Mandelbrot Set Visualization

Bit Draw Solution

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 #include <string.h>
 4 #include <math.h>
 5 #include <complex.h>
 6 #include <stdbool.h>
 7 
 8 #define XDIM 1536    //此项必须为8的倍数，否则有BUG
 9 #define YDIM 1536
10 
11 #define NUM 1000    //迭代次数
12 
13 // z = z*z + c
14 
15 bool tof_complex(int i, int j)  //复数版本 (1536*1536->1000(1 core):15.128s)
16 {
17     int n = NUM;
18     //坐标转换 
19     double complex c = (i-0.75*XDIM)/XDIM*2+(j-0.5*YDIM)*2/YDIM*I;
20     double complex z = 0;
21     while(n>0){
22         z = z*z+c;
23         if(cabs(z)>2)
24             return false;
25         n--;
26     }
27     return true;
28 }
29 
30 struct COMPLEX
31 {
32     double re;
33     double im;
34 };
35 
36 bool tof_real(int i,int j)  //纯实数版本 (1536*1536->1000(1 core):4.991s)
37 {
38     int n = NUM;
39     struct COMPLEX z = {0,0};
40     struct COMPLEX c = {
41         (i-0.75*XDIM)/XDIM*2,
42         (j-0.5*YDIM)*2/YDIM
43     };
44     while(n>0){
45         double z_re_bak = z.re;
46         z.re = z.re*z.re-z.im*z.im+c.re;
47         z.im = 2*z_re_bak*z.im+c.im;
48         if(z.re>2||z.im>2)
49             return false;
50         n--;
51     }
52     return true;
53 }
54 
55 void writeBit(bool bit, FILE * fp)
56 {
57     static int bitNum = 0;
58     static unsigned char Byte = 0;
59     if(bitNum==8)
60     {
61         fputc(Byte, fp);
62         Byte = 0;
63         bitNum = 0;
64     }
65     Byte ^= bit<<(7-bitNum);
66     bitNum++;
67 }
68 
69 int main() 
70 {
71     FILE *fp;
72     fp = fopen("picture.pbm","wb");
73     fprintf(fp, "P4 %d %d\n", XDIM, YDIM);
74     for(int j=0; j<YDIM; j++)
75         for(int i=0; i<XDIM; i++)
76             writeBit(tof_complex(i, j), fp);
77     fclose(fp);
78     return 0;
79 }

DEMO

Colorful Draw Solution

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 #include <string.h>
 4 #include <math.h>
 5 #include <complex.h>
 6 #include <stdbool.h>
 7 
 8 #define XDIM 1024
 9 #define YDIM 1024
10 
11 #define NUM 512    //迭代次数
12 
13 // z = z*z + c
14 
15 bool tof_complex(int i, int j)
16 {
17     double complex c = (i-0.75*XDIM)/XDIM*2+(j-0.5*YDIM)*2/YDIM*I;
18     double complex z = 0;
19     for(int t=1;t<=NUM;t++){
20         z = z*z+c;
21         if(cabs(z)>2)
22             return t;
23     }
24     return 0;
25 }
26 
27 struct COMPLEX
28 {
29     double re;
30     double im;
31 };
32 
33 int tof_real(int i, int j)
34 {
35     struct COMPLEX z = {0,0};
36     struct COMPLEX c = {
37         (i-0.75*XDIM)/XDIM*2,
38         (j-0.5*YDIM)*2/YDIM
39     };
40     for(int t=1;t<=NUM;t++){
41         double z_re_bak = z.re;
42         z.re = z.re*z.re-z.im*z.im+c.re;
43         z.im = 2*z_re_bak*z.im+c.im;
44         if(z.re>2||z.im>2)
45             return t;
46     }
47     return 0;
48 }
49 
50 struct RGB
51 {
52     unsigned char R;
53     unsigned char G;
54     unsigned char B;
55 };
56 
57 struct RGB translate2RGB(int code)  //code: 0 - 511
58 {
59     struct RGB ret = {0, 0, 0};//返回局部变量，危险
60     if(code){
61         ret.R = (int)(sqrt((double)code/NUM)*256);
62         ret.G = (int)(((double)code/NUM*(1.0-(double)code/NUM))*NUM);
63         ret.B = (int)(pow((1.0-(double)code/NUM), 108)*256);
64     }
65     return ret;
66 }
67 
68 int main()
69 {
70     FILE *fp = fopen("out.ppm", "wb");
71     fprintf(fp, "P6\n%d %d\n255\n", XDIM, YDIM);
72     for(int j=0;j<YDIM;j++)
73         for(int i=0;i<XDIM;i++)
74         {
75             struct RGB tof_ret = translate2RGB(tof_real(i, j));
76             fprintf(fp, "%c%c%c", tof_ret.R, tof_ret.G, tof_ret.B);
77         }
78     
79     fclose(fp);
80     return 0;
81 }

DEMO