unit Unit4;
{
This software has been designed and it is
CopyLefted by Han de Bruijn:

                          (===)
                         @-O^O-@
                          #/_\#
                           ###
}
INTERFACE

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtCtrls, Grafisch;

type
  TForm1 = class(TForm)
    Image1: TImage;
    procedure Toetsdruk(Sender: TObject; var Key: Char);
    procedure Scheppen(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

IMPLEMENTATION

{$R *.dfm}

var
  veel : integer;

procedure Stern_Brocot(getal : double);
{
  Walk through Stern-Brocot tree
}
const
  dik : integer = 4;
var
  m1,m2,n1,n2 : integer;
  OK : boolean;
begin
{ Initialize tree }
  m1 := 0; n1 := 1;
  m2 := 1; n2 := 0;
  with Form1.Image1.Canvas do
  begin
    Brush.Color := clBlack;
    Pen.Width := 1;
    Pen.Color := clBlack;
    Ellipse(x2i(n2)-dik,y2j(m2)-dik,x2i(n2)+dik,y2j(m2)+dik);
    Ellipse(x2i(n1)-dik,y2j(m1)-dik,x2i(n1)+dik,y2j(m1)+dik)
  end;

  while true do
  begin
    OK := (m1 < veel) and (m2 < veel)
      and (n1 < veel) and (n2 < veel);
    if not OK then Break;
    if getal < (m1+m2)/(n1+n2) then
  { Tightening }
    begin
    { Upper Bound }
      m2 := m1+m2;
      n2 := n1+n2;
      with Form1.Image1.Canvas do
        Ellipse(x2i(n2)-dik,y2j(m2)-dik,x2i(n2)+dik,y2j(m2)+dik);
    end else begin
    { Lower Bound }
      m1 := m1+m2;
      n1 := n1+n2;
      with Form1.Image1.Canvas do
        Ellipse(x2i(n1)-dik,y2j(m1)-dik,x2i(n1)+dik,y2j(m1)+dik);
    end;
  end;
end;

procedure tekenen(r : double; wat : integer);
var
  i,j : integer;
  x,y : double;
begin
  with Form1.Image1.Canvas do
  begin
    Brush.Color := clWhite;
    Pen.Width := 1;
    Pen.Color := clBlack;
  end;
  for i := 0 to veel do
  begin
    for j := -1 to veel-1 do
    begin
      with Form1.Image1.Canvas do
      Ellipse(x2i(i)-2,y2j(j)-2,x2i(i)+2,y2j(j)+2);
    end;
  end;
  with Form1.Image1.Canvas do
  begin
    Pen.Width := 2;
    if wat = 1 then
    begin
      Pen.Color := clRed;
      y := -ln(r)/ln(3);
      MoveTo(x2i(0),y2j(y));
      x := xmax;
      y := ln(2)/ln(3)*x - ln(r)/ln(3);
      LineTo(x2i(x),y2j(y));
    end;
    Pen.Color := clYellow;
    MoveTo(x2i(0),y2j(ymin));
    LineTo(x2i(0),y2j(ymax));
    MoveTo(x2i(xmin),y2j(0));
    LineTo(x2i(xmax),y2j(0));
    Pen.Color := clBlue;
    MoveTo(x2i(0),y2j(0));
    x := xmax;
    y := ln(2)/ln(3)*x;
    LineTo(x2i(x),y2j(y));
  end;
  if wat = 0 then Stern_Brocot(ln(2)/ln(3));
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  Inactive
}
begin
  veel := 25;
  xmax := veel;
  ymax := veel-1;
  ClearDevice;
  tekenen(sqrt(2),1);
  Form1.Image1.Picture.SaveToFile('red_blue.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  At moment of creation
}
begin
  veel := 50;
  xmin := 0; xmax := veel;
  ymin := -1 ; ymax := veel-1;
  TV(Form1.Image1);
  ClearDevice;
  tekenen(sqrt(2),0);
  Form1.Image1.Picture.SaveToFile('stern_brocot.bmp');
end;

END.