File:Sunot.jpg

Solution $x_0=x_0(q)$ of equation

$\mathrm{SuNe}_q(x_0)=1$

versus $q$.

Here, SuNe is native superfunction of the Nemtsov function costructed with exotic iteration at its fixed point zero.

Function $x_0$ is used to define function SuNem with

$\mathrm{SuNem})q(z)=\mathrm{SuNe}_q(x_0(q)+z)$

C++ generator of curve
//using namespace std; typedef std::complex z_type; //#include "conto.cin"
 * 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.)


 * 1) include "ado.cin"
 * 2) define M(x,y) fprintf(o,"%8.4lf %8.4lf M\n",0.+x,0.+y);
 * 3) define L(x,y) fprintf(o,"%8.4lf %8.4lf L\n",0.+x,0.+y);

DB Q; z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!

// DB Q=2.; // z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } // z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); }  // WARNING: Q is global!


 * 1) include "sune.cin"

DB SUNo=0;

z_type sunem(z_type z){ return sune(z + SUNo);}

int main{ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; // DB rr,ti; FILE *o;o=fopen("suno.eps","w");ado(o,620,1220); fprintf(o,"110 1010 translate\n 100 100 scale 2 setlinecap\n"); for(m=0;m<6;m+=1){ M(m,-10)L(m,2)} for(n=-10;n<3;n+=1){ M(0,n)L(5,n)} fprintf(o,".008 W 0 0 0 RGB 2 setlinecap S\n");

Q=-1; K=Q*Q; x=0; co; printf("Q=%9.4lf\n",Q); DO(n,300) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar;

M(Q,SUNo)

DO(m,640){ Q=-.99+.01*m; K=Q*Q; co; printf("Q=%9.4lf\n",Q); DO(n,60) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} L(Q,SUNo) if(SUNo<-10.) break;}

fprintf(o,".03 W .6 0 0 RGB 1 setlinejoin S\n");

/* DO(n,402){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} fprintf(o,".02 W 0 0 0 RGB 1 setlinejoin S\n");

Q=.5; K=Q*Q; x=0; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} fprintf(o,".01 W .7 0 .6 RGB 1 setlinejoin S\n");

Q=1; K=Q*Q; x=0; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} fprintf(o,".02 W .8 .2 0 RGB 1 setlinejoin S\n");

Q=2; K=Q*Q; x=0; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} fprintf(o,".02 W 0 .6 0 RGB 1 setlinejoin S\n");

Q=8; K=Q*Q; SUNo=-100.; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; //DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} //fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");

DO(m,81){Q=8.-.1*m; K=Q*Q;K=Q*Q; co; printf("Q=%9.4lf\n",Q); DO(n,30) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; }

Q=10; K=Q*Q; SUNo=-150.; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;} fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);

system("epstopdf suno.eps"); system( "open suno.pdf"); //mac

return 0; }

Latex generator of labels
\documentclass{mcom-l} % \documentclass[12pt]{article} \usepackage{graphics} \paperwidth 608pt \paperheight 1208pt \usepackage{geometry} \usepackage{rotating} \textwidth 2560pt \textheight 2260pt \topmargin -98pt \oddsidemargin -84pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document}

\begin{picture}(720,1220) %\put(4,0){\ing{sunemplo4}} \put(4,0){\ing{suno}} \put(64,1190){\sx{5}{$x_0$}} \put(80,1096){\sx{5}{$1$}} \put(80,996){\sx{5}{$0$}} \put(48,896){\sx{5}{$-1$}} \put(48,796){\sx{5}{$-2$}} \put(48,695){\sx{5}{$-3$}} \put(48,595){\sx{5}{$-4$}} \put(48,495){\sx{5}{$-5$}} \put(48,395){\sx{5}{$-6$}} \put(48,294){\sx{5}{$-7$}} \put(48,194){\sx{5}{$-8$}} \put(48,94){\sx{5}{$-9$}} % \put(202,976){\sx{5}{$1$}} \put(302,976){\sx{5}{$2$}} \put(402,976){\sx{5}{$3$}} \put(502,976){\sx{5}{$4$}} \put(590,980){\sx{5.2}{$q$}} %\put(706,980){\sx{4}{$6$}} %\put(322,932){\sx{3.4}{\rot{88}$q\!=\!8$\ero}}% %\put(348,834){\sx{3.4}{\rot{87}$q\!=\!2$\ero}}% %\put(361,734){\sx{3.4}{\rot{86}$q\!=\!1$\ero}}% %\put(372,614){\sx{3.4}{\rot{85}$q\!=\!0.5$\ero}}% %\put(392,518){\sx{3.4}{\rot{83}$q\!=\!0$\ero}}% \end{picture} \end{document}