Tetration/Code/Polynomial25power

// Generator of the upper right part of the figure 200px
// In order to generate the figure above, you need 
// the plotter routines
// ContourPlot/code/ado.cin , than makes the header of the eps file, and
// ContourPlot/code/conto.cin, that draws there the contour lines.
// With these routines, you may compile and execute the source below
//
// Copyleft 2008 by Dmitrii Kouznetsov

1. include <math.h>
2. include <stdio.h>
3. include <stdlib.h>
4. define DB double
5. define DO(x,y) for(x=0;x<y;x++)
6. include <complex.h>
7. define z_type complex<double>
8. define Re(x) x.real()
9. define Im(x) x.imag()
10. define I z_type(0.,1.)

z_type F4natu(z_type z) // polybonial approcimation { int K=51,k; DB coef[51]={ 1. , 1.091767351258322138 , 0.271483212901696469 , 0.212453248176258214 , 0.069540376139988952 , 0.044291952090474256 , 0.014736742096390039 , 0.008668781817225539 , 0.002796479398385586 , 0.001610631290584341 , 0.000489927231484419 , 0.000288181071154065 , 0.000080094612538551 , 0.000050291141793809 , 0.000012183790344901 , 0.000008665533667382 , 0.000001687782319318 , 0.000001493253248573 , 0.000000198760764204 , 0.000000260867356004 , 0.000000014709954143 , 0.000000046834497327 ,-0.000000001549241666 , 0.000000008741510781 ,-0.000000001125787310 , 0.000000001707959267 ,-0.000000000377858315 , 0.000000000349577877 ,-0.000000000105377012 , 0.000000000074590971 ,-0.000000000027175982 , 0.000000000016460766 ,-0.000000000006741873 , 0.000000000003725329 ,-0.000000000001639087 , 0.000000000000858364 ,-0.000000000000394374 , 0.000000000000200252 ,-0.000000000000094420 , 0.000000000000047121 ,-0.000000000000022563 , 0.000000000000011155 ,-0.000000000000005391 , 0.000000000000002652 ,-0.000000000000001289 , 0.000000000000000633 ,-0.000000000000000309 , 0.000000000000000151 ,-0.000000000000000074 , 0.000000000000000036 ,-0.000000000000000018 }; z_type s=1.,t=z; for(k=1;k<=25;k++) { s+=coef[k]*t; t*=z; } //only 25 terms are used return s; }

1. include "conto.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z_type Zo=z_type(.31813150520476413, 1.3372357014306895); z_type Zc=z_type(.31813150520476413,-1.3372357014306895);

int M=150,M1=M+1; int N=151,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("TetrationPolynom25terms.eps","w");ado(o,0,0,124,124); fprintf(o,"62 62 translate\n 20 20 scale\n");

DO(m,M1) X[m]=-3+.04*m; DO(n,N1) Y[n]=-3+.04*(n-.5); //DO(n,N1) Y[n]=sy*sinh(.04*(n-N/2-.5));

for(m=-3;m<4;m++) { if(m==0){M(m,-3.1)L(m,3.1)} else {M(m,-3)L(m,3)} } for(n=-3;n<4;n++) {M( -3,n)L(3,n)} fprintf(o,".006 W 0 0 0 RGB S\n");

z_type tm,tp,F[M1*N1];

DO(m,M1)DO(n,N1){ g[m*N1+n]=9999; f[m*N1+n]=9999; } for(m=0;m<M1;m++){x=X[m]; DO(n,N1){y=Y[n]; z=z_type(x,y); c=F4natu(z); F[m*N1+n]=c; } }

//for(m=45;m<M1;m++) DO(n,N1){ F[m*N1+n] = exp( F[(m-10)*N1+n] ); } //for(m=34;m>=0;m--) DO(n,N1){ F[m*N1+n] = log( F[(m+10)*N1+n] ); }

DO(m,M1) DO(n,N1){ c=(F[m*N1+n]); p=Re(c); q=Im(c); if(p>-999 && p<999) g[m*N1+n]=p; if(q>-999 && q<999) f[m*N1+n]=q; }

p=1;q=99;

                 conto(o,f,w,v,X,Y,M,N, (-3*M_PI ),-q,q); fprintf(o,".04 W 1 0 1 RGB S\n");
                 conto(o,f,w,v,X,Y,M,N, ( -M_PI  ),-q,q); fprintf(o,".04 W 1 0 1 RGB S\n");

for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-3.+.1*n),-p, p); fprintf(o,".01 W 0 1 0 RGB S\n");

                 conto(o,f,w,v,X,Y,M,N, (-2.     ),-q ,q); fprintf(o,".03 W 1 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-2.+.1*n),-p ,p); fprintf(o,".01 W 0 1 0 RGB S\n");

                 conto(o,f,w,v,X,Y,M,N, (-1.     ),-q,q); fprintf(o,".03 W 1 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-1.+.1*n),-p ,p); fprintf(o,".01 W 0 1 0 RGB S\n");

                 conto(o,f,w,v,X,Y,M,N, (0.      ),-q,q); fprintf(o,".02 W 0 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( .1*n),-p ,p); fprintf(o,".01 W 0 1 0 RGB S\n");

                 conto(o,f,w,v,X,Y,M,N, ( 1.     ),-q ,q); fprintf(o,".03 W 0 0 1 RGB S\n");

for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 1.+.1*n),-p ,p); fprintf(o,".01 W 0 1 0 RGB S\n"); conto(o,f,w,v,X,Y,M,N, ( 2. ),-q ,q); fprintf(o,".03 W 0 0 1 RGB S\n"); for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 2.+.1*n),-p, p); fprintf(o,".01 W 0 1 0 RGB S\n");

                 conto(o,f,w,v,X,Y,M,N, ( M_PI   ),-q,q); fprintf(o,".04 W 1 0 1 RGB S\n");
                 conto(o,f,w,v,X,Y,M,N, (3*M_PI  ),-q,q); fprintf(o,".04 W 1 0 1 RGB S\n");

                 conto(o,g,w,v,X,Y,M,N, (-2.     ),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-2.+.1*n),-p,p); fprintf(o,".01 W 1 0 0 RGB S\n");

                 conto(o,g,w,v,X,Y,M,N, (-1.     ),-q,q); fprintf(o,".03 W 0 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-1.+.1*n),-p,p); fprintf(o,".01 W 1 0 0 RGB S\n");

                 conto(o,g,w,v,X,Y,M,N, (0.      ),-q,q); fprintf(o,".03 W 0 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( .1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");

                 conto(o,g,w,v,X,Y,M,N, ( 1.     ),-q,q); fprintf(o,".03 W 0 0 0 RGB S\n");

for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 1.+.1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");

                 conto(o,g,w,v,X,Y,M,N, ( 2.     ),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
                 conto(o,g,w,v,X,Y,M,N, ( 3.     ),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
                 conto(o,g,w,v,X,Y,M,N, ( 4.     ),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");

//M(-10,0)L(-2,0)fprintf(o,".04 W 1 0 1 RGB S\n"); fprintf(o,"showpage\n\%\%\%Trailer"); fclose(o); //system( "ggv TetrationPolynom25Terms.eps"); system( "open TetrationPolynom25Terms.eps"); system("ps2pdf TetrationPolynom25terms.eps"); getchar(); system("killall Preview"); }

// end of plotting program //