T3


These images are generated like the Mandelbrot set fractals for the iterative sequence Z[0]=0 and z[n+1]<-z[n]^4+c. The colour at a point c represents the number of iterations necessary for the system to reach a value from which we know the sequence diverges to infinity. The edge of the set is tracked by computing the variance the colours in a 16x24 tile, and then a random choice is made amongst the seven tiles with highest variance.

The iteration program is written in C, and the A.I. features (edge detection) are written in APL. The Image Magick package does conversions from .XPM format to .gif format.


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/* mandelbrot tile
mt -zone y0 x0 y1 x1 -size ny nx -ofile file
minimum memory varsion. Allocate only one line
*/

#include 
#include 

#define ERROR   -1

double  zw[4]   = {-2,-2,2,2};
int     size[2] = {24,80};                                            
int     kf      = 0;                                                  
double  eps     =  1.0e-18;     /* -eps epsilon */                    
int     bailout = 35;           /* maximum iteration */               
char   *ofile   = NULL;                                               
char   *lut     = ".123456789ABCDEF";                                 
int     nlut;                                                         
                                                                      
                                                                      
int j_orbit(), j3_orbit(), j4_orbit(), j5_orbit(), j6_orbit();        
int (*func[])() = {j_orbit, j3_orbit, j4_orbit, j5_orbit, j6_orbit};  
                                                                      
main(argc, argv)                                                      
int argc;                                                             
char **argv;                                                          
{                                                                     
extern  double  atof();                                               
extern  char   *malloc();                                             
FILE   *ofp = NULL;                                                   
char   *s;                                                            
char   *rup, *t;                                                      
int     i, j, k;                                                      
double  x, y, dx, dy;                                                 
                                                                      
for(argv++, argc--; 0 < argc--; argv++) {                             
    s = *argv;                                                        
    if (s[0] == '-') switch(s[1]) {                                   
        case 'z':   /* zone */                                        
                zw[0] = atof(*++argv);                                
                zw[1] = atof(*++argv);                                
                zw[2] = atof(*++argv);                                
                zw[3] = atof(*++argv);                                
                argc -= 4;                                            
        break;                                                        
        case 's':   /* size */                                        
                size[0] = atoi(*++argv);                              
                size[1] = atoi(*++argv);                              
                argc -=2;                                             
        break;                                                        
        case 'l':       /* lut */                                     
                lut = *++argv;                                        
                argc--;                                               
        break;                                                        
        case 'o':       /* ofile */                                   
                ofile = *++argv;                                      
                argc--;                                               
        break;                                                        
        case 'b':       /* -bailout */                                
                bailout = atoi(*++argv);                              
                argc--;                                               
        break;                                                        
        case 'e':       /* -eps */                                    
                eps = atof(*++argv);                                  
                argc--;                                               
        break;                                                        
        case 'f':       /* -function */                               
                kf = atoi(*++argv);                                   
                argc--;                                               
        break;                                                        
        default: break;                                               
        }                                                             
    }                                                                 
nlut = strlen(lut);                                                   
                                                                      
if (ofile) {                                                          
    ofp = fopen(ofile, "w");                                          
    if (ofp == NULL) return ERROR;                                    
    }                                                                 
else    ofp = stdout;                                                 
                                                                      
fprintf(ofp, "-size %d %d -zone %f %f %f %f\n",                       
        size[0], size[1], zw[0], zw[1], zw[2], zw[3]);                
                                                                      
if (NULL == (rup = malloc(1+size[1]))) return ERROR;                  
dy=(zw[2]-zw[0])/(size[0]-1);                                         
dx=(zw[3]-zw[1])/(size[1]-1);                                         
for (i=0, y=zw[0]; i < size[0]; i++, y +=dy) {                        
    for (t=rup, j=0, x=zw[1]; j < size[1]; j++, x += dx) {            
/*      k =j_orbit(y, x);       */                                    
        k = (func[kf])(y,x);                                          
       *t++ = (k == 0) ? ' ': lut[k % nlut];                          
        }                                                             
    for (t = rup, j=0; j < size[1]; j++) fputc(*t++, ofp);            
    fputc('\n', ofp);                                                 
    }                                                                 
if (ofile) fclose (ofp);                                              
return 0;                                                             
}                                                                     
                                                                      
/*      dynamic system z<-z^2+c with global parameters eps, bailout */
                                                                      
int     j_orbit(cy, cx)                                               
double  cy, cx;                                                       
{                                                                     
double  x = 0.0, y = 0.0;                                             
double  x1, y1, x2, y2;                                               
int     j;                                                            
for(j = 0; j < bailout; j++) {                                        
    x2= x*x; y2=y*y;                                                  
    if (4.1 < x2+y2) return j;                                        
    x1 = cx + x2-y2;                                                  
    y1 = cy + 2*x*y;                                                  
    x = x1;                                                           
    y = y1;                                                           
    }                                                                 
return 0;                                                             
}                                                                     
                                                                      
/*      dynamic system z<-z^3+c  */                                   
                                                                      
int     j3_orbit(cy, cx)                                              
double  cy, cx;                                                       
{                                                                     
double  x = 0.0, y = 0.0;                                             
double  x1, y1, x2, y2;                                               
int     j;                                                            
for(j = 0; j < bailout; j++) {                                        
    x2= x*x; y2=y*y;                                                  
    if (4.1 < x2+y2) return j;                                        
    x1 = cx + x*(x2-3*y2);                                            
    y1 = cy + y*(3*x2-y2);                                            
    x = x1;                                                           
    y = y1;                                                           
    }                                                                 
return 0;                                                             
}                                                                     
                                                                      
/*      dynamic system z<-z^4+c  */                                   
                                                                      
int     j4_orbit(cy, cx)                                              
double  cy, cx;                                                       
{                                                                     
double  x = 0.0, y = 0.0;                                             
double  x1, y1, x2, y2;                                               
int     j;                                                            
for(j = 0; j < bailout; j++) {                                        
    x2= x*x; y2=y*y;                                                  
    if (4.1 < x2+y2) return j;                                        
    x1 = cx + x2*x2+y2*y2-6*x2*y2;                                    
    y1 = cy + 4*x*y*(x2-y2);                                          
    x = x1;                                                           
    y = y1;                                                           
    }                                                                 
return 0;                                                             
}                                                                     
                                                                      
/*      dynamic system z<-z^5+c  */                                   
                                                                      
int     j5_orbit(cy, cx)                                              
double  cy, cx;                                                       
{                                                                     
double  x = 0.0, y = 0.0;                                             
double  x1, y1, x2, y2, x2y2, x4, y4;                                 
int     j;                                                            
for(j = 0; j < bailout; j++) {                                        
    x2= x*x; y2=y*y; x2y2=x2*y2; x4=x2*x2; y4=y2*y2;                  
    if (4.1 < x2+y2) return j;                                        
    x1 = cx + x*(x2*x2+5*y2*y2-10*x2y2);                              
    y1 = cy + y*(5*x4-10*x2y2+y4);                                    
    x = x1;                                                           
    y = y1;                                                           
    }                                                                 
return 0;                                                             
}                                                                     
                                                                      
/*      dynamic system z<-z^6+c  */                                   
                                                                      
int     j6_orbit(cy, cx)                                              
double  cy, cx;                                                       
{                                                                     
double  x = 0.0, y = 0.0;                                             
double  x1, y1, x2, y2, x2y2, x4, y4;                                 
int     j;                                                            
for(j = 0; j < bailout; j++) {                                        
    x2= x*x; y2=y*y; x2y2=x2*y2; x4=x2*x2; y4=y2*y2;                  
    if (4.1 < x2+y2) return j;                                        
    x1 = cx + x2*x2*(x2-16*y2)+y2*y2*(15*x2-y2);                      
    y1 = cy + x*y*(6*(x4+y4)-20*x2y2);                                
    x = x1;                                                           
    y = y1;                                                           
    }                                                                 
return 0;                                                             
}