File:Tetma.jpg
Original file (3,341 × 1,675 pixels, file size: 1.89 MB, MIME type: image/jpeg)
Summary
Title / Description
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Complex map of the natural tetration tet |
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Citizendium author
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Dmitrii Kouznetsov |
Date created
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2014 |
Country of first publication
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Japan |
Notes
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I had loaded this image also to the www.ingimahe.com, but I cannot find it in their catalogue;
so, I upload it here. |
Other versions
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http://mizugadro.mydns.jp/t/index.php/File:Tetma.jpg , the C++ generator is available
The zoomin of the central part is available also at http://mizugadro.mydns.jp/t/index.php/File:B271t3T.png |
Using this image on CZ
|
| , then copy the code below to add this image to a Citizendium article, changing the size, alignment, and caption as necessary.
Please send email to manager A T citizendium.org .
Licensing
This media, Tetma.jpg, is licenced under the Creative Commons CC0 1.0 Universal License
No copyright:
The person who associated a work with this licence waives all rights to the work under copyright law and all related or neighboring legal rights in the work, to the extent allowable by law.
Patent or trademark rights, or rights other persons may have either in the work itself or in how the work is used such as publicity or privacy rights, are not affected.
Read the full licence.
Description
Tetration tet is shown with
lines and lines
The tetration and its maps are described in the Mathematica of Computation:
http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670. DOI:10.1090/S0025-5718-09-02188-7.
The fast algorithm of evaluation of tetration is described in the Vladikavkaz mathematical Journal: http://www.ils.uec.ac.jp/~dima/PAPERS/2010vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
The image is used at the front cover of the book about Superfunctions, the Book is in Russian and is available at
https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
http://mizugadro.mydns.jp/BOOK/201.pdf}
http://www.ils.uec.ac.jp/~dima/BOOK/201.pdf}
http://mizugadro.mydns.jp/t/index.php/Суперфункции
C++ generator of the image
#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 "fsexp.cin" //#include "fslog.cin" int 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], 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("b271t0.eps","w"); ado(o,87,87); FILE *o;o=fopen("tetma.eps","w"); ado(o,1604,804); fprintf(o,"802 402 translate\n 100 100 scale\n"); DO(m,M1) X[m]=-8.+.02*(m-.5); DO(n,N1) Y[n]=-4.+.02*(n-.5); for(m=-8;m<17;m++) {M(m,-4)L(m,4)} for(n=-4;n<5;n++) {M( -8,n)L(8,n)} fprintf(o,"2 setlinecap .006 W 0 0 0 RGB S\n"); //fprintf(o,"/adobe-Roman findfont .6 scalefont setfont\n"); DO(m,M1)DO(n,N1){ g[m*N1+n]=9999; f[m*N1+n]=9999;} //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.)>.04) { c=FSEXP(z); // c=FSLOG(z); p=Re(c); q=Im(c); if(p>-9999 && p<9999 && fabs(q)>1.e-12) g[m*N1+n]=p; if(q>-9999 && q<9999 && fabs(q)>1.e-12) f[m*N1+n]=q; } }} fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=2.; q=1.1;; //#include "plofu.cin" p=2;q=1; for(m=-19;m<19;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".02 W 0 1 0 RGB S\n"); for(m=0;m<29;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".01 W 1 0 0 RGB S\n"); for(m=0;m<29;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".01 W 0 0 1 RGB S\n"); for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".03 W 1 0 0 RGB S\n"); for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".03 W 0 0 1 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 W .8 0 .8 RGB S\n"); for(m=-31;m<32;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".03 W 0 0 0 RGB S\n"); fprintf(o,"0 setlinejoin 0 setlinecap\n"); fprintf(o,"showpage\n"); fprintf(o,"%cTrailer\n",'%'); fclose(o); system("epstopdf tetma.eps"); system( "open tetma.pdf"); //for macintosh getchar(); system("killall Preview"); // For macintosh
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current | 19:52, 11 March 2022 | 3,341 × 1,675 (1.89 MB) | Maintenance script (talk | contribs) | == Summary == Importing file |
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