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Tetration/Code/ApproLP100

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// generator of figure of approximation of tetration with elementary function.
TetrationApproLP100.jpg

// For the compillation of this code, the two graphical routines are required:

// ContourPlot/code/ado.cin (function that makes header of the eps file)

// ContourPlot/code/conto.cin (function which draws a level)

// Copyleft 2008 by Dmitrii Kouznetosv.

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex.h>
#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
z_type F4natu(z_type z)
{ 
int K=100,k;
//int K=96,k;
DB d[120]={
  0.30685281944005469058 
, 1.18353470251664338875
, 1.58593285160678321155
, 1.36629265207672068172
, 1.36264601823980036066
, 1.21734246689515424045
, 1.10981816083559525765
, 0.96674692974769849130
, 0.84089872598668435888
, 0.71353210966804747617
, 0.60168548504001373445
, 0.49928574281440518678
, 0.41140086629121763728
, 0.33506195665178500898
, 0.27104779243942234146
, 0.21728554054610033086
, 0.17311050207880035456
, 0.13690016038526570119
, 0.10765949732729711286
, 0.08413804539743192923
, 0.06542450487497340761
, 0.05060001212013485322
, 0.03895655493977817629
, 0.02985084640296329153
, 0.02277908979501017117
, 0.01730960309240666892
, 0.01310389615589767874
, 0.00988251130733762764
, 0.00742735935367278347
, 0.00556296426263720549
, 0.00415334478103463346
, 0.00309116153137843543
, 0.00229387529664008653
, 0.00169729976398295653
, 0.00125245885041635465
, 0.00092172809095368547
, 0.00067661152429638357
, 0.00049544127485341987
, 0.00036192128589181518
, 0.00026376927786672476
, 0.00019180840045267570
, 0.00013917553105723647
, 0.00010077412023867018
, 0.00007281884753121133
, 0.00005251474516228446
, 0.00003779882770351268
, 0.00002715594536867241
, 0.00001947408515177282
, 0.00001394059355016322
, 0.00000996213949015693
, 0.00000710713872292710
, 0.00000506199803708578
, 0.00000359960968975399
, 0.00000255569149787694
, 0.00000181175810338313
, 0.00000128245831538430
, 0.00000090647322737496
, 0.00000063980422418981
, 0.00000045095738191441
, 0.00000031741772125007
, 0.00000022312521183625
, 0.00000015663840476155
, 0.00000010982301013230
, 0.00000007690305934973
, 0.00000005378502675604
, 0.00000003757126131521
, 0.00000002621429405247
, 0.00000001826909956818
, 0.00000001271754463425
, 0.00000000884310192977
, 0.00000000614230041407
, 0.00000000426177146865
, 0.00000000295386817285
, 0.00000000204522503591
, 0.00000000141464900426
, 0.00000000097750884878
, 0.00000000067478454029
, 0.00000000046535930671
, 0.00000000032062550784
, 0.00000000022069891976
, 0.00000000015177557961
, 0.00000000010428189463
, 0.00000000007158597119
, 0.00000000004909806710
, 0.00000000003364531769
, 0.00000000002303635851
, 0.00000000001575933679
, 0.00000000001077213757
, 0.00000000000735717912
, 0.00000000000502077719
, 0.00000000000342362421
, 0.00000000000233271256
, 0.00000000000158818623
, 0.00000000000108046566
, 0.00000000000073450488
, 0.00000000000049894945
, 0.00000000000033868911
, 0.00000000000022973789
, 0.00000000000015572383
, 0.00000000000010548054
, 0.00000000000007139840
, 0.00000000000004829557
, 0.00000000000003264619
, 0.00000000000002205299
, 0.00000000000001488731
, 0.00000000000001004347
, 0.00000000000000677124
, 0.00000000000000456225
, 0.00000000000000307196
, 0.00000000000000206720
, 0.00000000000000139022
, 0.00000000000000093437
, 0.00000000000000062762
, 0.00000000000000042133
, 0.00000000000000028267
, 0.00000000000000018954
, 0.00000000000000012701
, 0.00000000000000008507
, 0.00000000000000005694
, 0.00000000000000003809
};
z_type s=0.;
z_type z2=z/2.;
z_type t=1.; 
for(k=0;k<=K;k++) { s+=d[k]*t; t*=z2; }
//s+=4.+z;
return s+log(z+2.);
return s;
}
#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=300,M1=M+1;
int N=600,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("TetrationApproLP100.eps","w");ado(o,0,0,604,604);
fprintf(o,"302 302 translate\n 100 100 scale\n");
DO(m,M1) X[m]=-3+.02*m;
DO(n,N1) Y[n]=-3+.01*(n+.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 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; // log(c);
				}
		}
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=2;q=9;
                  conto(o,f,w,v,X,Y,M,N, (-4      ),-q,q); fprintf(o,".004 W 1 0 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-3      ),-q,q); fprintf(o,".004 W 1 0 0 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,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-2.     ),-q,q); fprintf(o,".004 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,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-1.     ),-q,q); fprintf(o,".004 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,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 0.  ),-99,99); fprintf(o,".004 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 0.+.1*n),-p,p); fprintf(o,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 1.     ),-q,q); fprintf(o,".004 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,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 2.     ),-q,q); fprintf(o,".004 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,".002 W 0 .8 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 3      ),-q,q); fprintf(o,".004 W 0 0 1 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 4      ),-q,q); fprintf(o,".004 W 0 0 1 RGB S\n");
//
                  conto(o,g,w,v,X,Y,M,N, (-4.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (-3.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-3.+.1*n),-p,p); fprintf(o,".002 W 1 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (-2.     ),-p,p); fprintf(o,".004 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,".002 W 1 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (-1.     ),-q,q); fprintf(o,".004 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,".002 W 1 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (0.    ),-99,99); fprintf(o,".004 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,".002 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 1.     ),-q,q); fprintf(o,".004 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,".002 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 2.     ),-p,p); fprintf(o,".004 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,".002 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 3.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 4.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 5.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 6.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 7.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 8.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 9.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (10.     ),-p,p); fprintf(o,".004 W 0 0 0 RGB S\n");
//
                  conto(o,f,w,v,X,Y,M,N, ( Im(Zo)     ),-p,p); fprintf(o,".005 W 0 .6 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-Im(Zo)     ),-p,p); fprintf(o,".005 W 0 .6 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (Re(Zo)     ),-p,p); fprintf(o,".005 W .7 0 .7 RGB S\n");
//M(-10,0)L(-2,0)fprintf(o,".04 W 1 0 1 RGB S\n"); //draw the pink cutline
fprintf(o,"showpage\n\%\%\%Trailer"); fclose(o);
//system( "ggv TetrationApproLP100.eps"); //for linux
system(  "open TetrationApproLP100.eps"); //for macintosh
system("ps2pdf TetrationApproLP100.eps");
getchar(); system("killall Preview");	  //for macintosh
} 
// end of file TetrationApproLP100.cc