imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user-pd
| | Importing file |
| |description = [[Complex map]] of the natural [[tetration]] tet
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2014
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| |pub-country = Japan
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| |notes = I had loaded this image also to the www.ingimahe.com, but I cannot find it in their catalogue;
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| so, I upload it here.
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| |versions = http://mizugadro.mydns.jp/t/index.php/File:Tetma.jpg , the [[C++]] generator is available
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| The zoomin of the central part is available also at http://mizugadro.mydns.jp/t/index.php/File:B271t3T.png
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| }}
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| == Licensing ==
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| {{CC|zero|1.0}}
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| ==Description==
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| [[Tetration]] tet is shown with
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| lines
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| <math>
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| u=\Re(\mathrm{tet}(x\!+\!\mathrm i y))= \mathrm {const}
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| </math>
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| and lines
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| <math>
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| u=\Im(\mathrm{tet}(x\!+\!\mathrm i y))= \mathrm {const}
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| </math>
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| in the x,y plane. In order to simplify the incorporation to various texts, the labels of the lines and those of the axes are suppressed.
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| The tetration and its maps are described in the [[Mathematica of Computation]]:
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| 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.
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| The fast algorithm of evaluation of tetration is described in the [[Vladikavkaz mathematical Journal]]:
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| 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.
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| The image is used at the front cover of the book about Superfunctions, the Book is in Russian and is available at <br>
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| https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
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| http://mizugadro.mydns.jp/BOOK/201.pdf <br>
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| http://www.ils.uec.ac.jp/~dima/BOOK/201.pdf <br>
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| http://mizugadro.mydns.jp/t/index.php/Суперфункции
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| ==[[C++]] generator of the image==
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| Files
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| [[ado.cin]],
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| [[conto.cin]],
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| [[fslog.cin]]
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| should be loaded into the working directory in order to compile the code below:
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| <nowiki>
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| #include <math.h>
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| #include <stdio.h>
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| #include <stdlib.h>
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| //using namespace std;
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| #include<complex>
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| typedef std::complex<double> z_type;
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define I z_type(0.,1.)
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| #include "conto.cin"
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| #include "fsexp.cin"
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| //#include "fslog.cin"
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| int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
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| int M=801,M1=M+1;
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| int N=401,N1=N+1;
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| DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
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| char v[M1*N1]; // v is working array
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| //FILE *o;o=fopen("b271t0.eps","w"); ado(o,87,87);
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| FILE *o;o=fopen("tetma.eps","w"); ado(o,1604,804);
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| fprintf(o,"802 402 translate\n 100 100 scale\n");
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| DO(m,M1) X[m]=-8.+.02*(m-.5);
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| DO(n,N1) Y[n]=-4.+.02*(n-.5);
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| for(m=-8;m<17;m++) {M(m,-4)L(m,4)}
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| for(n=-4;n<5;n++) {M( -8,n)L(8,n)} fprintf(o,"2 setlinecap .006 W 0 0 0 RGB S\n");
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| //fprintf(o,"/adobe-Roman findfont .6 scalefont setfont\n");
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| DO(m,M1)DO(n,N1){ g[m*N1+n]=9999;
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| f[m*N1+n]=9999;}
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| //DB b=sqrt(2);
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| DO(m,M1){x=X[m]; printf("x=%6.3f\n",x);
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| DO(n,N1){y=Y[n]; z=z_type(x,y); if(abs(z+2.)>.04)
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| { c=FSEXP(z);
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| // c=FSLOG(z);
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| p=Re(c); q=Im(c);
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| if(p>-9999 && p<9999 && fabs(q)>1.e-12) g[m*N1+n]=p;
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| if(q>-9999 && q<9999 && fabs(q)>1.e-12) f[m*N1+n]=q;
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| }
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| }}
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| fprintf(o,"1 setlinejoin 2 setlinecap\n");
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| p=2.; q=1.1;;
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| //#include "plofu.cin"
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| p=2;q=1;
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| 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);
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| fprintf(o,".02 W 0 1 0 RGB S\n");
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| 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);
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| fprintf(o,".01 W 1 0 0 RGB S\n");
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| 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);
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| fprintf(o,".01 W 0 0 1 RGB S\n");
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| 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");
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| 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");
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| conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 W .8 0 .8 RGB S\n");
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| 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");
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| fprintf(o,"0 setlinejoin 0 setlinecap\n");
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| fprintf(o,"showpage\n");
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| fprintf(o,"%cTrailer\n",'%');
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| fclose(o);
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| system("epstopdf tetma.eps");
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| system( "open tetma.pdf"); //for macintosh
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| getchar(); system("killall Preview"); // For macintosh
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| </nowiki>
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| [[Category:Complex map]]
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| [[Category:Tetration]]
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| [[Category:Superfunctions]]
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