matlab分形曼德勃罗,曼德勃罗集合分形图案

三、曼德勃罗集合(Mandelbrot Set)

曼德勃罗集合(Mandelbrot Set)或曼德勃罗复数集合，是一种在复平面上组成分形的点的集合，因由曼德勃罗提出而得名。曼德博集合可以使复二次多项式

最后，我们给出一个利用C语言生成Mandelbrot集合并绘制图形的程序(该程序来自文献【1】)：

#include

#include

#include

#define width_size 800

#define height_size 600

#define Maxval 255

static const float orig_x = width_size * 2/3;

static const float orig_y = height_size * 1/2;

static const pixel dim_gray = { 105, 105, 105 };

typedef struct _pixel {

unsigned char r;

unsigned char g;

unsigned char b;

} pixel;static unsigned char iteration(int x, int y)

{

const int limit = Maxval + 1;

int i;

complex c = ((x – orig_x) / (width_size / 3)) +

((orig_y – y) / (height_size / 2)) * I;

complex z = 0;

for (i = 0; i

/* basic formula */

z = z * z + c;

if (creal(z) > 2 || cimag(z) > 2)

break;

}

return (unsigned char) (i == limit : i);

}

int main()

{

FILE *f = fopen(“mandelbrot.ppm”, “w+”);

/* PPM header */

fprintf(f,

“P6n” /* PPM magic number */

“#Mandelbrot Setn”

“%d ” /* width, in ASCII decimal */

“%dn” /* height, in ASCII decimal */

“%dn”, /* maximum color value, in ASCII decimal */

width_size, height_size, Maxval);

/* Write every pixel generated by Mandelbrot Set */

for (int i = 0; i

for (int j = 0; j

unsigned char iter = iteration(j, i);

if (iter) {

pixel p = {

.r = iter,

.g = (float) abs(j – orig_x) / width_size * Maxval,

.b = (float) abs(i – orig_y) / height_size * Maxval };

fwrite(&p, sizeof(pixel), 1, f);

} else {

fwrite(&dim_gray, sizeof(pixel), 1, f);

}

}

}

fclose(f);

return 0;

}

上述程序所生成的图像结果如下图所示，需要补充说明的是：该图像文件格式为ppm，在Windows下你可以使用Photoshop来查看这种类型的图像文件，在OS X系统下你可以使用免费的GIMP软件来查看它。

标签：unsigned,int,曼德勃罗,height,图案,width,分形,pixel,size

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