VC分形学 - 可以无穷放大的 Mandelbrot Set (曼德布洛特集)

// 程序名称：分形学 - 可以无穷放大的 Mandelbrot Set (曼德布洛特集)

// 编译环境：Visual C++ 6.0，EasyX 2011惊蛰版

// 最后更新：2010-9-9

//

#include <graphics.h>

#include <conio.h>

// 定义常量

#define ITERATIONS 1000 // 迭代次数，越高，图像越精细

#define MAXCOLOR 64 // 颜色数

/////////////////////////////////////////////////

// 定义复数及乘、加运算

/////////////////////////////////////////////////

// 定义复数

struct COMPLEX

{

double re;

double im;

};

// 定义复数“乘”运算

COMPLEX operator * (COMPLEX a, COMPLEX b)

{

COMPLEX c;

c.re = a.re * b.re - a.im * b.im;

c.im = a.im * b.re + a.re * b.im;

return c;

}

// 定义复数“加”运算

COMPLEX operator + (COMPLEX a, COMPLEX b)

{

COMPLEX c;

c.re = a.re + b.re;

c.im = a.im + b.im;

return c;

}

/////////////////////////////////////////////////

// 定义颜色及初始化颜色

/////////////////////////////////////////////////

// 定义颜色

int Color[MAXCOLOR];

// 初始化颜色

void InitColor()

{

// 使用 HSL 颜色模式产生角度 h1 到 h2 的渐变色

int h1 = 240, h2 = 30;

for(int i=0; i<MAXCOLOR/2; i++)

{

Color[i] = HSLtoRGB((float)h1, 1.0f, i * 2.0f / MAXCOLOR);

Color[MAXCOLOR-1-i] = HSLtoRGB((float)h2, 1.0f, i * 2.0f / MAXCOLOR); }

}

/////////////////////////////////////////////////

// 绘制 Mandelbrot Set (曼德布洛特集)

/////////////////////////////////////////////////

void Draw(double fromx, double fromy, double tox, double toy)

{

COMPLEX z, c;

int x, y, k; // 定义循环变量

for(x = 0; x < 640; x++)

{

c.re = fromx + (tox - fromx) * (x / 640.0);

for(y = 0; y < 480; y++)

{

c.im = fromy + (toy - fromy) * (y / 480.0);

z.re = z.im = 0;

for(k = 0; k < ITERATIONS; k++)

{

if ( z.re * z.re + z.im * z.im > 4.0 ) break;

z = z * z + c;

}

putpixel(x, y, (k >= ITERATIONS) ? 0 : Color[k % MAXCOLOR]); }

}

}

/////////////////////////////////////////////////

// 主函数

/////////////////////////////////////////////////

void main()

{

// 初始化绘图窗口及颜色

initgraph(640, 480);

InitColor();

// 初始化 Mandelbrot Set(曼德布洛特集)坐标系 double fromx, fromy, tox, toy;

fromx = -2.1; tox = 1.1;

fromy = -1.2; toy = 1.2;

Draw(fromx, fromy, tox, toy);

// 捕获鼠标操作，实现放大鼠标选中区域

MOUSEMSG m;

bool isLDown = false;

int selfx, selfy, seltx, selty; // 定义选区

while(!kbhit())

{

m = GetMouseMsg(); // 获取一条鼠标消息

switch(m.uMsg)

{

// 按鼠标中键恢复原图形坐标系

case WM_MBUTTONUP:

fromx = -2.1; tox = 1.1;

fromy = -1.2; toy = 1.2;

Draw(fromx, fromy, tox, toy);

break;

// 按鼠标左键并拖动，选择区域

case WM_MOUSEMOVE:

if (isLDown)

{

rectangle(selfx, selfy, seltx, selty); seltx = m.x;

selty = m.y;

rectangle(selfx, selfy, seltx, selty); }

break;

// 按鼠标左键并拖动，选择区域 case WM_LBUTTONDOWN: setcolor(WHITE); setwritemode(R2_XORPEN); isLDown = true; selfx = seltx = m.x; selfy = selty = m.y; rectangle(selfx, selfy, seltx, selty); break; // 按鼠标左键并拖动，选择区域 case WM_LBUTTONUP: rectangle(selfx, selfy, seltx, selty); setwritemode(R2_COPYPEN); isLDown = false; seltx = m.x; selty = m.y; if (selfx == seltx || selfy == selty) break; // 修正选区为 4:3 int tmp; if (selfx > seltx) {tmp = selfx; selfx = seltx; seltx = tmp;} if (selfy > selty) {tmp = selfy; selfy = selty; selty = tmp;} if ( (seltx - selfx) * 0.75 < (selty - selfy) ) { selty += (3 - (selty - selfy) % 3); selfx -= (selty - selfy) / 3 * 4 / 2 - (seltx - selfx) / 2; seltx = selfx + (selty - selfy) / 3 * 4; } else { seltx += (4 - (seltx - selfx) % 4); selfy -= (seltx - selfx) * 3 / 4 / 2 - (selty - selfy ) / 2; selty = selfy + (seltx - selfx ) * 3 / 4; } // 更新坐标系 double f, t; f = fromx + (tox - fromx) * selfx / 640; t = fromx + (tox - fromx) * seltx / 640;

} } } tox = t; f = fromy + (toy - fromy) * selfy / 480; t = fromy + (toy - fromy) * selty / 480; fromy = f; toy = t; // 画图形 Draw(fromx, fromy, tox, toy); break; getch(); closegraph();

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