(* IFS for a disk using two maps                        *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, Aug 1993  *)
(*  n = number of points, e.g. 1000                     *)
(*  In polars,  r = radius,  a = angle                  *)

DiskIFS0[n_] :=
 Block[{r = Random[], a = 2 Pi Random[], pts = {}, rr},
  For[i=0, i < n, i++,
	rr = N[a/(2*Pi)];
	a = N[Pi(r + Random[Integer])];
	r = rr;
	AppendTo[pts, {r*Cos[a], r*Sin[a]}]
  ];
  ListPlot[pts,
	PlotStyle->{PointSize[0.01]}, 
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic
  ]
 ]
 
DiskIFS0[1000]

(* IFS for a disk with constant density, using two maps *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, Aug 1993  *)
(*  n = number of points, e.g. 1000                     *)
(*  In polars,  r = radius,  a = angle                  *)

DiskIFS[n_] :=
 Block[{r = Random[], s, pts = {}, j, rr},
  s = r*Random[];
  For[i=0, i < n, i++,
	j = Random[Integer];
	rr = 0.5*s + r*(0.5 - j) + j;
	s = 0.5*r + s*(j - 0.5);
	r = rr;
	a = If[r==0, 0, N[2*Pi*s/r]];
	AppendTo[pts, {r*Cos[a], r*Sin[a]}]
  ];
  ListPlot[pts,
	PlotStyle->{PointSize[0.01]}, 
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic
  ]
 ]
 
DiskIFS[1000]

(* IFS for a disk with constant density, using two maps *)
(* with two colours                                     *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, Aug 1993  *)
(*  n = number of points, e.g. 1000                     *)
(*  r = radius in polars,  a = angle,                   *)
(*  0 <= r <= 1,  -r <= s <= r,  j = 0 or 1             *)

DiskIFS2[n_] := 
 Block[{r = Random[], s, pts, j, rr},
  s = r*Random[];
  pts[0] = {}; pts[1] = {};
  For[i=0, i < n, i++,
	j = Random[Integer];
	rr = 1 - 0.5*r - (0.5 - j)*s;
	s = (0.5 - j)*r - 0.5*s;
	r = rr;
	a = If[r==0, 0, N[(Pi*s/r)]];
	AppendTo[pts[j], Point[{r*Cos[a],r*Sin[a]}]]
  ];
  Show[Graphics[{
  	{PointSize[0.01], RGBColor[0,0,1], pts[0]},
	{PointSize[0.01], RGBColor[1,0,0], pts[1]}}],
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic, Axes -> True
  ]
 ]
 
DiskIFS2[1000]

(* IFS for a disk with constant density, using two maps *)
(* with four colours                                    *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, May 1994  *)
(*  n = number of points, e.g. 1000                     *)
(*  r = radius in polars,  a = angle,                   *)
(*  0 <= r <= 1,  -r <= s <= r                          *)  
(*  j = 0 or 1, j1 = 0 or 1                             *)

DiskIFS4[n_] := 
 Block[{r = Random[], s, pts, j, j1, rr},
  s = r*Random[];
  pts[0] = {}; pts[1] = {}; 
  pts[2] = {}; pts[3] = {};
  For[i=0, i < n, i++,
	j = Random[Integer];
	rr = 1 - 0.5*r - (0.5 - j)*s;
	s = (0.5 - j)*r - 0.5*s;
	r = rr;
	a = If[r==0, 0, N[(Pi*s/r)]];
	AppendTo[pts[2*j1+j], 
		Point[{r*Cos[a],r*Sin[a]}]];
	j1 = j
  ];
 Show[Graphics[{
 	{PointSize[0.01], RGBColor[0,0.7,1], pts[0]},
  	{PointSize[0.01], RGBColor[1,0,0], pts[1]},
  	{PointSize[0.01], RGBColor[0,0,1], pts[2]},
	{PointSize[0.01], RGBColor[1,0.5,0], pts[3]}}],
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic, Axes -> True
  ]
 ]
 
DiskIFS4[1000]

(* Yin-Yang IFS for a disk,                             *)
(* using two maps with two colours                      *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, May 1994  *)
(*  n = number of points, e.g. 1000                     *)
(*  r = radius in polars,  a = angle,                   *)
(*  0 <= r <= 1,  -r <= s <= r,  j = 0 or 1             *)

YinYangIFS[n_] := 
 Block[{r = Random[], s, pts, j, rr, a},
  s = r*Random[];
  pts[0] = {}; pts[1] = {};
  For[i=0, i < n, i++,
	j = Random[Integer];
	rr = 1 - 0.5*r - (0.5 - j)*s;
	s = (0.5 - j)*r - 0.5*s;
	r = rr;
	a = If[r==0, 0, N[(Pi*s/r) + ArcCos[r]]];
	AppendTo[pts[j], Point[{r*Cos[a],r*Sin[a]}]]
  ];
  Show[Graphics[{
  	{PointSize[0.01], RGBColor[0,0,1], pts[0]},
	{PointSize[0.01], RGBColor[1,0,0], pts[1]}}],
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic, Axes -> True
  ]
 ]
 
YinYangIFS[1000]

(* Yin-Yang IFS for a disk,                             *)
(* using two maps with four colours                     *)
(* Mathematica 3.0 code                                 *)
(* written by Will Gilbert, Univ of Waterloo, May 1994  *)
(*  n = number of points, e.g. 1000                     *)
(*  r = radius in polars,  a = angle,                   *)
(*  0 <= r <= 1,  -r <= s <= r,  j = 0 or 1             *)

YinYangIFS4[n_] := 
 Block[{r = Random[], s, pts, j, j1, rr, a},
  s = r*Random[];
  pts[0] = {}; pts[1] = {};
  pts[2] = {}; pts[3] = {};
  For[i=0, i < n, i++,
	j = Random[Integer];
	rr = 1 - 0.5*r - (0.5 - j)*s;
	s = (0.5 - j)*r - 0.5*s;
	r = rr;
	a = If[r==0, 0, N[(Pi*s/r) + ArcCos[r]]];
	AppendTo[pts[2*j1+j], 	
		Point[{r*Cos[a],r*Sin[a]}]];
 	j1 = j
 ];
  Show[Graphics[{
 	{PointSize[0.01], RGBColor[0,0.7,1], pts[0]},
  	{PointSize[0.01], RGBColor[1,0,0], pts[1]},
  	{PointSize[0.01], RGBColor[0,0,1], pts[2]},
	{PointSize[0.01], RGBColor[1,0.5,0], pts[3]}}],
	PlotRange->{{-1,1},{-1,1}}, 
	AspectRatio->Automatic, Axes -> True
  ]
 ]
 
YinYangIFS4[1000]