unit Unit12;
{
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}

const
  veel : integer = 100;

procedure test(r : double);
var
  a : double;
  tel : integer;
  OK : boolean;
begin
  a := 1;
  tel := 0;
  while tel < veel do
  begin
    if a < r then
    begin
      a := a * 2;
    end else begin
      a := a / 3;
    end;
    tel := tel + 1;
    OK := (1/3 < a/r) and (a/r < 2);
    if not OK then Continue;
    with Form1.Image1.Canvas do
    begin
      MoveTo(x2i(a/r),y2j(0));
      LineTo(x2i(a/r),y2j(1));
    end;
  end;
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clRed;
    Pen.Width := 2;
    MoveTo(x2i(1),y2j(0));
    LineTo(x2i(1),y2j(1));
  end;
end;

procedure proef(r : double);
var
  a,l2,l3,lr : double;
  m,n,tel : integer;
  OK : boolean;
begin
  l2 := ln(2); l3 := ln(3);
  lr := ln(r);
  m := 0; n := 0;
  tel := 0;
  while tel < veel do
  begin
    a := m*l2 - n*l3 - lr;
    if a < 0 then m := m + 1 else n := n + 1;
    tel := tel + 1;
    OK := (-ln(3) < a) and (a < ln(2));
    if not OK then Continue;
    with Form1.Image1.Canvas do
    begin
      MoveTo(x2i(a),y2j(0));
      LineTo(x2i(a),y2j(1));
    end;
  end;
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clRed;
    Pen.Width := 2;
    MoveTo(x2i(0),y2j(0));
    LineTo(x2i(0),y2j(1));
  end;
end;

procedure tekenen(wat : integer);
begin
  with Form1.Image1.Canvas do
  begin
    Pen.Width := 1;
    Pen.Color := clBlack;
  end;
  if wat = 0 then test(0.001) else proef(0.001);
  with Form1.Image1.Canvas do
  begin
    Pen.Width := 2;
    Pen.Color := clYellow;
    MoveTo(x2i(xmin),y2j(0));
    LineTo(x2i(xmax),y2j(0));
  end;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  Inactive
}
begin
  xmin := -ln(3); xmax := ln(2);
  ClearDevice;
  tekenen(1);
  Form1.Image1.Picture.SaveToFile('logaritm.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  At moment of creation
}
begin
  xmin := 1/3; xmax := 2;
  ymin := -1 ; ymax := 2;
  TV(Form1.Image1);
  ClearDevice;
  tekenen(0);
  Form1.Image1.Picture.SaveToFile('original.bmp');
end;

END.