Mandelbrot和Julia

概述

mandelbrot

julia

Mandelbrot

对全体复数z，满足x_n+1 =  x_n² + z从x₀ = 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 = 0, y = 0 , xx = 0, yy = 0;
    int n = 0;
    while(n++ < MaxIteration)
    {
        y = 2 * x * y + b;
        x = xx - yy + a;
        xx = x * x;
        yy = y * y;
        if ((xx + yy) > 4)
        {
            return n;
        }
    }
    return 0;
}

void myDisplay()
{
    double min_a, max_a, min_b, max_b, step_a, step_b, a, b;
    int MaxIteration = 64;
    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 = 0; x < g_width; x++)
    {
        b = min_b;
        for (y = 0; y < g_height; y++)
        {
            Iteration = 255 - 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(0, (height - width / w_aspect) / 2,
            width, width / w_aspect);
    }

    else
        glViewport((width - height * w_aspect) / 2, 0,
        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(400, 300);

    glutInitWindowPosition(200, 100);

    glutCreateWindow("Mandelbort");

    glClearColor(0.0, 0.0, 0.0, 0.0);

    glutDisplayFunc(&myDisplay);

    glutReshapeFunc(reshape);

    glutMainLoop();
}

结果如下

 

Julia集

在x_n+1 =  x_n² + z，对给定的复数z，所有使|x|不发散的x₀属于Julia集

给定的z = -0.7454 + 0.1131i；x₀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 = 0;
    xx = x * x;
    yy = y * y;
    while(n++ < MaxIteration)
    {
        y = 2 * x * y + zy;
        x = xx - yy + zx;
        xx = x * x;
        yy = y * y;
        if ((xx + yy) > 4)
        {
            return n;
        }
    }
    return 0;
}

结果如下：