Mandelbrot和Julia

概述

mandelbrot

julia

Mandelbrot

对全体复数z，满足x =  x + z从x = 0起，|x|随n值增加不趋于无穷大，则z属于Mandelbrot集

代码

#include <glut.h>

int g_width, g_height;

/*********************************

input:    z = a + bi

          MaxIteration,迭代次数上限

output：  灰度级n

*********************************/

int GrayLevel(double a, double b, int MaxIteration)

{

    double x = , y =  , xx = , yy = ;

    int n = ;

    while(n++ < MaxIteration)

    {

        y =  * x * y + b;

        x = xx - yy + a;

        xx = x * x;

        yy = y * y;

        if ((xx + yy) > )

        {

            return n;

        }

    }

    return ;

}

void myDisplay()

{

    double min_a, max_a, min_b, max_b, step_a, step_b, a, b;

    int MaxIteration = ;

    int Iteration;

    float scale = 255.0 / MaxIteration;

    int x,y;

    min_a = -2.0;

    max_a = 0.5;

    min_b = -1.25;

    max_b = 1.25;

    step_a = (max_a - min_a) / g_width;

    step_b = (max_b - min_b) / g_height;

    glClear(GL_COLOR_BUFFER_BIT);

    glBegin(GL_POINTS);

    a = min_a;

    for (x = ; x < g_width; x++)

    {

        b = min_b;

        for (y = ; y < g_height; y++)

        {

            Iteration =  - scale * GrayLevel(a, b, MaxIteration);

            glColor3ub(Iteration, Iteration, Iteration);

            glVertex2i(x, y);

            b += step_b;

        }

        a += step_a;

    }

    glEnd();

    glFlush();

}

void reshape(GLsizei width, GLsizei height)

{

    float w_aspect = 4.0 / 3.0;

    float aspect = ((float)width) / height;

    g_width = width;

    g_height = height;

    if (aspect <= w_aspect)

    {

        glViewport(, (height - width / w_aspect) / ,

            width, width / w_aspect);

    }

    else

        glViewport((width - height * w_aspect) / , ,

        height * w_aspect, height);

    glMatrixMode(GL_PROJECTION);

    glLoadIdentity();

    gluOrtho2D(-0.0, 400.0, -0.0, 300.0);

}

void main(int argc, char* *argv)

{

    glutInit(&argc, argv);

    glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);

    glutInitWindowSize(, );

    glutInitWindowPosition(, );

    glutCreateWindow("Mandelbort");

    glClearColor(0.0, 0.0, 0.0, 0.0);

    glutDisplayFunc(&myDisplay);

    glutReshapeFunc(reshape);

    glutMainLoop();

}

结果如下

Julia集

在x =  x + z，对给定的复数z，所有使|x|不发散的x属于Julia集

给定的z = -0.7454 + 0.1131i；x的实部为[-1.6,1.6]，虚部为[-1.2,1.2]

代码

#include <glut.h>

int g_width, g_height;

/*********************************

输入: z = a + bi

      MaxIteration,迭代次数上限

输出: 灰度级n, 0表示白色

思路:

*********************************/

int GrayLevel(double x, double y, int MaxIteration)

{

    double xx, yy, zx = -0.7454, zy = 0.1131;

    int n = ;

    xx = x * x;

    yy = y * y;

    while(n++ < MaxIteration)

    {

        y =  * x * y + zy;

        x = xx - yy + zx;

        xx = x * x;

        yy = y * y;

        if ((xx + yy) > )

        {

            return n;

        }

    }

    return ;

}

结果如下：