Difference between revisions of "File:Shelima600.png"

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Explicit plot of real and imaginary part of [[tetration to Sheldon base]] of imaginary argument.
−
Importing image file
  
  +
  +
$b=1.52598338517 + 0.0178411853321~ \mathrm{i}$.
  +
  +
The blue curve shows $y=\Re\Big( \mathrm{tet}_b(\mathrm i x)\Big)$
  +
  +
The red curve shows $y=\Im\Big( \mathrm{tet}_b(\mathrm i x)\Big)$
  +
  +
==Usage==
  +
The image is prototype of figure 18.5 of the English version of the book [[Superfunctions]]
  +
<ref>
  +
http://mizugadro.mydns.jp/BOOK/437.pdf
  +
D.Kouznetsov. Superfunctions. 2015.
  +
</ref>.
  +
  +
In the first Russian version [[Суперфункции]] of the book, this image is absent.
  +
  +
==References==
  +
<references/>
  +
  +
==Table of values ==
  +
<poem>
  +
$~ ~x~ ~$ $~ ~\Re(\mathrm{tet}_b(\mathrm i x))~ ~$ $~ ~\Im(\mathrm{tet}_b(\mathrm i x))$
  +
-10.00 2.2202212609 -1.3393771522
  +
-9.90 2.2196731381 -1.3388553660
  +
-9.80 2.2190910829 -1.3383114251
  +
-9.70 2.2184731185 -1.3377444826
  +
-9.60 2.2178171599 -1.3371536640
  +
-9.50 2.2171210078 -1.3365380660
  +
-9.40 2.2163823431 -1.3358967563
  +
-9.30 2.2155987208 -1.3352287720
  +
-9.20 2.2147675635 -1.3345331194
  +
-9.10 2.2138861545 -1.3338087726
  +
-9.00 2.2129516317 -1.3330546724
  +
-8.90 2.2119609791 -1.3322697257
  +
-8.80 2.2109110202 -1.3314528034
  +
-8.70 2.2097984096 -1.3306027402
  +
-8.60 2.2086196248 -1.3297183321
  +
-8.50 2.2073709574 -1.3287983354
  +
-8.40 2.2060485042 -1.3278414651
  +
-8.30 2.2046481579 -1.3268463926
  +
-8.20 2.2031655968 -1.3258117437
  +
-8.10 2.2015962752 -1.3247360964
  +
-8.00 2.1999354119 -1.3236179782
  +
-7.90 2.1981779800 -1.3224558632
  +
-7.80 2.1963186945 -1.3212481688
  +
-7.70 2.1943520007 -1.3199932521
  +
-7.60 2.1922720612 -1.3186894058
  +
-7.50 2.1900727435 -1.3173348536
  +
-7.40 2.1877476059 -1.3159277450
  +
-7.30 2.1852898835 -1.3144661496
  +
-7.20 2.1826924737 -1.3129480506
  +
-7.10 2.1799479207 -1.3113713370
  +
-7.00 2.1770484004 -1.3097337961
  +
-6.90 2.1739857032 -1.3080331037
  +
-6.80 2.1707512180 -1.3062668134
  +
-6.70 2.1673359142 -1.3044323456
  +
-6.60 2.1637303238 -1.3025269736
  +
-6.50 2.1599245231 -1.3005478090
  +
-6.40 2.1559081133 -1.2984917849
  +
-6.30 2.1516702011 -1.2963556371
  +
-6.20 2.1471993787 -1.2941358833
  +
-6.10 2.1424837030 -1.2918287992
  +
-6.00 2.1375106749 -1.2894303921
  +
-5.90 2.1322672181 -1.2869363712
  +
-5.80 2.1267396576 -1.2843421145
  +
-5.70 2.1209136985 -1.2816426317
  +
-5.60 2.1147744042 -1.2788325222
  +
-5.50 2.1083061753 -1.2759059295
  +
-5.40 2.1014927291 -1.2728564888
  +
-5.30 2.0943170796 -1.2696772695
  +
-5.20 2.0867615183 -1.2663607109
  +
-5.10 2.0788075973 -1.2628985502
  +
-5.00 2.0704361133 -1.2592817434
  +
-4.90 2.0616270956 -1.2555003763
  +
-4.80 2.0523597956 -1.2515435664
  +
-4.70 2.0426126821 -1.2473993541
  +
-4.60 2.0323634408 -1.2430545817
  +
-4.50 2.0215889804 -1.2384947601
  +
-4.40 2.0102654464 -1.2337039220
  +
-4.30 1.9983682448 -1.2286644588
  +
-4.20 1.9858720768 -1.2233569428
  +
-4.10 1.9727509879 -1.2177599308
  +
-4.00 1.9589784331 -1.2118497494
  +
-3.90 1.9445273631 -1.2056002612
  +
-3.80 1.9293703334 -1.1989826096
  +
-3.70 1.9134796423 -1.1919649425
  +
-3.60 1.8968275023 -1.1845121140
  +
-3.50 1.8793862518 -1.1765853645
  +
-3.40 1.8611286122 -1.1681419794
  +
-3.30 1.8420280011 -1.1591349277
  +
-3.20 1.8220589080 -1.1495124836
  +
-3.10 1.8011973445 -1.1392178346
  +
-3.00 1.7794213797 -1.1281886816
  +
-2.90 1.7567117731 -1.1163568397
  +
-2.80 1.7330527191 -1.1036478499
  +
-2.70 1.7084327173 -1.0899806167
  +
-2.60 1.6828455826 -1.0752670901
  +
-2.50 1.6562916111 -1.0594120161
  +
-2.40 1.6287789134 -1.0423127871
  +
-2.30 1.6003249281 -1.0238594279
  +
-2.20 1.5709581198 -1.0039347646
  +
-2.10 1.5407198646 -0.9824148312
  +
-2.00 1.5096665094 -0.9591695767
  +
-1.90 1.4778715856 -0.9340639471
  +
-1.80 1.4454281312 -0.9069594235
  +
-1.70 1.4124510594 -0.8777161012
  +
-1.60 1.3790794751 -0.8461953971
  +
-1.50 1.3454788118 -0.8122634650
  +
-1.40 1.3118426170 -0.7757953788
  +
-1.30 1.2783937743 -0.7366801138
  +
-1.20 1.2453849119 -0.6948263040
  +
-1.10 1.2130977120 -0.6501686844
  +
-1.00 1.1818408268 -0.6026750337
  +
-0.90 1.1519461162 -0.5523533237
  +
-0.80 1.1237629810 -0.4992586603
  +
-0.70 1.0976506656 -0.4434994833
  +
-0.60 1.0739685645 -0.3852424012
  +
-0.50 1.0530647752 -0.3247149921
  +
-0.40 1.0352633815 -0.2622059382
  +
-0.30 1.0208511970 -0.1980619898
  +
-0.20 1.0100649016 -0.1326814891
  +
-0.10 1.0030796228 -0.0665045046
  +
0.00 1.0000000000 0.0000000000
  +
0.10 1.0008546120 0.0663491799
  +
0.20 1.0055943462 0.1320624338
  +
0.30 1.0140948929 0.1966774148
  +
0.40 1.0261631142 0.2597647135
  +
0.50 1.0415466506 0.3209401766
  +
0.60 1.0599458447 0.3798741265
  +
0.70 1.0810269204 0.4362971165
  +
0.80 1.1044353661 0.4900022286
  +
0.90 1.1298086052 0.5408442355
  +
1.00 1.1567872534 0.5887361692
  +
1.10 1.1850245145 0.6336439551
  +
1.20 1.2141935082 0.6755797922
  +
1.30 1.2439925335 0.7145949050
  +
1.40 1.2741484179 0.7507721909
  +
1.50 1.3044182070 0.7842191660
  +
1.60 1.3345894889 0.8150614867
  +
1.70 1.3644796637 0.8434372142
  +
1.80 1.3939344425 0.8694918991
  +
1.90 1.4228258303 0.8933744915
  +
2.00 1.4510498021 0.9152340382
  +
2.10 1.4785238390 0.9352170954
  +
2.20 1.5051844494 0.9534657700
  +
2.30 1.5309847655 0.9701163005
  +
2.40 1.5558922770 0.9852980850
  +
2.50 1.5798867375 0.9991330757
  +
2.60 1.6029582648 1.0117354642
  +
2.70 1.6251056396 1.0232115932
  +
2.80 1.6463348018 1.0336600413
  +
2.90 1.6666575325 1.0431718336
  +
3.00 1.6860903115 1.0518307431
  +
3.10 1.7046533328 1.0597136520
  +
3.20 1.7223696637 1.0668909512
  +
3.30 1.7392645315 1.0734269577
  +
3.40 1.7553647215 1.0793803392
  +
3.50 1.7706980741 1.0848045336
  +
3.60 1.7852930661 1.0897481563
  +
3.70 1.7991784654 1.0942553916
  +
3.80 1.8123830487 1.0983663636
  +
3.90 1.8249353724 1.1021174851
  +
4.00 1.8368635897 1.1055417832
  +
4.10 1.8481953050 1.1086692018
  +
4.20 1.8589574618 1.1115268814
  +
4.30 1.8691762567 1.1141394158
  +
4.40 1.8788770769 1.1165290889
  +
4.50 1.8880844555 1.1187160898
  +
4.60 1.8968220432 1.1207187105
  +
4.70 1.9051125920 1.1225535247
  +
4.80 1.9129779496 1.1242355514
  +
4.90 1.9204390625 1.1257784031
  +
5.00 1.9275159849 1.1271944198
  +
5.10 1.9342278938 1.1284947908
  +
5.20 1.9405931079 1.1296896652
  +
5.30 1.9466291099 1.1307882509
  +
5.40 1.9523525708 1.1317989054
  +
5.50 1.9577793759 1.1327292168
  +
5.60 1.9629246530 1.1335860773
  +
5.70 1.9678027996 1.1343757500
  +
5.80 1.9724275118 1.1351039284
  +
5.90 1.9768118128 1.1357757907
  +
6.00 1.9809680809 1.1363960488
  +
6.10 1.9849080779 1.1369689923
  +
6.20 1.9886429758 1.1374985283
  +
6.30 1.9921833839 1.1379882174
  +
6.40 1.9955393749 1.1384413061
  +
6.50 1.9987205098 1.1388607560
  +
6.60 2.0017358620 1.1392492708
  +
6.70 2.0045940414 1.1396093194
  +
6.80 2.0073032162 1.1399431581
  +
6.90 2.0098711350 1.1402528501
  +
7.00 2.0123051475 1.1405402826
  +
7.10 2.0146122241 1.1408071836
  +
7.20 2.0167989751 1.1410551358
  +
7.30 2.0188716688 1.1412855895
  +
7.40 2.0208362487 1.1414998751
  +
7.50 2.0226983501 1.1416992133
  +
7.60 2.0244633157 1.1418847248
  +
7.70 2.0261362105 1.1420574393
  +
7.80 2.0277218365 1.1422183034
  +
7.90 2.0292247454 1.1423681880
  +
8.00 2.0306492523 1.1425078945
  +
8.10 2.0319994475 1.1426381610
  +
8.20 2.0332792080 1.1427596676
  +
8.30 2.0344922089 1.1428730416
  +
8.40 2.0356419337 1.1429788616
  +
8.50 2.0367316841 1.1430776619
  +
8.60 2.0377645897 1.1431699357
  +
8.70 2.0387436168 1.1432561392
  +
8.80 2.0396715769 1.1433366941
  +
8.90 2.0405511348 1.1434119905
  +
9.00 2.0413848162 1.1434823898
  +
9.10 2.0421750149 1.1435482264
  +
9.20 2.0429239999 1.1436098105
  +
9.30 2.0436339216 1.1436674297
  +
9.40 2.0443068184 1.1437213507
  +
9.50 2.0449446220 1.1437718210
  +
9.60 2.0455491634 1.1438190707
  +
9.70 2.0461221781 1.1438633134
  +
9.80 2.0466653107 1.1439047477
  +
9.90 2.0471801203 1.1439435581
  +
10.00 2.0476680845 1.1439799167
  +
</poem>
  +
  +
==[[C++]] generator of curves==
  +
  +
Files
  +
[[GLxw2048.inc]] ,
  +
[[TetSheldonIma.inc]] ,
  +
[[ado.cin]] ,
  +
[[conto.cin]] ,
  +
[[filog.cin]]
  +
should be loaded in order to compile the code below:
  +
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
// using namespace std;
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
#include "conto.cin"
  +
#include "filog.cin"
  +
z_type b=z_type( 1.5259833851700000, 0.0178411853321000);
  +
z_type a=log(b);
  +
z_type Zo=Filog(a);
  +
z_type Zc=conj(Filog(conj(a)));
  +
DB A=32.;
  +
z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd;
  +
#include "GLxw2048.inc"
  +
int K=2048;
  +
//#include "ima6.inc"
  +
#include "TetSheldonIma.inc"
  +
z_type E[2048],G[2048];
  +
DO(k,K){c=F[k]; E[k]=log(c)/a; G[k]=exp(a*c);}
  +
c=0.;
  +
// z+=z_type(0.1196573712872846, 0.1299776198056910);
  +
z+=z_type( 0.1196591376539 , 0.1299777213955 );
  +
DO(k,K){t=A*GLx[k];c+=GLw[k]*(G[k]/(z_type( 1.,t)-z)-E[k]/(z_type(-1.,t)-z));}
  +
cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) );
  +
cd=.5-I/(2.*M_PI)*log( (z_type(1.,-A)-z)/(z_type(1., A)+z) );
  +
c=c*(A/(2.*M_PI)) +Zo*cu+Zc*cd;
  +
return c;}
  +
  +
int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d;
  +
  +
// FILE *o;o=fopen("tetsheldonmap.eps","w");ado(o,602,202);
  +
FILE *o;
  +
o=fopen("04.eps","w");ado(o,202,62);
  +
fprintf(o,"101 31 translate\n 10 10 scale\n");
  +
  +
for(m=-10;m<11;m++){if(m==0){M(m,-3.2)L(m,3.2)} else{M(m,-3)L(m,3)}}
  +
for(n=-3;n<4;n++){ M( -10,n)L(10,n)}
  +
fprintf(o,".008 W 0 0 0 RGB S\n");
  +
  +
DO(m,201){x=.1*(m-100); z=z_type(0,x); c=tetb(z);
  +
p=Re(c); q=Im(c);
  +
y=p; if(m==0) M(x,y) else L(x,y)
  +
printf("%6.2lf %14.10lf %14.10lf\n",x,p,q);
  +
}
  +
fprintf(o,".04 W 0 0 1 RGB S\n");
  +
  +
DO(m,201){x=.1*(m-100); z=z_type(0,x); c=tetb(z);
  +
p=Re(c); q=Im(c);
  +
y=q; if(m==0) M(x,y) else L(x,y) }
  +
fprintf(o,".04 W 1 0 0 RGB S\n");
  +
  +
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf 04.eps");
  +
system( "open 04.pdf");
  +
getchar(); system("killall Preview");
  +
}
  +
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry}
  +
\paperwidth 204pt
  +
\paperheight 64pt
  +
%\textwidth 700pt
  +
\usepackage{graphics}
  +
\newcommand \sx \scalebox
  +
\newcommand \ing \includegraphics
  +
\parindent 0pt
  +
\topmargin -108pt
  +
\oddsidemargin -72pt
  +
\begin{document}
  +
\begin{picture}(602,62)
  +
\put(0,0){\ing{04}}
  +
\put(97,59){\sx{.6}{$y$}}
  +
\put(97,49){\sx{.6}{$2$}}
  +
\put(97,39){\sx{.6}{$1$}}
  +
\put(97,29){\sx{.6}{$0$}}
  +
\put(92,19){\sx{.6}{$-1$}}
  +
\put(92, 9){\sx{.6}{$-2$}}
  +
  +
\put(15,25){\sx{.6}{$-8$}}
  +
\put(35,25){\sx{.6}{$-6$}}
  +
\put(55,25){\sx{.6}{$-4$}}
  +
\put(75,25){\sx{.6}{$-2$}}
  +
\put(100,25){\sx{.6}{$0$}}
  +
\put(120,25){\sx{.6}{$2$}}
  +
\put(140,25){\sx{.6}{$4$}}
  +
\put(160,25){\sx{.6}{$6$}}
  +
\put(180,25){\sx{.6}{$8$}}
  +
\put(199,25){\sx{.6}{$x$}}
  +
  +
\put(10,56){\sx{.7}{$y\!=\! \Re\big(\mathrm{tet}_b(\mathrm i x)\big)$}}
  +
\put(10,11){\sx{.7}{$y\!=\! \Im\big(\mathrm{tet}_b(\mathrm i x)\big)$}}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
  +
[[Category:Book]]
  +
[[Category:BookPlot]]
  +
[[Category:C++]]
  +
[[Category:Explicit plot]]
  +
[[Category:Latex]]
  +
[[Category:Tetration]]
  +
[[Category:Tetration to Sheldon base]]
  +
[[Category:Sheldon base]]

Latest revision as of 08:51, 1 December 2018

Explicit plot of real and imaginary part of tetration to Sheldon base of imaginary argument.

$b=1.52598338517 + 0.0178411853321~ \mathrm{i}$.

The blue curve shows $y=\Re\Big( \mathrm{tet}_b(\mathrm i x)\Big)$

The red curve shows $y=\Im\Big( \mathrm{tet}_b(\mathrm i x)\Big)$

Usage

The image is prototype of figure 18.5 of the English version of the book Superfunctions [1].

In the first Russian version Суперфункции of the book, this image is absent.

References

  1. ↑ http://mizugadro.mydns.jp/BOOK/437.pdf D.Kouznetsov. Superfunctions. 2015.

Table of values

$~ ~x~ ~$ $~ ~\Re(\mathrm{tet}_b(\mathrm i x))~ ~$ $~ ~\Im(\mathrm{tet}_b(\mathrm i x))$
-10.00 2.2202212609 -1.3393771522
 -9.90 2.2196731381 -1.3388553660
 -9.80 2.2190910829 -1.3383114251
 -9.70 2.2184731185 -1.3377444826
 -9.60 2.2178171599 -1.3371536640
 -9.50 2.2171210078 -1.3365380660
 -9.40 2.2163823431 -1.3358967563
 -9.30 2.2155987208 -1.3352287720
 -9.20 2.2147675635 -1.3345331194
 -9.10 2.2138861545 -1.3338087726
 -9.00 2.2129516317 -1.3330546724
 -8.90 2.2119609791 -1.3322697257
 -8.80 2.2109110202 -1.3314528034
 -8.70 2.2097984096 -1.3306027402
 -8.60 2.2086196248 -1.3297183321
 -8.50 2.2073709574 -1.3287983354
 -8.40 2.2060485042 -1.3278414651
 -8.30 2.2046481579 -1.3268463926
 -8.20 2.2031655968 -1.3258117437
 -8.10 2.2015962752 -1.3247360964
 -8.00 2.1999354119 -1.3236179782
 -7.90 2.1981779800 -1.3224558632
 -7.80 2.1963186945 -1.3212481688
 -7.70 2.1943520007 -1.3199932521
 -7.60 2.1922720612 -1.3186894058
 -7.50 2.1900727435 -1.3173348536
 -7.40 2.1877476059 -1.3159277450
 -7.30 2.1852898835 -1.3144661496
 -7.20 2.1826924737 -1.3129480506
 -7.10 2.1799479207 -1.3113713370
 -7.00 2.1770484004 -1.3097337961
 -6.90 2.1739857032 -1.3080331037
 -6.80 2.1707512180 -1.3062668134
 -6.70 2.1673359142 -1.3044323456
 -6.60 2.1637303238 -1.3025269736
 -6.50 2.1599245231 -1.3005478090
 -6.40 2.1559081133 -1.2984917849
 -6.30 2.1516702011 -1.2963556371
 -6.20 2.1471993787 -1.2941358833
 -6.10 2.1424837030 -1.2918287992
 -6.00 2.1375106749 -1.2894303921
 -5.90 2.1322672181 -1.2869363712
 -5.80 2.1267396576 -1.2843421145
 -5.70 2.1209136985 -1.2816426317
 -5.60 2.1147744042 -1.2788325222
 -5.50 2.1083061753 -1.2759059295
 -5.40 2.1014927291 -1.2728564888
 -5.30 2.0943170796 -1.2696772695
 -5.20 2.0867615183 -1.2663607109
 -5.10 2.0788075973 -1.2628985502
 -5.00 2.0704361133 -1.2592817434
 -4.90 2.0616270956 -1.2555003763
 -4.80 2.0523597956 -1.2515435664
 -4.70 2.0426126821 -1.2473993541
 -4.60 2.0323634408 -1.2430545817
 -4.50 2.0215889804 -1.2384947601
 -4.40 2.0102654464 -1.2337039220
 -4.30 1.9983682448 -1.2286644588
 -4.20 1.9858720768 -1.2233569428
 -4.10 1.9727509879 -1.2177599308
 -4.00 1.9589784331 -1.2118497494
 -3.90 1.9445273631 -1.2056002612
 -3.80 1.9293703334 -1.1989826096
 -3.70 1.9134796423 -1.1919649425
 -3.60 1.8968275023 -1.1845121140
 -3.50 1.8793862518 -1.1765853645
 -3.40 1.8611286122 -1.1681419794
 -3.30 1.8420280011 -1.1591349277
 -3.20 1.8220589080 -1.1495124836
 -3.10 1.8011973445 -1.1392178346
 -3.00 1.7794213797 -1.1281886816
 -2.90 1.7567117731 -1.1163568397
 -2.80 1.7330527191 -1.1036478499
 -2.70 1.7084327173 -1.0899806167
 -2.60 1.6828455826 -1.0752670901
 -2.50 1.6562916111 -1.0594120161
 -2.40 1.6287789134 -1.0423127871
 -2.30 1.6003249281 -1.0238594279
 -2.20 1.5709581198 -1.0039347646
 -2.10 1.5407198646 -0.9824148312
 -2.00 1.5096665094 -0.9591695767
 -1.90 1.4778715856 -0.9340639471
 -1.80 1.4454281312 -0.9069594235
 -1.70 1.4124510594 -0.8777161012
 -1.60 1.3790794751 -0.8461953971
 -1.50 1.3454788118 -0.8122634650
 -1.40 1.3118426170 -0.7757953788
 -1.30 1.2783937743 -0.7366801138
 -1.20 1.2453849119 -0.6948263040
 -1.10 1.2130977120 -0.6501686844
 -1.00 1.1818408268 -0.6026750337
 -0.90 1.1519461162 -0.5523533237
 -0.80 1.1237629810 -0.4992586603
 -0.70 1.0976506656 -0.4434994833
 -0.60 1.0739685645 -0.3852424012
 -0.50 1.0530647752 -0.3247149921
 -0.40 1.0352633815 -0.2622059382
 -0.30 1.0208511970 -0.1980619898
 -0.20 1.0100649016 -0.1326814891
 -0.10 1.0030796228 -0.0665045046
  0.00 1.0000000000 0.0000000000
  0.10 1.0008546120 0.0663491799
  0.20 1.0055943462 0.1320624338
  0.30 1.0140948929 0.1966774148
  0.40 1.0261631142 0.2597647135
  0.50 1.0415466506 0.3209401766
  0.60 1.0599458447 0.3798741265
  0.70 1.0810269204 0.4362971165
  0.80 1.1044353661 0.4900022286
  0.90 1.1298086052 0.5408442355
  1.00 1.1567872534 0.5887361692
  1.10 1.1850245145 0.6336439551
  1.20 1.2141935082 0.6755797922
  1.30 1.2439925335 0.7145949050
  1.40 1.2741484179 0.7507721909
  1.50 1.3044182070 0.7842191660
  1.60 1.3345894889 0.8150614867
  1.70 1.3644796637 0.8434372142
  1.80 1.3939344425 0.8694918991
  1.90 1.4228258303 0.8933744915
  2.00 1.4510498021 0.9152340382
  2.10 1.4785238390 0.9352170954
  2.20 1.5051844494 0.9534657700
  2.30 1.5309847655 0.9701163005
  2.40 1.5558922770 0.9852980850
  2.50 1.5798867375 0.9991330757
  2.60 1.6029582648 1.0117354642
  2.70 1.6251056396 1.0232115932
  2.80 1.6463348018 1.0336600413
  2.90 1.6666575325 1.0431718336
  3.00 1.6860903115 1.0518307431
  3.10 1.7046533328 1.0597136520
  3.20 1.7223696637 1.0668909512
  3.30 1.7392645315 1.0734269577
  3.40 1.7553647215 1.0793803392
  3.50 1.7706980741 1.0848045336
  3.60 1.7852930661 1.0897481563
  3.70 1.7991784654 1.0942553916
  3.80 1.8123830487 1.0983663636
  3.90 1.8249353724 1.1021174851
  4.00 1.8368635897 1.1055417832
  4.10 1.8481953050 1.1086692018
  4.20 1.8589574618 1.1115268814
  4.30 1.8691762567 1.1141394158
  4.40 1.8788770769 1.1165290889
  4.50 1.8880844555 1.1187160898
  4.60 1.8968220432 1.1207187105
  4.70 1.9051125920 1.1225535247
  4.80 1.9129779496 1.1242355514
  4.90 1.9204390625 1.1257784031
  5.00 1.9275159849 1.1271944198
  5.10 1.9342278938 1.1284947908
  5.20 1.9405931079 1.1296896652
  5.30 1.9466291099 1.1307882509
  5.40 1.9523525708 1.1317989054
  5.50 1.9577793759 1.1327292168
  5.60 1.9629246530 1.1335860773
  5.70 1.9678027996 1.1343757500
  5.80 1.9724275118 1.1351039284
  5.90 1.9768118128 1.1357757907
  6.00 1.9809680809 1.1363960488
  6.10 1.9849080779 1.1369689923
  6.20 1.9886429758 1.1374985283
  6.30 1.9921833839 1.1379882174
  6.40 1.9955393749 1.1384413061
  6.50 1.9987205098 1.1388607560
  6.60 2.0017358620 1.1392492708
  6.70 2.0045940414 1.1396093194
  6.80 2.0073032162 1.1399431581
  6.90 2.0098711350 1.1402528501
  7.00 2.0123051475 1.1405402826
  7.10 2.0146122241 1.1408071836
  7.20 2.0167989751 1.1410551358
  7.30 2.0188716688 1.1412855895
  7.40 2.0208362487 1.1414998751
  7.50 2.0226983501 1.1416992133
  7.60 2.0244633157 1.1418847248
  7.70 2.0261362105 1.1420574393
  7.80 2.0277218365 1.1422183034
  7.90 2.0292247454 1.1423681880
  8.00 2.0306492523 1.1425078945
  8.10 2.0319994475 1.1426381610
  8.20 2.0332792080 1.1427596676
  8.30 2.0344922089 1.1428730416
  8.40 2.0356419337 1.1429788616
  8.50 2.0367316841 1.1430776619
  8.60 2.0377645897 1.1431699357
  8.70 2.0387436168 1.1432561392
  8.80 2.0396715769 1.1433366941
  8.90 2.0405511348 1.1434119905
  9.00 2.0413848162 1.1434823898
  9.10 2.0421750149 1.1435482264
  9.20 2.0429239999 1.1436098105
  9.30 2.0436339216 1.1436674297
  9.40 2.0443068184 1.1437213507
  9.50 2.0449446220 1.1437718210
  9.60 2.0455491634 1.1438190707
  9.70 2.0461221781 1.1438633134
  9.80 2.0466653107 1.1439047477
  9.90 2.0471801203 1.1439435581
10.00 2.0476680845 1.1439799167

C++ generator of curves

Files GLxw2048.inc , TetSheldonIma.inc , ado.cin , conto.cin , filog.cin should be loaded in order to compile the code below:


 #include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
 #define DB double
 #define DO(x,y) for(x=0;x<y;x++)
// using namespace std;
 #include <complex>
 typedef std::complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)
 #include "conto.cin"
 #include "filog.cin"
z_type b=z_type( 1.5259833851700000, 0.0178411853321000);
z_type a=log(b);
z_type Zo=Filog(a);
z_type Zc=conj(Filog(conj(a)));
DB A=32.;
z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd;
#include "GLxw2048.inc"
int K=2048;
//#include "ima6.inc"
#include "TetSheldonIma.inc"
z_type E[2048],G[2048];
DO(k,K){c=F[k]; E[k]=log(c)/a; G[k]=exp(a*c);}
c=0.;
// z+=z_type(0.1196573712872846, 0.1299776198056910);
z+=z_type( 0.1196591376539 , 0.1299777213955 );
DO(k,K){t=A*GLx[k];c+=GLw[k]*(G[k]/(z_type( 1.,t)-z)-E[k]/(z_type(-1.,t)-z));}
 cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) );
 cd=.5-I/(2.*M_PI)*log( (z_type(1.,-A)-z)/(z_type(1., A)+z) );
 c=c*(A/(2.*M_PI)) +Zo*cu+Zc*cd;
 return c;}

int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d;

// FILE *o;o=fopen("tetsheldonmap.eps","w");ado(o,602,202);
FILE *o;
o=fopen("04.eps","w");ado(o,202,62);
 fprintf(o,"101 31 translate\n 10 10 scale\n");

 for(m=-10;m<11;m++){if(m==0){M(m,-3.2)L(m,3.2)} else{M(m,-3)L(m,3)}}
 for(n=-3;n<4;n++){ M( -10,n)L(10,n)}
 fprintf(o,".008 W 0 0 0 RGB S\n");

DO(m,201){x=.1*(m-100); z=z_type(0,x); c=tetb(z);
        p=Re(c); q=Im(c);
        y=p; if(m==0) M(x,y) else L(x,y)
        printf("%6.2lf %14.10lf %14.10lf\n",x,p,q);
        }
 fprintf(o,".04 W 0 0 1 RGB S\n");

DO(m,201){x=.1*(m-100); z=z_type(0,x); c=tetb(z);
        p=Re(c); q=Im(c);
        y=q; if(m==0) M(x,y) else L(x,y) }
 fprintf(o,".04 W 1 0 0 RGB S\n");


 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf 04.eps");
        system( "open 04.pdf");
        getchar(); system("killall Preview");
 }

Latex generator of labels


 \documentclass[12pt]{article}
 \usepackage{geometry}
 \paperwidth 204pt
 \paperheight 64pt
 %\textwidth 700pt
 \usepackage{graphics}
 \newcommand \sx \scalebox
 \newcommand \ing \includegraphics
\parindent 0pt
\topmargin -108pt
\oddsidemargin -72pt
\begin{document}
\begin{picture}(602,62)
\put(0,0){\ing{04}}
\put(97,59){\sx{.6}{$y$}}
\put(97,49){\sx{.6}{$2$}}
\put(97,39){\sx{.6}{$1$}}
\put(97,29){\sx{.6}{$0$}}
\put(92,19){\sx{.6}{$-1$}}
\put(92, 9){\sx{.6}{$-2$}}

\put(15,25){\sx{.6}{$-8$}}
\put(35,25){\sx{.6}{$-6$}}
\put(55,25){\sx{.6}{$-4$}}
\put(75,25){\sx{.6}{$-2$}}
\put(100,25){\sx{.6}{$0$}}
\put(120,25){\sx{.6}{$2$}}
\put(140,25){\sx{.6}{$4$}}
\put(160,25){\sx{.6}{$6$}}
\put(180,25){\sx{.6}{$8$}}
\put(199,25){\sx{.6}{$x$}}

\put(10,56){\sx{.7}{$y\!=\! \Re\big(\mathrm{tet}_b(\mathrm i x)\big)$}}
\put(10,11){\sx{.7}{$y\!=\! \Im\big(\mathrm{tet}_b(\mathrm i x)\big)$}}
\end{picture}
\end{document}

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