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

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 <math.h>

#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;
}

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原文地址：https://www.cnblogs.com/ncgds/p/6652165.html

win32_c语言绘制曼德博集合（分形绘制）

目录

计算的方法