File:B271t3T.png: Difference between revisions

Summary

Title / Description	Complex map of natural tetration tet, id est, tetration to natural base ${\displaystyle b=\mathrm {e} \approx 1.71}$ ; ${\displaystyle u}$ has sense of the real part, and ${\displaystyle v}$ has sense of imaginary part of ${\displaystyle \mathrm {tet} (x\!+\!\mathrm {i} y)}$
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
Using this image on CZ	Please click here to add the credit line, then copy the code below to add this image to a Citizendium article, changing the size, alignment, and caption as necessary. {{Image|B271t3T.png|right|350px|Add image caption here.}}

Licensing

   

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

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

References