win32_c语言绘制曼德博集合（分形绘制）

• 先了解一下曼德博集合

下面引用百科

曼德布洛特集合（Mandelbrot set）是在复平面上组成分形的点的集合，一种 分形图案。

 

中文名

曼德勃罗集合

外文名

Mandelbrot set

含    义

复平面上组成分形的点的集合

性    质

分形图案

目录

1. 1 定义
2. 2 计算的方法

 

 

曼德布洛特复数集合（Mandelbrot set，或译为曼德博集合）是一种在 复平面上组成分形的点的集合，以数学家 本华·曼德博的名字命名。曼德博集合与 朱利亚集合有些相似的地方，例如使用相同的复二次多项式来进行 迭代。

曼德布洛特集合可以用复二次多项式: f_c( z) =  z^2 + c

来定义 其中 c是一个复参数。对于每一个 c，从开始对 f c( z)进行迭代。

序列 的值或者延伸到无限大，或者只停留在有限半径的圆盘内。

曼德布洛特集合就是使以上序列不延伸至无限大的所有 c点的集合。

从数学上来讲，曼德布洛特集合是一个 复数的集合。一个给定的复数 c或者属于曼德布洛特集合 M，或者不是。

计算的方法

曼德布洛特集合一般用 计算机程序计算。对于大多数的分形软件，例如Ultra fractal，内部已经有了比较成熟的例子。下面的程序是一段 伪代码，表达了曼德布洛特集合的计算思路[1]。

For Each z0 in Complex repeats = 0 z=z0 Do z=z^2+z0 repeate = repeats+1 Loop until abs(z)>Bailout or repeats >= MaxRepeats If repeats >= MaxRepeats Then Draw z0,Black Else Draw z0,f(z,z0,Repeats) 'f返回颜色 End IfNextf函数的一些例子直接利用循环终止时的Repeats 综合利用z和Repeats Orbit Traps也可以用Mathematica制作 DensityPlot[Block[{z, t = 0}, z = x + y*I; While[(Abs[z] < 2.0) && (t < 100), ++t; z = z^2 + x + y*I]; Return[t]],{x, -2, 0.8}, {y, -1.5, 1.5}, PlotPoints -> 500, Mesh -> False

效果

 

• 实现代码

  // 曼德博集合.cpp : Defines the entry point for the application.
  //
  
  #include "stdafx.h"
  #include "resource.h"
  #include 
  
  #define MAX_LOADSTRING 100
  
  // Global Variables:
  HINSTANCE hInst;                                // current instance
  TCHAR szTitle[MAX_LOADSTRING];                                // The title bar text
  TCHAR szWindowClass[MAX_LOADSTRING];                                // The title bar text
  
  const int iXmax = 600;
  const int iYmax = 600;
  const double CxMin = -2.5;
  const double CxMax = 1.5;
  const double CyMin = -2.0;
  const double CyMax =  2.0;
  const int IterationMax = 200;
  const double EscapeRadius = 2;
  
  
  
  // Foward declarations of functions included in this code module:
  ATOM                MyRegisterClass(HINSTANCE hInstance);
  BOOL                InitInstance(HINSTANCE, int);
  LRESULT CALLBACK    WndProc(HWND, UINT, WPARAM, LPARAM);
  LRESULT CALLBACK    About(HWND, UINT, WPARAM, LPARAM);
  
  int APIENTRY WinMain(HINSTANCE hInstance,
                       HINSTANCE hPrevInstance,
                       LPSTR     lpCmdLine,
                       int       nCmdShow)
  {
       // TODO: Place code here.
      MSG msg;
      HACCEL hAccelTable;
  
      // Initialize global strings
      LoadString(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
      LoadString(hInstance, IDC_MY, szWindowClass, MAX_LOADSTRING);
      MyRegisterClass(hInstance);
  
      // Perform application initialization:
      if (!InitInstance (hInstance, nCmdShow)) 
      {
          return FALSE;
      }
  
      hAccelTable = LoadAccelerators(hInstance, (LPCTSTR)IDC_MY);
  
      // Main message loop:
      while (GetMessage(&msg, NULL, 0, 0)) 
      {
          if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg)) 
          {
              TranslateMessage(&msg);
              DispatchMessage(&msg);
          }
      }
  
      return msg.wParam;
  }
  
  
  
  //
  //  FUNCTION: MyRegisterClass()
  //
  //  PURPOSE: Registers the window class.
  //
  //  COMMENTS:
  //
  //    This function and its usage is only necessary if you want this code
  //    to be compatible with Win32 systems prior to the 'RegisterClassEx'
  //    function that was added to Windows 95. It is important to call this function
  //    so that the application will get 'well formed' small icons associated
  //    with it.
  //
  ATOM MyRegisterClass(HINSTANCE hInstance)
  {
      WNDCLASSEX wcex;
  
      wcex.cbSize = sizeof(WNDCLASSEX); 
  
      wcex.style            = CS_HREDRAW | CS_VREDRAW;
      wcex.lpfnWndProc    = (WNDPROC)WndProc;
      wcex.cbClsExtra        = 0;
      wcex.cbWndExtra        = 0;
      wcex.hInstance        = hInstance;
      wcex.hIcon            = LoadIcon(hInstance, (LPCTSTR)IDI_MY);
      wcex.hCursor        = LoadCursor(NULL, IDC_ARROW);
      wcex.hbrBackground    = (HBRUSH)(COLOR_WINDOW+1);
      wcex.lpszMenuName    = (LPCSTR)IDC_MY;
      wcex.lpszClassName    = szWindowClass;
      wcex.hIconSm        = LoadIcon(wcex.hInstance, (LPCTSTR)IDI_SMALL);
  
      return RegisterClassEx(&wcex);
  }
  
  //
  //   FUNCTION: InitInstance(HANDLE, int)
  //
  //   PURPOSE: Saves instance handle and creates main window
  //
  //   COMMENTS:
  //
  //        In this function, we save the instance handle in a global variable and
  //        create and display the main program window.
  //
  BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
  {
     HWND hWnd;
  
     hInst = hInstance; // Store instance handle in our global variable
  
     hWnd = CreateWindow(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
        CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, NULL, NULL, hInstance, NULL);
  
     if (!hWnd)
     {
        return FALSE;
     }
  
     ShowWindow(hWnd, nCmdShow);
     UpdateWindow(hWnd);
  
     return TRUE;
  }
  
  //
  //  FUNCTION: WndProc(HWND, unsigned, WORD, LONG)
  //
  //  PURPOSE:  Processes messages for the main window.
  //
  //  WM_COMMAND    - process the application menu
  //  WM_PAINT    - Paint the main window
  //  WM_DESTROY    - post a quit message and return
  //
  //
  LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
  {
      int wmId, wmEvent;
      PAINTSTRUCT ps;
      HDC hdc;
      TCHAR szHello[MAX_LOADSTRING];
      LoadString(hInst, IDS_HELLO, szHello, MAX_LOADSTRING);
  
      switch (message) 
      {
          case WM_COMMAND:
              wmId    = LOWORD(wParam); 
              wmEvent = HIWORD(wParam); 
              // Parse the menu selections:
              switch (wmId)
              {
                  case IDM_ABOUT:
                     DialogBox(hInst, (LPCTSTR)IDD_ABOUTBOX, hWnd, (DLGPROC)About);
                     break;
                  case IDM_EXIT:
                     DestroyWindow(hWnd);
                     break;
                  default:
                     return DefWindowProc(hWnd, message, wParam, lParam);
              }
              break;
          case WM_PAINT:
              {
           //添加大括号，使内部的变量初始化赋值编译通过
              hdc = BeginPaint(hWnd, &ps);
              // TODO: Add any drawing code here...
              int iX,iY;
              double Cx,Cy;
              double PixelWidth = (CxMax - CxMin)/iXmax;
              double PixelHeight;
              PixelHeight = (CyMax - CyMin)/iYmax;
              COLORREF color;
              double Zx,Zy;
              double Zx2,Zy2;
              INT Iteration;
              double ER2;
              ER2 = EscapeRadius *EscapeRadius;
              //依据曼德博集合计算原理，获取每个像素的属性
              for(iY = 0;iY < iYmax;iY++)//循环每一行
              {
                  Cy = CyMin + iY*PixelHeight;
                  if(fabs(Cy) < PixelHeight/2)
                      Cy = 0.0;
                  for(iX=0;iX < iXmax;iX++)//循环每一列
                  {
                      Cx = CxMin +iX* PixelHeight;
                      Zx = Zy= Zy2=Zx2 = 0.0;
                      Iteration = 0;
                      //针对每个像素进行循环计算
                      while(Iteration < IterationMax && ((Zx2 + Zy2)<ER2))
                      {
                          Zy = 2* Zx*Zy + Cy;
                          Zx = Zx2 - Zy2 + Cx;
                          Zx2 = Zx*Zx;
                          Zy2 = Zy *Zy;
                          Iteration++;
                      
                      }
                      if(Iteration == IterationMax)
                          color =  RGB(0,0,0);//前景色黑色
                      else
                          color =  RGB(255,255,255);//背景色白色
  
                      SetPixel(hdc,iX,iY,color);
                  
                  }
              }
  
      
  
          //    RECT rt;
          //    GetClientRect(hWnd, &rt);
          //    DrawText(hdc, szHello, strlen(szHello), &rt, DT_CENTER);
          
              
              EndPaint(hWnd, &ps);
              break;
              }
          case WM_DESTROY:
              PostQuitMessage(0);
              break;
          default:
              return DefWindowProc(hWnd, message, wParam, lParam);
     }
     return 0;
  }
  
  // Mesage handler for about box.
  LRESULT CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
  {
      switch (message)
      {
          case WM_INITDIALOG:
                  return TRUE;
  
          case WM_COMMAND:
              if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL) 
              {
                  EndDialog(hDlg, LOWORD(wParam));
                  return TRUE;
              }
              break;
      }
      return FALSE;
  }

   

转载于:https://www.cnblogs.com/ncgds/p/6652165.html