Tetre2215.cc

// Generator of picture tetre2215.pdf // used to make figure tetreal2215.pdf // that is convetred to tetreal2215.jpg // used in the article tetration // Plot of tetrational \(f={\rm tet}_b(z)\) // for \(-2<x<2\) and \(1<b<5\) the \(x\),\(b\) coordinates shown with lines \(f=\)const. // The functions defined in conto.cin and ado.cin should be downloaded for the compoillation. // The file tetreal2215.tex may be necessary to make beutiful figure with this picture. // WARNING! This is preliminary version! // The numerical implementation of the complex tet(complex,complex) // is valid only while the imaginary parts of the arguments are small; // and even in this case, the function returns only few correct decmal digits; // this is sufficient to make the camera-ready real-real plot, // but for the serious numerial analysis the number of terms in the expansion should be increased; // and for large values of the imaginary part, the asymptotic representaton should be used instead. // At the re-use, please, indicate the source: this helps to trace errors, if any. // Please let me know if any problem at the compillation or the execution. // Copyleft 2011 by Dmitrii Kouznetsov.

using namespace std; typedef complex z_type;
 * 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"

z_type old0(z_type d){ z_type q=sqrt(d); return -1.0018 +(0.15128484821526975*(1.+33.04715298851381*q-3.51771875598067*d)*q)/ (1.+3.2255053261256337*q) +  (-0.5 + log(2.))/d;}

z_type old1(z_type d){ z_type q=sqrt(d); return 1.1 - 2.608785958462561*(1. - 0.6663562294911147*sqrt(d))* sqrt(d) - (-0.625 + log(2.) )/d ;}

z_type old2(z_type d){ z_type q=sqrt(d); return -0.96 + 3.0912038297987596*(1.+0.6021398048785328*d)*q/(1. + 4.240467556480155*d) + (-0.6666666666666666 + log(2.))/d;}

z_type old3(z_type d){ z_type q=sqrt(d); return 1.2 - 10.44604984418533* (1.+0.2137568928431227*q+0.3693275254470449*d)*q/ (1.+4.95715636660691*q + 7.70233216637738*d) - ( - 131./192. + log(2.))/d ;}

z_type new0(z_type d){ z_type q=sqrt(d); return q*(0.137467 + q*(4.94969 + q*0.0474179))/( 1. + q*(3.23171 + q*0.471222)) + (-(1./2.)+log(2.))/d -1.;}

z_type new1(z_type d){ z_type q=sqrt(d); return q*(-0.424278 +q*(1.75166 +q*(-1.46524 + q*0.93347)))/ ( 0.0312142+q*(-0.267478 + q)) + (-(5./8.) + log(2.))/d -1. ;}

/* z_type new2(z_type d){ z_type q=sqrt(d); return -1 + (3.3925530969774065` Sqrt[d] + 16.10456932466758` d -  19.52156841142778` d^(3/2) + 10.745842280690756` d^2)/(  1 + 4.127401286122306` Sqrt[d] + 5.2544878228486915` d) +.. log(2.))/d -1. ;} NO HIGH PRECISION AT THE PRELIMINARY VERSION, PLEASE!!!*/

z_type new2(z_type d){ z_type q=sqrt(d); return q*(3.39255 + q*(16.1046 +q*(-19.5216 + q*10.7458)))/ ( 1. + q*(4.1274 + q*5.25449)) + (-(2./3.) + log(2.))/d -1.;}

z_type new3(z_type d){ z_type q=sqrt(d); return // This is not misprint, there is d, not q. 0.16*q*(1. + q*(27.7934 + q*(358.688 +q*(-259.233 + d*61.6566))))/ (1. - 8.1192*q + 37.087*d) + (-131./192. + log(2))/d -1. ;}

// z_type git(z_type d, z_type x) { return //    old0(d) + x*( old1(d) + x* ( old2(d) + x*old3(d)));}

z_type git(z_type d, z_type x) { if(Re(d)>log(2.)) return new0(d)+x*(new1(d)+x*(new2(d)+x*new3(d))); return old0(d)+x*(old1(d)+x*(old2(d)+x*old3(d))); }

z_type fit1(z_type d, z_type x) { DB L=log(2.); if(Re(d)<.001) { if(Re(x)>-1) return 1.; if(Re(x)<-1) return -990.; } return (x+1.)*(git(d,x)*x+1.)+ log(x+2.)/d - log(2.)/d*(1.+x);}

z_type FIT1(z_type d,z_type z){ if(Re(d)<.03) { if(Re(z)<-1.) return (-30.); return 1.;} if(Re(z)<-.5)return log(FIT1(d,z+1.))/d; if(Re(z)>.5) return exp(d*FIT1(d,z-1.)); return fit1(d,z);}

main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=159,M1=M+1; int N=121,N1=N+1; DB X[M1],Y[N1], g[M1*N1], w[M1*N1]; // w is working array. char v[M1*N1]; // v is working array FILE *o;o=fopen("tetre2215.eps","w");ado(o,408,408); fprintf(o,"202 2 translate\n 100 100 scale\n"); DO(m,M1) X[m]=-2. +.02501*(m+.8); DO(n,N1) Y[n]=   +.033*(n); for(m=-20;m<21;m+=10){	M(.1*m, 0)L(.1*m,4)} for(n=0;n<41;n+=10){ 	M(-2,.1*n)L(2.,.1*n)} M(-2,M_E-1.)L(2,M_E-1.) //M(-2,.5)L(2,.5) M(-2,exp(1./M_E)-1.)L(2,exp(1./M_E)-1.) //M(-2,sqrt(2.)-1.)L(2,sqrt(2.)-1.) fprintf(o,".006 W 0 0 0 RGB S\n"); DO(m,M1)DO(n,N1){g[m*N1+n]=9999;} DO(m,M1){x=X[m]; //printf("run at x=%6.3f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y); p=Re(FIT1(log(1.+y),x)); //	p=Re(fit1(log(1.+y),x)); // For the debugging only! if(p>-85 && p<85) g[m*N1+n]=p; }}

fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=8.;q=2.; for(m=0;m<3;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".01 W .9 0 0 RGB S\n"); for(m=0;m<3;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".01 W 0 0 .9 RGB S\n"); for(m=-5;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"); m=-10; conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); // m=-20; conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); m=10; conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); //   m=20; conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); //   m=100; conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); // (Too many lines are difficylt to describe) fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf tetre2215.eps"); system(   "open tetre2215.pdf"); //these 2 commands may be specific for macintosh //getchar; system("killall Preview");// if run at another operational sysetm, may need to modify }

/*

(End of generator)*/