/**************************************************************************
*                    FRACTALS:   SET OF MANDELBROT                        *
* ----------------------------------------------------------------------- *
* TUTORIAL:                                                               *
*                                                                         *
* The set of Mandelbrot is a figure in the complex plane, that is (for no *
* mathematicians) the plane allowing to represent complex numbers having  *
* the form a + i b, a is the real part (ox componant) and b is the        *
* imaginary part (oy componant). The imaginary number i is the unity of   *
* axis oy, defined as i x i  = -1. In the following, we will use the      *
* multiplication of two complex numbers and the module value of a complex *
* number before defining the set of Mandelbrot itself.                    *
*                                                                         *
* Multiply z1 by z2                                                       *
*                                                                         *
* Let be z1 = a1 + i b1 and z2 = a2 + i b2, two complex numbers. To cal-  *
* culate Z = z1 x z2, one just has to algebraically develop the expression*
* (a1 + i b1)*(a2 + i b2), replacing i² by -1 and separating constant     *
* terms from i terms. One easily obtains:                                 *
*                                                                         *
*          Z = (a² - b²) + i (2ab)                                        *
*                                                                         *
* Module of a complex number                                              *
*                                                                         *
* Every complex number a + i b can be represented as the point of coordi- *
* nates (a, b) in the complex plane. Its module is nothing other than the *
* distance of this point from origin (0,0), that is to say:               *
*                                                                         *
*        | Z | = square root of (a² + b²)                                 *
*                                                                         *
* We can now define the iterative process that will lead us to the magni- *
* ficent "Set of Mandelbrot":                                             *
*                                                                         *
* We take, as a starting point, a fixed complex number c, and we calculate*
* the complex expression z² + c, z being a variable complex number.       *
* Let us take z = 0, then z² + c equals c. Let us replace z by c in the   *
* formula z² + c, then we obtain c² + c. Let us again remplace z by this  *
* new value, then we obtain (c²+c)² + c. Such a process is indefinitly    *
* resumed, each new value z² + c is taken as new value z. This provides   *
* an unlimited series of z numbers.                                       *
*                                                                         *
* The mathematician Mandelbrot was the first to notice that, according to *
* the chosen value c, the series of complex numbers z so obtained could   *
* have a module, either rapidly tending towards infinity, or tending      *
* towards a finite value, whatever the number of iterations may be.       * 
*                                                                         *
* Two examples:                                                           *
*                                                                         *
* 1)  c = 1 + i                                                           *
*                                                                         *
*	iteration	new z	        module of z                       *
*	____________________________________________                      *
*	1		1 + 3i		3,16227...                        *
*	2		-7 + 7i		9,89949...                        *
*	3		1-97i		97,00515...                       *
*   	4      	   	-9407-193i	9408,97965                        *
*                                                                         *
* The module of z increases very rapidly.                                 *
*                                                                         *
* 2)  c = -1 + 0,25 i                                                     *
*                                                                         *
*	iteration	new z	        module de z                       *
*	____________________________________________                      *
*	1		-0,5 - 0i	0,5                               *
*	2		-0,25 + 0,5i	0,55902...                        *
*	3		-0,687 + 0,25i	0,73154...                        *
*                                                                         *
* At 80th iteration, z = 0.40868 + 0,27513 i, the module equals 0,49266...*
* The module remains with a finite value, whatever the number of itera-   *
* tions may be. Practically, we will consider that the limit is obtained  *
* after 100 iterations, if the module of z is < 4. The set of Mandelbrot, *
* still called the Mandelbrot man, because of its shape, is constituted   *
* by all the points for which  the expression z² + c has a finite value   *
* whatever the number of iterations may be.                               *
*                                                                         *
* See also programs mandbrot.pas and julia.pas.                           *
*                                                                         *
* ----------------------------------------------------------------------- *
* REFERENCE:                                                              *
*     "Graphisme dans le plan et dans l'espace avec Turbo Pascal 4.0      *
*      By R. Dony - MASSON, Paris 1990" [BIBLI 12].                       *
*                                                                         *
*                                   Visual C++ version by J-P Moreau      *
*                               (to be used with mandel.mak and Gr2d.cpp) *
*                                         (www.jpmoreau.fr)               *
**************************************************************************/ 
#include <windows.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

HDC  hdc;
RECT rect;


//"home made" graphic commands for hdc environment used by above functions
void DrawPixel(int ix,int iy) {
  //sorry, no other available command found
  Rectangle(hdc,rect.left+ix,rect.top+iy,
	            rect.left+ix+2,rect.top+iy+1);
}

void Swap(int *i1,int *i2) {
  int it;
  it=*i1; *i1=*i2; *i2=it;
}

void DrawLine(int ix1,int iy1,int ix2,int iy2) {
  int i,il,ix,iy;
  float dx,dy;
  if (ix2<ix1) {
	Swap(&ix1,&ix2); Swap(&iy1,&iy2);
  }
  il=(int) sqrt((ix2-ix1)*(ix2-ix1)+(iy2-iy1)*(iy2-iy1));
  dx=(float) (ix2-ix1)/il; 
  dy=(float) (iy2-iy1)/il;
  ix=ix1; iy=iy1;
  for (i=1;i<il+1; i++) {
	DrawPixel(ix,iy);
	ix=(int) (ix1+i*dx); 
	iy=(int) (iy1+i*dy);
  }
}

void OutText(int ix,int iy,char *s) {
  RECT rct;
  rct.left=ix; rct.right=ix+10*strlen(s);
  rct.top=iy-5; rct.bottom=iy+15;
  DrawText(hdc, s, -1, &rct,
     DT_SINGLELINE | DT_CENTER | DT_VCENTER);
}

//Draw the set of Mandelbrot
void Draw_Mandelbrot() {
  
  int    xmargin = 50, ymargin = 30;

  double incX,incY,x1,x2,y1,y2;
  int    lim,ligne,colonne,compt,sx;
  double p0,q0,module,x,y,aux;
  char   sx1[12],sx2[12],sy1[12],sy2[12],slim[12];
  char   s[80];

  int     MaxX, MaxY;   //size of drawing in pixels

  //client drawing zone in pixels
  MaxX=(rect.right-rect.left);
  MaxY=(rect.bottom-rect.top);
  //draw outside frame (all commands here in pixels)
  DrawLine(25,25,MaxX-25,25);
  DrawLine(MaxX-25,25,MaxX-25,MaxY-25);
  DrawLine(MaxX-25,MaxY-25,25,MaxY-25);
  DrawLine(25,MaxY-25,25,25);
  //initialize drawing parameters
  x1=-1.6; x2=0.55; y1=-1.15; y2=-y1;
  lim=250;  //this parameter commands the finesse of the drawing
  incX=(x2-x1)/(MaxX-2*xmargin);
  incY=(y2-y1)/(MaxY-2*ymargin);
  //prepare drawing caption (parameter values)
  sprintf(sx1,"x1=%5.2f",x1); sprintf(sx2,"  x2=%5.2f",x2);
  sprintf(sy1,"  y1=%5.2f",y1); sprintf(sy2,"  y2=%5.2f",y2);
  sprintf(slim,"  Lim=%4d",lim);
  strcpy(s,sx1); strcat(s,sx2); strcat(s,sy1); strcat(s,sy2); strcat(s,slim); 
  sx=(MaxX-xmargin-10*strlen(s)) / 2;    //center caption horizontaly
  OutText(sx,5,s);                       //display caption

  // main loop to display Mandelbrot man line by line
  // with a symmetry with respect to 0x axis
  colonne=1;
  while (colonne <= MaxX-xmargin) {
    p0=x1+colonne*incX;
    ligne=1;
    while (ligne <= ((MaxY-ymargin) / 2)) {
      q0=y1+ligne*incY;
      x=0; y=0;
      compt=1; module=0;
      while ((compt <= lim) && (module < 4)) {
        aux=x;
        x=x*x-y*y+p0;
        y=2*y*aux+q0;
        module=x*x+y*y;
        compt++;
      }
      if (module < 4) {
        DrawPixel(xmargin+colonne,ymargin+ligne);
        DrawPixel(xmargin+colonne,MaxY-ymargin-ligne);
	  }
      ligne++;
    }
    colonne++;
  }

} //Draw_Mandelbrot()


//Handle window Paint and Destroy messages
long FAR PASCAL /*_export*/ WndProc(HWND hwnd,
    UINT message, UINT wParam, LONG lParam) 
{
    HPEN        hpen, hpenOld;
    PAINTSTRUCT ps;

    switch (message) {
        case WM_PAINT:
	    hdc = BeginPaint(hwnd, &ps);
	    GetClientRect(hwnd, &rect);
            hpen = CreatePen(PS_SOLID, 1, RGB(0, 0, 255));
            hpenOld = SelectObject(hdc,hpen);

            Draw_Mandelbrot();
               
            SelectObject(hdc,hpenOld);
            DeleteObject(hpen);
            EndPaint(hwnd, &ps);
            return 0;
        case WM_DESTROY:
            PostQuitMessage(0);
            return 0;
    }
    return DefWindowProc(hwnd, message, wParam, lParam);
}

// main program
int PASCAL WinMain(HANDLE hInstance, HANDLE hPrevInstance,
    LPSTR lpszCmdParam, int nCmdShow)
{
    static char szAppName[] = "Mandel";
    HWND        hwnd;
    MSG         msg;
    WNDCLASS    wndclass;

    if (!hPrevInstance) {
        wndclass.style         = CS_HREDRAW | CS_VREDRAW;
        wndclass.lpfnWndProc   = WndProc;
        wndclass.cbClsExtra    = 0;
        wndclass.cbWndExtra    = 0;
        wndclass.hInstance     = hInstance;
        wndclass.hIcon         = LoadIcon(NULL, IDI_APPLICATION);
        wndclass.hCursor       = LoadCursor(NULL, IDC_ARROW);
        wndclass.hbrBackground = GetStockObject(WHITE_BRUSH);
        wndclass.lpszMenuName  = NULL;
        wndclass.lpszClassName = szAppName;

        RegisterClass(&wndclass);
    }

    hwnd = CreateWindow(szAppName,  // window class name
        " SET OF MANDELBROT",       // window caption
        WS_OVERLAPPEDWINDOW,        // window style                       
        CW_USEDEFAULT,              // initial x position
        CW_USEDEFAULT,              // initial y position
        CW_USEDEFAULT,              // initial x size
        CW_USEDEFAULT,              // initial y size
        NULL,                       // parent window handle
        NULL,                       // window menu handle
        hInstance,                  // program instance handle
        NULL);                      // creation parameters

   ShowWindow(hwnd, nCmdShow);
   UpdateWindow(hwnd);

   while (GetMessage(&msg, NULL, 0, 0)) {
       TranslateMessage(&msg);
       DispatchMessage(&msg);
   }
   return msg.wParam;
}

//end of file mandel.cpp