File:B271t3T.png: Difference between revisions

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imported>Dmitrii Kouznetsov
({{Image_Details|user |description = Complex map of natural tetration tet, id est, tetration to natural base <math>b=\mathrm e\approx 1.71</math> ; <math>u</math> has sense of the real part, and <math>v</math> ha sense of imaginary part of <nath>\mathrm{tet}(x\!+\!\mathrm i y)</math> |author = ~~~ |date-created = year 2014 |pub-country = Japan, Germany |notes = Similar map is used at the cover of the Russian book Суперфункции <ref> https://www.morebooks.de/store...)
 
imported>Dmitrii Kouznetsov
(generators)
Line 18: Line 18:
== Licensing ==
== Licensing ==
{{CC|by|3.0}}
{{CC|by|3.0}}
==[[C++]] generator of map==
Files [[fsexp.cin]], [[ado.cin]] and [[conto.cin]] should be loaded to the working directory in order to compile the [[C++]] code below
<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 complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "fsexp.cin"
//#include "fslog.cin"
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
int M=801,M1=M+1;
int N=401,N1=N+1;
DB X[M1],Y[N1];
DB *g, *f, *w; // w is working array.
g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
char v[M1*N1]; // v is working array
FILE *o;o=fopen("b271tMap3.eps","w");  ado(o,802,802);
fprintf(o,"401 401 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
DO(m,M1) X[m]=-4.+.01*(m-.5);
for(n=0;n<N1;n++) Y[n]=sinh((2./200.)*(n-200.5));
for(m=-4;m<5;m++) {M(m,-4)L(m,4)}
for(n=-4;n<5;n++) {M(  -4,n)L(4,n)} fprintf(o,".006 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){      g[m*N1+n]=999;
                      f[m*N1+n]=999;}
DB b=sqrt(2);
DO(m,M1){x=X[m]; printf("x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
      {
      c=FSEXP(z);
        p=Re(c); q=Im(c);
        if(p>-12 && p<12 && fabs(q)>1.e-12) g[m*N1+n]=p;
        if(q>-12 && q<12 && fabs(q)>1.e-12) f[m*N1+n]=q;
      }
      }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");
p=1.;q=.3;
for(m=-8;m<8;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n");
for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n");
for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n");
for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n");
for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n");
              conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n");
for(m=-10;m<11;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(-2,0)L(-4,0)fprintf(o,"0 setlinecap .03 W 1 1 1 RGB S\n");
for(n=0;n<11;n++){ M(-2-.2*(n+.2),0) L(-2-.2*(n+.45),0) } fprintf(o,".04 W 1 .5 0 RGB S\n");
for(n=0;n<21;n++){ M(-2-.2*(n+.7),0) L(-2-.2*(n+.95),0) } fprintf(o,".04 W 0 .5 1 RGB S\n");
fprintf(o,"0 setlinejoin 0 setlinecap\n");
fprintf(o,"showpage\n");
fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o);
free(f);
free(g);
free(w);
      system("epstopdf b271tMap3.eps");
      system(    "open b271tMap3.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}
</nowiki>
==[[Latex]] generator of labels==
% <nowiki>
\documentclass[12pt]{article} % <br>
\paperheight 828px % <br>
\paperwidth 836px % <br>
\textwidth 1294px % <br>
\textheight 1100px % <br>
\topmargin -104px % <br>
\oddsidemargin -78px % <br>
\usepackage{graphics} % <br>
\usepackage{rotating} % <br>
\newcommand \sx {\scalebox} % <br>
\newcommand \rot {\begin{rotate}} % <br>
\newcommand \ero {\end{rotate}} % <br>
\newcommand \ing {\includegraphics} % <br>
\newcommand \rmi {\mathrm{i}} % <br>
\begin{document} % <br>
\newcommand \zoomax { % <br>
\put(18, 806){\sx{3.3}{$y$}} % <br>
\put(18, 713){\sx{3}{$3$}} % <br>
\put(18, 613){\sx{3}{$2$}} % <br>
\put(18, 513){\sx{3}{$1$}} % <br>
\put(18, 413){\sx{3}{$0$}} % <br>
\put(-6, 313){\sx{3}{$-1$}} % <br>
\put(-6, 213){\sx{3}{$-2$}} % <br>
\put(-6, 113){\sx{3}{$-3$}} % <br>
\put(014, -5){\sx{3}{$-4$}} % <br>
\put(114, -5){\sx{3}{$-3$}} % <br>
\put(214, -5){\sx{3}{$-2$}} % <br>
\put(314, -5){\sx{3}{$-1$}} % <br>
\put(435, -5){\sx{3}{$0$}} % <br>
\put(535, -5){\sx{3}{$1$}} % <br>
\put(635, -5){\sx{3}{$2$}} % <br>
\put(735, -5){\sx{3}{$3$}} % <br>
\put(827,-4){\sx{3}{$x$}} % <br>
} % <br>
\parindent 0pt % <br>
\sx{1}{\begin{picture}(852,820) \put(40,20){\ing{b271tMap3}} % <br>
\zoomax % <br>
\put(60,415){\sx{2.8}{\bf cut}} % <br>
\put(340,548){\sx{3}{$v\!=\!1$}} % <br>
\put(360,414){\sx{3}{$v\!=\!0$}} % <br>
\put(760,414){\sx{3}{$v\!=\!0$}} % <br>
\put(340,280){\sx{3}{$v\!=\!-1$}} % <br>
\put(70,800){\sx{2.5}{$f\approx L\approx0.318+1.337i$}} % <br>
\put(60,60){\sx{2.5}{$f\approx L^*\approx0.318-1.337i$}} % <br>
\put(100,638){\sx{2.5}{$v\!=\!1.4$}}  % <br>
\put(552,745){\sx{2.5}{$v\!=\!1.4$}} % <br>
\put(100,198){\sx{2.5}{$v\!=\!-\!1.4$}}%  <br>
\put(540,90){\sx{2.5}{$v\!=\!-\!1.4$}} % <br>
\put(666,726){\sx{2.5}{$u\!=\!0.2$}} % <br>
\put(216,616){\sx{2.5}{$u\!=\!0.2$}} % <br>
\put(660,642){\sx{3}{$u\!=\!0$}} %  <br>
\put(210,536){\sx{3}{$u\!=\!0$}} %  <br>
\put(410,700){\sx{2.5}{$u\!=\!0.4$}} % <br>
\put(217,213){\sx{2.5}{$u\!=\!0.2$}} %  <br>
\put(410,130){\sx{2.5}{$u\!=\!0.4$}} % <br>
\end{picture}} % <br>
\end{document} % <br>
</nowiki>
==References==
<references/>
[[Category:Superfunction]]
[[Category:Tetration]]
[[Category:Complex map]]
[[Category:TORI]]

Revision as of 10:46, 4 September 2014

Summary

Title / Description


Complex map of natural tetration tet, id est, tetration to natural base  ; has sense of the real part, and ha sense of imaginary part of <nath>\mathrm{tet}(x\!+\!\mathrm i y)</math>
Citizendium author
& Copyright holder


Copyright © Dmitrii Kouznetsov.
See below for licence/re-use information.
Date created


year 2014
Country of first publication


Japan, Germany
Notes


Similar map is used at the cover of the Russian book Суперфункции [1].

The format of this map is adjisted to that of the natural pentation at http://en.citizendium.org/wiki/File:Penmap.jpg in order to simplify the comparison

Other versions


http://mizugadro.mydns.jp/t/index.php/File:B271t3T.png
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Licensing

This media, B271t3T.png, is licenced under the Creative Commons Attribution 3.0 Unported License

You are free: To Share — To copy, distribute and transmit the work; To Remix — To adapt the work.
Under the following conditions: Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
For any reuse or distribution, you must make clear to others the licence terms of this work (the best way to do this is with a link to this licence's web page). Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this licence impairs or restricts the author's moral rights.
Read the full licence.


C++ generator of map

Files fsexp.cin, ado.cin and conto.cin should be loaded to the working directory in order to compile the C++ 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 complex<double> z_type; #define Re(x) x.real() #define Im(x) x.imag() #define I z_type(0.,1.) #include "conto.cin" #include "fsexp.cin" //#include "fslog.cin" main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; int M=801,M1=M+1; int N=401,N1=N+1; DB X[M1],Y[N1]; DB *g, *f, *w; // w is working array. g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); char v[M1*N1]; // v is working array FILE *o;o=fopen("b271tMap3.eps","w"); ado(o,802,802); fprintf(o,"401 401 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); DO(m,M1) X[m]=-4.+.01*(m-.5); for(n=0;n<N1;n++) Y[n]=sinh((2./200.)*(n-200.5)); for(m=-4;m<5;m++) {M(m,-4)L(m,4)} for(n=-4;n<5;n++) {M( -4,n)L(4,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); DO(m,M1)DO(n,N1){ g[m*N1+n]=999; f[m*N1+n]=999;} DB b=sqrt(2); DO(m,M1){x=X[m]; printf("x=%6.3f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019) { c=FSEXP(z); p=Re(c); q=Im(c); if(p>-12 && p<12 && fabs(q)>1.e-12) g[m*N1+n]=p; if(q>-12 && q<12 && fabs(q)>1.e-12) f[m*N1+n]=q; } }} fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.;q=.3; for(m=-8;m<8;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n"); for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n"); for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n"); for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n"); for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n"); for(m=-10;m<11;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(-2,0)L(-4,0)fprintf(o,"0 setlinecap .03 W 1 1 1 RGB S\n"); for(n=0;n<11;n++){ M(-2-.2*(n+.2),0) L(-2-.2*(n+.45),0) } fprintf(o,".04 W 1 .5 0 RGB S\n"); for(n=0;n<21;n++){ M(-2-.2*(n+.7),0) L(-2-.2*(n+.95),0) } fprintf(o,".04 W 0 .5 1 RGB S\n"); fprintf(o,"0 setlinejoin 0 setlinecap\n"); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); free(f); free(g); free(w); system("epstopdf b271tMap3.eps"); system( "open b271tMap3.pdf"); //for macintosh getchar(); system("killall Preview"); // For macintosh }

Latex generator of labels

% \documentclass[12pt]{article} % <br> \paperheight 828px % <br> \paperwidth 836px % <br> \textwidth 1294px % <br> \textheight 1100px % <br> \topmargin -104px % <br> \oddsidemargin -78px % <br> \usepackage{graphics} % <br> \usepackage{rotating} % <br> \newcommand \sx {\scalebox} % <br> \newcommand \rot {\begin{rotate}} % <br> \newcommand \ero {\end{rotate}} % <br> \newcommand \ing {\includegraphics} % <br> \newcommand \rmi {\mathrm{i}} % <br> \begin{document} % <br> \newcommand \zoomax { % <br> \put(18, 806){\sx{3.3}{$y$}} % <br> \put(18, 713){\sx{3}{$3$}} % <br> \put(18, 613){\sx{3}{$2$}} % <br> \put(18, 513){\sx{3}{$1$}} % <br> \put(18, 413){\sx{3}{$0$}} % <br> \put(-6, 313){\sx{3}{$-1$}} % <br> \put(-6, 213){\sx{3}{$-2$}} % <br> \put(-6, 113){\sx{3}{$-3$}} % <br> \put(014, -5){\sx{3}{$-4$}} % <br> \put(114, -5){\sx{3}{$-3$}} % <br> \put(214, -5){\sx{3}{$-2$}} % <br> \put(314, -5){\sx{3}{$-1$}} % <br> \put(435, -5){\sx{3}{$0$}} % <br> \put(535, -5){\sx{3}{$1$}} % <br> \put(635, -5){\sx{3}{$2$}} % <br> \put(735, -5){\sx{3}{$3$}} % <br> \put(827,-4){\sx{3}{$x$}} % <br> } % <br> \parindent 0pt % <br> \sx{1}{\begin{picture}(852,820) \put(40,20){\ing{b271tMap3}} % <br> \zoomax % <br> \put(60,415){\sx{2.8}{\bf cut}} % <br> \put(340,548){\sx{3}{$v\!=\!1$}} % <br> \put(360,414){\sx{3}{$v\!=\!0$}} % <br> \put(760,414){\sx{3}{$v\!=\!0$}} % <br> \put(340,280){\sx{3}{$v\!=\!-1$}} % <br> \put(70,800){\sx{2.5}{$f\approx L\approx0.318+1.337i$}} % <br> \put(60,60){\sx{2.5}{$f\approx L^*\approx0.318-1.337i$}} % <br> \put(100,638){\sx{2.5}{$v\!=\!1.4$}}  % <br> \put(552,745){\sx{2.5}{$v\!=\!1.4$}} % <br> \put(100,198){\sx{2.5}{$v\!=\!-\!1.4$}}% <br> \put(540,90){\sx{2.5}{$v\!=\!-\!1.4$}} % <br> \put(666,726){\sx{2.5}{$u\!=\!0.2$}} % <br> \put(216,616){\sx{2.5}{$u\!=\!0.2$}} % <br> \put(660,642){\sx{3}{$u\!=\!0$}} % <br> \put(210,536){\sx{3}{$u\!=\!0$}} % <br> \put(410,700){\sx{2.5}{$u\!=\!0.4$}} % <br> \put(217,213){\sx{2.5}{$u\!=\!0.2$}} % <br> \put(410,130){\sx{2.5}{$u\!=\!0.4$}} % <br> \end{picture}} % <br> \end{document} % <br>

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