pop pop                 % kill locals
			    0 setgray                   % black
			    xsize ysize 5 index 3 index box 
			    exit
			} if
			3 1 roll              % put counter back
			
		} loop
    		            % end step val
		1 index add     % end step val'
		dup 3 index     % end step val' val' end
		gt {exit} if    % loop?
    		            % end step val'            		
	} loop pop pop pop
                    % end step val
	1 index add     % end step val+step
	dup 3 index     % end step val+step val+step end
	gt {exit} if    % loop?
		            % end step val'
} loop pop pop pop

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