(*^

::[paletteColors = 128; 
	fontset = title, "New York", 24, L3, center, bold, nohscroll;
	fontset = subtitle, "New York", 18, L2, center, bold, nohscroll;
	fontset = subsubtitle, "New York", 14, L2, center, bold, nohscroll;
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	fontset = subsection, "New York", 12, L2, bold, nohscroll, blackBox;
	fontset = subsubsection, "New York", 10, L2, bold, nohscroll, whiteBox;
	fontset = text, "New York", 12, L2, nohscroll;
	fontset = smalltext, "New York", 10, L2, nohscroll;
	fontset = input, "Courier", 12, L2, bold, nowordwrap;
	fontset = output, "Courier", 12, L2, nowordwrap;
	fontset = message, "Courier", 12, L2, R65535, nowordwrap;
	fontset = print, "Courier", 12, L2, nowordwrap;
	fontset = info, "Courier", 12, L2, nowordwrap;
	fontset = postscript, "Courier", 12, L2, nowordwrap;
	fontset = name, "Geneva", 10, L2, italic, B65535, nowordwrap, nohscroll;
	fontset = header, "Times", 10, L2;
	fontset = footer, "Times", 12, L2, center;
	fontset = help, "Geneva", 10, L2, nohscroll;
	fontset = clipboard, "New York", 12, L2;
	fontset = completions, "New York", 12, L2, nowordwrap;
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	fontset = special4, "New York", 12, L2, nowordwrap;
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:[font = input; initialization; ]
*)
BeginPackage["RDS`"]

RDSPlot::usage ="\n
  RDSPlot[exp,{x,xmin,xmax},{y,ymin,ymax}] returns a random-dot\n
  stereogram of the graph of the function given by exp. Options:\n
    PlotPoints (can be an integer or pair of integers; defaults to 120);\n
    Periods (6); PlotRange ({-1,1}); Density (.5); Depth (1.);\n
    Guides (True); BasicBlock (Rectangle[#,#+1]&).\n
    Other options are passed on to Graphics."

SetAttributes[RDSPlot,HoldFirst];

Options[RDSPlot] := {PlotPoints -> 120, Periods -> 6, Guides -> True,
  PlotRange -> {-1,1}, Density -> .5, Depth -> 1,
  BasicBlock :> (Rectangle[#1-#2,#1+#2]&)}

Begin["`private`"]

Unprotect[Display]
Display[channel_,graphics_?(!FreeQ[#,RDSArray]&)] :=
  (Display[channel,graphics /. 
    (RDSArray[basicblock_,dims_,pts_] :> 
      (basicblock[#,dims]& /@ pts))];
  graphics)
Protect[Display]

RDSPlot[expr_,{x_,xmin_,xmax_},{y_,ymin_,ymax_},opts___] :=
  Block[{pts = PlotPoints /. {opts} /. Options[RDSPlot],
    periods  = Periods    /. {opts} /. Options[RDSPlot],
    zrange   = PlotRange  /. {opts} /. Options[RDSPlot],
    density  = Density    /. {opts} /. Options[RDSPlot],
    depth    = Depth      /. {opts} /. Options[RDSPlot],
    basicblock=BasicBlock /. {opts} /. Options[RDSPlot],
    guides   = Guides     /. {opts} /. Options[RDSPlot],
    strip,xpts,ypts,dx,dy,xval,yval,zmin,zmax,exprnorm},

    {zmin,zmax} = zrange; 
    {xpts,ypts} = If[Length[pts]==2,pts,{pts,pts}];
    dy=(ymax-ymin)/ypts;
    dx=(xmax-xmin)/xpts; strip=Floor[xpts/periods]dx;
    exprnorm=(.25 depth(xmax-xmin)/(periods(zmax-zmin)))*
      (Max[zmin,Min[zmax,expr]]-(zmax+zmin)/2);

    Graphics[{
      RDSArray[basicblock,{dx,dy}/2,
        Flatten[
          Table[
            If[Random[]<density, 
               Thread[{images[exprnorm/.y->yval,{x,xval,xmax,strip}],yval}],
              {}], 
            {yval,ymin+.5dy,ymax,dy}, 
            {xval,xmin+.5dx,image[exprnorm/.y->yval,{x,xmin,strip}],dx}],
          2]],
      If[guides, 
        makeguides[{.5xmax+.5xmin,1.1ymin-.1ymax}, .5strip], 
        {}]},
      Sequence @@
        Select[{opts},
          !MemberQ[First /@ Options[RDSPlot],First[#]]&]]]

image[expr_,{x_,xval_,dx_}] := xval+dx-N[expr/.x->xval+dx/2]

images[expr_,{x_,xval_,xmax_,dx_}] := 
  If[xval<=xmax,
    Prepend[
      images[expr,{x,image[expr,{x,xval,dx}],xmax,dx}],
      xval],
    {}]

makeguides[pos_,size_] := 
  Apply[Rectangle, 
    Map[pos+size #&,
      {{{-1.1,-.1},{-.9,.1}},{{.9,-.1},{1.1,.1}}},{2}],1]

End[]
EndPackage[]
(*
;[o]
BeginPackage[RDS`]; Null; 
 
  RDSPlot::usage = 
 
      RDSPlot[exp,{x,xmin,xmax},{y,ymin,ymax}] returns a\
    
     random-dot                                              ; 
      stereogram of the graph of the function given by exp.\
    
     Options:
        PlotPoints (can be an integer or pair of integers;\
    
     defaults to 120);
        Periods (6); PlotRange ({-1,1}); Density (.5); Depth\
    
     (1.);
        Guides (True); BasicBlock (Rectangle[#,#+1]&).
        Other options are passed on to Graphics.
 
  Null; (SetAttributes[RDSPlot, HoldFirst]; ); Null; 
 
  Options[RDSPlot] := 
 
   {PlotPoints -> 120, Periods -> 6, Guides -> True, 
 
    PlotRange -> {-1, 1}, Density -> 0.5, Depth -> 1, 
 
    BasicBlock :> (Rectangle[#1 - #2, #1 + #2] & )}; Null; 
 
  Begin[`private`]; Null; Unprotect[Display]; 
 
  Display[channel_, (graphics_)?(!FreeQ[#1, RDSArray] & )] := 
 
   (Display[channel, graphics /. 
 
       RDSArray[basicblock_, dims_, pts_] :> 
 
        (basicblock[#1, dims] & ) /@ pts]; graphics); 
 
  Protect[Display]; Null; 
 
  RDSPlot[expr_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, 
 
    opts___] := 
 
   Block[{pts = PlotPoints /. {opts} /. Options[RDSPlot], 
 
     periods = Periods /. {opts} /. Options[RDSPlot], 
 
     zrange = PlotRange /. {opts} /. Options[RDSPlot], 
 
     density = Density /. {opts} /. Options[RDSPlot], 
 
     depth = Depth /. {opts} /. Options[RDSPlot], 
 
     basicblock = BasicBlock /. {opts} /. Options[RDSPlot], 
 
     guides = Guides /. {opts} /. Options[RDSPlot], strip, 
 
     xpts, ypts, dx, dy, xval, yval, zmin, zmax, exprnorm}, 
 
    {zmin, zmax} = zrange; 
 
     {xpts, ypts} = If[Length[pts] == 2, pts, {pts, pts}]; 
 
          ymax - ymin       xmax - xmin
     dy = -----------; dx = -----------; 
             ypts              xpts
 
                    xpts
     strip = Floor[-------] dx; 
                   periods
 
     exprnorm = 
 
      (0.25 depth (xmax - xmin) 
 
                                       zmax + zmin
         (Max[zmin, Min[zmax, expr]] - -----------)) / 
                                            2
 
       (periods (zmax - zmin)); -Graphics-]; Null; 
 
  image[expr_, {x_, xval_, dx_}] := 
 
                                       dx
   (xval + dx) - N[expr /. x -> xval + --]; Null; 
                                       2
 
  images[expr_, {x_, xval_, xmax_, dx_}] := 
 
   If[xval <= xmax, Prepend[images[expr, 
 
      {x, image[expr, {x, xval, dx}], xmax, dx}], xval], {}]; 
 
  Null; makeguides[pos_, size_] := 
 
   Apply[Rectangle, Map[pos + size #1 & , 
 
     {{{-1.1, -0.1}, {-0.9, 0.1}}, {{0.9, -0.1}, {1.1, 0.1}}}, 
 
     {2}], 1]; Null; End[]; EndPackage[]
:[font = input; startGroup; ]
SetOptions[RDSPlot,Periods -> 3, PlotPoints -> 18, Guides -> False]

:[font = output; inactive; output; endGroup; ]
{PlotPoints -> 18, Periods -> 3, Guides -> False, 
  PlotRange -> {-1, 1}, Density -> 0.5, Depth -> 1, 
  BasicBlock :> (Rectangle[#1 - #2, #1 + #2] & )}
;[o]
{PlotPoints -> 18, Periods -> 3, Guides -> False, 
 
  PlotRange -> {-1, 1}, Density -> 0.5, Depth -> 1, 
 
  BasicBlock :> (Rectangle[#1 - #2, #1 + #2] & )}
:[font = input; startGroup; ]
Show[
  RDSPlot[0,{x,-1,1},{y,-1,1},
    BasicBlock :> (Line[
          {#1+{1,1}#2,#1+{1,-1}#2,#1+{-1,-1}#2,#1+{-1,1}#2,#1+{1,1}#2}]&),
    Density->1],
  RDSPlot[.5 y,{x,-1,1},{y,-1,1},
    BasicBlock :> (Rectangle[#1-.5#2,#1+.5#2]&), Density->.6],
  AspectRatio -> Automatic]
:[font = postscript; inactive; PostScript; output; pictureLeft = 37; pictureWidth = 282; pictureHeight = 278; preserveAspect; ]
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