%!
%
% Date: Tue, 25 Oct 88 10:42:30 EDT
% To: NeWS-makers@brillig.umd.edu
% Subject: Wallpaper for the Mind
% From: pterodactyl.cis.ohio-state.edu!zwicky@tut.cis.ohio-state.edu  (Elizabeth D. Zwicky)
% 
% This program colors in a window, picking the color of each point by
% calculating the value of a formula in x and y. Unfortunately, you
% must specify the formula in PostScript (I wasn't up to writing a small
% mathematical language to use to specify the formula in). It is cute in
% black and white, and spectacular in colour.
% 
% 	Elizabeth Zwicky  (zwicky@cis.ohio-state.edu)
% 

% Send comments to Elizabeth Zwicky (zwicky@cis.ohio-state.edu)

%
% Date: Mon, 6 Nov 89 01:26:23 -0500
% To: NeWS-makers@brillig.umd.edu
% Subject: Integers, mod, and some wallpaper patches
% From: zodiac!sparkyfs!sparkyfs.itstd.sri.com!zwicky@ames.arc.nasa.gov  (Elizabeth Zwicky)
% 
% Wallpaper, as many of you know, is a little program of mine that
% wastes CPU cycles charmingly by coloring in the points in a window
% according to the value of an equation in x and y which you type at it.
% It calculates the colour to make the points with a mod (by 2 in
% monochrome, by 6 in colour). You can only mod an integer. Thus, I have
% learned more about integers in NeWS than I ever wanted to know.
% 
% In particular, div and exp are both documented in the Red Book as
% always returning reals. In NeWS, when div returns an integer, it is
% type integer. This makes sense, given that the NeWS manual says that
% any real small enough to be an integer (i.e., that will fit in 16 bits
% of integer and 16 bits of fraction), will be an integer, which will
% magically look like a real to type. So div should be returning a real,
% which is small enough to be converted into an integer, which then gets
% turned back into a real if it has a fractional part. Confusing, but
% fine. That is, until you get to exp, which really truly does always
% return a real; "2 2 exp dup = type =" will give you "4 realtype". What
% a nusiance.
% 
% Next, we have mod and idiv, both of which are documented in the red
% book as requiring integer arguments. mod does in fact require
% arguments of type integer, and will return a typecheck if run on 2.4,
% 2 2 exp, or any number over 32767. idiv neither requires integer
% arguments, *nor is guaranteed to return them*; try "2 17 exp 2 idiv
% type =". I assume this is due to the magic conversion of integers to
% reals once they get to big; on the other hand, since mod will return a
% typecheck, it is not helpful. Then again, cvi does no better; try
% "32768 cvi type =". Just what I wanted; a real result from converting
% to an integer. And once again, mod will blow up.
% 
% Enough complaint: on to the promised patches. If you plug this in, and
% change all existing instances of "mod" to "mod*" you will allow
% wallpaper to cope with numbers up to 32767^2, which should be enough
% latitiude to do something amusing:
%  /mod*{ % mod big numbers. Initial stack: number-to-mod number-to-mod-by
%    /to-mod-by exch def /to-mod exch def
%    to-mod 32767 gt
%      {
%      /to-mod-idiv to-mod 32767 idiv cvi def
%      /to-mod-mod to-mod 32767 to-mod-idiv mul sub cvi def
%      to-mod-idiv 32767 to-mod-by mod mul
%      to-mod-mod to-mod-by mod add
%      to-mod-by mod
%      }
%      {to-mod  cvi to-mod-by mod}
%    ifelse
%  } def
% 
% If you replace the definition of "dot" with this, it will scale
% correctly even under OpenWindows:
% /dot {-.5 -.5 rmoveto 0 1 rlineto 1 0 rlineto 0 -1 rlineto -1 0
%  rlineto closepath fill pause} def
% (This compensates for a new bug in OpenWindows, in which a degenerate
% line (what you get with 0 0 rlineto) does appear if it is a single
% dot, even if the linecaps are set to 0, but does not appear at above
% that size, even if linecap is set to 2. The linecaps matter because
% the Red Book says so, although I admit to having used the previous
% NeWS bug, which allowed you to use linecap 1 on single-point paths,
% giving nice square dots.)
% 
% 	Elizabeth

% 
% Set up LiteItem if nothing else has
systemdict /Item known not { (NeWS/liteitem.ps) run } if

% If I redefine something, I want it redefined!
false setautobind

% Predefinitions
/height null def /width null def
/Red 1 0 0 rgbcolor def 
/Blue 0 0 1 rgbcolor def
/Green .2 1 .2 rgbcolor def
/Yellow 1 1 0 rgbcolor def
/Purple .7 0 1 rgbcolor def
/Orange 1 .5 0 rgbcolor def
/colors [Red Orange Yellow Green Blue Purple] def
/startx{1} def /starty{1} def
/div*{ dup 0 eq {pop pop 0}{div}ifelse}def
/magnify 1 def
/scalefactor 1 def
/x{realx magnify div}def
/y{realy magnify div} def
/detail 1 def
/formula{x cos y mul y sin x mul add} def
/function{ formula detail mul}def
/first true def
/helpwindow null def
/called false def

% Draw a dot; works with linecap 1 or 2 on NeWS, but only with 1 in standard
%/dot{ 0 0 rlineto stroke  pause} def
/dot {-.5 -.5 rmoveto 0 1 rlineto 1 0 rlineto 0 -1 rlineto -1 0
 rlineto closepath fill pause} def

/mod*{ % mod big numbers. Initial stack: number-to-mod number-to-mod-by
  /to-mod-by exch def /to-mod exch def
  to-mod 32767 gt
    {
    /to-mod-idiv to-mod 32767 idiv cvi def
    /to-mod-mod to-mod 32767 to-mod-idiv mul sub cvi def
    to-mod-idiv 32767 to-mod-by mod mul
    to-mod-mod to-mod-by mod add
    to-mod-by mod
    }
    {to-mod  cvi to-mod-by mod}
  ifelse
} def

% Draw a row of dots
/line{
    width{
	gsave 
	colorcanvas 
	   {colors function cvi 6 mod* abs get setcolor dot} 
	   {function cvi 2 mod* abs 1 eq {dot} if} 
	ifelse 
	grestore
	1 0 rmoveto
	/realx realx 1 add def 
    }repeat
    gsave 
    colorcanvas 
        {colors function cvi 6 mod* abs get setcolor dot} 
        {function cvi 2 mod* abs 1 eq {dot} if} 
    ifelse 
    grestore
}def

% Draw a windowfull of rows
/square{
    width 0 rmoveto 
    height{
	width neg 1 rmoveto 
	/realx startx def 
	/realy realy 1 add def 
	line
    }repeat
}def

% Create window to draw in
/paperwindow framebuffer /new DefaultWindow send def

{% Set up main window
    /PaintClient{ % Clear, reset size, position, color, current point,
	% and redraw 
	erasepage 
	2 setlinecap 1 setlinewidth
	scalefactor scalefactor scale
	clipcanvaspath pathbbox /height exch store /width exch  store 
	/width width scalefactor div truncate 1 add scalefactor mul store
	/height height scalefactor div truncate 1 add scalefactor mul store
	0 setgray  0 0 moveto
	/realx startx def /realy starty def 
	square
    } def

    /FrameLabel (Wallpaper) def

    /destroy{
	% Kill subwindows
	first not {/destroy helpwindow send} if
	% Will die even during redraw
	PaintProcess null ne
	{
	PaintProcess killprocessgroup}
	if
	FrameEventMgr null ne
	{
	FrameCanvas /Mapped false put FrameEventMgr killprocessgroup} 
	if
	currentprocess killprocessgroup
	
    } def

    /ClientMenu [
	(Zoom In) 
	{/magnify magnify 2 mul store /paint paperwindow send}
	(Zoom Out)
	{/magnify magnify 2 div store /paint paperwindow send} 
	(Scale Up)
	{/scalefactor scalefactor 2 mul store /paint paperwindow send }
	(Scale Down)
	{/scalefactor scalefactor 2 div store /paint paperwindow send}
	(Add Detail)
	{/detail detail 2 mul store /paint paperwindow send}
	(Remove Detail) {/detail detail 2 div store /paint paperwindow send}
	(Move Bottom Left Corner) 
	{
	    /xhair /xhair_m paperwindow /ClientCanvas get setstandardcursor
	    getclick 
	    /starty exch starty add store 
	    /startx exch startx add store
	    /ptr /ptr_m paperwindow /ClientCanvas get setstandardcursor
	    /paint paperwindow send
	} 
	(Help) {first {help} if }
    ]
    /new DefaultMenu send def
}paperwindow send

/help {% Put up help file in window
    % Make help window
    /helpwindow framebuffer /new DefaultWindow send store
    (Times-Roman) findfont 14 scalefont setfont
    0 0  310 460 /reshape helpwindow send
    framebuffer setcanvas 
    paperwindow /FrameCanvas get getcanvaslocation 570 sub
    /move helpwindow send

    helpwindow /ClientCanvas get setcanvas
	{
	    /PaintClient{
		clippath pathbbox  /place exch def pop pop pop
		helptext
		 { 
		     /place place 14 sub def
		     5 place moveto
		     show
		 } forall
	     } def
	     /destroy { % Gentle destroy; does not take other things with it
		 helpwindow /IconCanvas get /Mapped false put
		 helpwindow /FrameCanvas get /Mapped false put
		 helpwindow /ClientCanvas get /Mapped false put
		 helpwindow /FrameEventMgr get killprocess
		 /first true store
	     }def
	 } helpwindow send
     /first false store
     /map helpwindow send
 } def

 % Actually put main window up
 /reshapefromuser paperwindow send
 /map paperwindow send

 % Create, position and size formulawindow
 /formulawindow framebuffer /new DefaultWindow send def
 100 100 300 110 /reshape formulawindow send
 paperwindow /FrameCanvas get getcanvaslocation 110 sub /move formulawindow send
 {	
    /destroy{
	/destroy paperwindow send
    } def
 } formulawindow send
 % Don't want the string every time it's changed; gonotify really
 % does the notification
 /formulanotify {}  def 
 /gonotify{/formula itemdict /formulaitem get /ItemValue get dup length string copy cvx store /paint paperwindow send} def

 /itemdict dictbegin 
     /formulaitem (Formula:)(x cos y mul y sin x mul add)
	 /Right /formulanotify 
	formulawindow /ClientCanvas get 
	1500 10  %Plenty long for real complex formulas!
	/new TextItem send 
	dup 0 0  /move 3 index send pop def 
     /goitem (Press When Formula Is Correct) /gonotify formulawindow /ClientCanvas get 10 40 /new ButtonItem send dup 0 30 /move 3 index send pop def
 dictend def
 itemdict paintitems (Food for randomness) itemdict forkitems
 {/PaintClient {itemdict paintitems} def
  } formulawindow send
 /map formulawindow send

/helptext[
    ("Wallpaper" was inspired by one of Martin)
    (Gardner's Mathematical Recreations columns)
    (in the magazine "Scientific American". It)
    (colors in a coordinate plane by)
    (calculating the value of formula in x and)
    (y for the x and y values of that point,)
    (and picking a color based on that value.)
    (On a color display it uses 6 colors, which)
    (are meant to be red, blue, yellow, purple,)
    (green and orange. On a monochrome screen)
    (it uses only black and white.)
    (  )
    (The formula is specified in the lower)
    (window in PostScript.  A special function,)
    (div*, is available; it is exactly like)
    ("div" except that if you attempt to divide)
    (by zero it returns zero instead of an)
    (error.)
    ( )
    (The "Zoom In" and "Zoom Out" menu options)
    (change the magnification of the plane by)
    (factors of 2; it starts out at device)
    (resolution. Similarly, the "Add Detail")
    (and "Remove Detail" menu options change a)
    (multiplier that is applied to the result)
    (of the formula by factors of 2. The)
    (multiplier starts at 1.  "Move Bottom Left)
    (Corner" places the bottom left corner at)
    (the point on the plane indicated by your)
    (next click (it starts at 0,0).)
]def