实验六分形图的生成班级 08信计学号60姓名杨平萍分数一、实验目的和要求：1、掌握分形基本原理2、熟悉分形的计算机模拟算法3、上机操作迭代函数系统算法4、编译并执行谢宾斯基(Sierpinski)三角形二、实验内容：1、编程实现分形的迭代函数系统算法，并输出图形；2、编译曼德布洛特集和可放大的曼德布洛特集。
.三、编程并实现Mandelbrot Set (曼德布洛特集)的运行程序：#include <graphics.h>#include <conio.h>struct COMPLEX{double re;double im;};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;}COMPLEX operator + (COMPLEX a, COMPLEX b){COMPLEX c;c.re = a.re + b.re;c.im = a.im + b.im;return c;}void main(){initgraph(640, 480);COMPLEX z, c;int x, y, k; // 定义循环变量for(x = 0; x < 640; x++){c.re = -2.1 + (1.1 - -2.1) * (x / 640.0);for(y = 0; y < 480; y++){c.im = -1.2 + (1.2 - -1.2) * (y / 480.0);z.re = z.im = 0;for(k = 0; k < 180; k++){if ( z.re * z.re + z.im * z.im > 4.0 ) break;z = z * z + c;}putpixel(x, y, (k >= 180) ? 0 : HSLtoRGB((float)((k << 5) % 360), 1.0, 0.5));}}getch();closegraph();}程序截图可以无穷放大的Mandelbrot Set (曼德布洛特集)的运行程序：#include <graphics.h>#include <conio.h>#define ITERATIONS 1000#define MAXCOLOR 64struct COMPLEX{double re;double im;};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;}COMPLEX operator + (COMPLEX a, COMPLEX b){COMPLEX c;c.re = a.re + b.re;c.im = a.im + b.im;return c;}int Color[MAXCOLOR];void InitColor(){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);}}void Draw(double fromx, double fromy, double tox, double toy){COMPLEX z, c;int x, y, k;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]);}}}void main(){initgraph(640, 480);InitColor();double fromx, fromy, tox, toy;fromx = -2.1; tox = 1.1;fromy = -1.2; toy = 1.2;Draw(fromx, fromy, tox, toy);MOUSEMSG m;bool isLDown = false;int selfx, selfy, seltx, selty;while(!kbhit()){m = GetMouseMsg();switch(m.uMsg){case WM_MBUTTONUP:fromx = -2.1; tox = 1.1;fromy = -1.2; toy = 1.2;Draw(fromx, fromy, tox, toy);break;case WM_MOUSEMOVE:if (isLDown){rectangle(selfx, selfy, seltx, selty);seltx = m.x;selty = m.y;rectangle(selfx, selfy, seltx, selty);}break;case WM_LBUTTONDOWN:setcolor(WHITE);setwritemode(R2_XORPEN);isLDown = true;selfx = seltx = m.x;selfy = selty = m.y;rectangle(selfx, selfy, seltx, selty);break;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;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;}double f, t;f = fromx + (tox - fromx) * selfx / 640;t = fromx + (tox - fromx) * seltx / 640;fromx = f;tox = t;f = fromy + (toy - fromy) * selfy / 480;t = fromy + (toy - fromy) * selty / 480;fromy = f;toy = t;Draw(fromx, fromy, tox, toy);break;}}getch();closegraph();}程序截图：四、实验结果分析分形的对称性即表现了传统几何的上下、左右及中心对称。
