File:Logi2d3T1500.png

Complex map of function ArcLogisticSequence with parameter $s\!=\!3$;

$u\!+\!\mathrm i v= \mathrm{ArcLogisticSequence}_3(x\!+\!\mathrm i y)$ in the $x$, $y$ plane.

C++ generator of curves

// Files efjh.cin, ado.cin and conto.cin should be loaded in the working directory in order to compile the C++ code below:

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "efjh.cin"
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 int M=401,M1=M+1;
 int N=601,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("logi2d3a.eps","w");ado(o,124,124);
fprintf(o,"62 62 translate\n 20 20 scale\n");
DO(m,M1) X[m]=-3.+.015*(m-.5);
DO(n,N1) Y[n]=-3.+.010*(n-.5);
fprintf(o,"1 setlinejoin 2 setlinecap\n"); 
for(m=-3;m<4;m++){if(m==0){M(m,-3.04)L(m,3.04)} else{M(m,-3)L(m,3)}}
for(n=-3;n<4;n++){         M(  -3  ,n)L(3,n)}
fprintf(o,".008 W 0 0 0 RGB S\n");
maq(3.);
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); 
       c=E(z);
       p=Re(c);q=Im(c);        
       if(p>-4.9 && p<4.9)     {g[m*N1+n]=p;}
       if(q>-4.9 && q<4.9 && fabs(q)>1.e-11 )  {f[m*N1+n]=q;}
                       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n"); 
p=2.;q=.5;
for(m=-3;m<3;m++) 
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".005 W 0 .6 0 RGB S\n");
for(m=0;m<2;m++) 
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".005 W .9 0 0 RGB S\n");
for(m=0;m<2;m++) 
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".005 W 0 0 .9 RGB S\n");
for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);   fprintf(o,".02 W .9 0 0 RGB S\n");
for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);   fprintf(o,".02 W 0 0 .9 RGB S\n");
for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p);   fprintf(o,".02 W 0 0 0 RGB S\n");
                                      conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p);   fprintf(o,".02 W .6 0 .6 RGB S\n");
fprintf(o,"0 setlinejoin 0 setlinecap\n");
M(-3.02,0)L(0,0)  M(1.-1./Q,0)L(3,0)  fprintf(o,"0.03 W 1 1 1 RGB S\n");
for(n=0;n<16;n++) {M(-.2*n,0)L(-.2*(n+.4),0)}
for(n=0;n<13;n++) {     M(1-1./Q+.2* n,0)
                       L(1-1./Q+.2*(n+.4),0)}
fprintf(o,"0.04 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf logi2d3a.eps"); // for linux
       system(    "open logi2d3a.pdf"); // for mac
       getchar(); system("killall Preview");
}

Latex generator of labels

References