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:

using namespace std; typedef complex z_type; 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"); }
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "conto.cin"
 * 5) include "efjh.cin"