imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of [[tetration]] to base <math>b=\sqrt{2}</math>
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = August 2014
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| |pub-country = Japan
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| |notes = I plan to use this image in the article
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| D.Kouznetsov. Holomorphic ackermann. 2015, in preparation.
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| |versions = http://mizugadro.mydns.jp/t/index.php/File:Ack3a600.jpg
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| The real-real plot of this function is one of curves at http://en.citizendium.org/wiki/File:Tetreal10bx10d.png
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| }}
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| == Licensing ==
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| {{CC|by|3.0}}
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| ==[[C++]] generator of map==
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| Files
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| [[ado.cin]],
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| [[conto.cin]],
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| [[sqrt2f21e.cin]]
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| should be loaded to 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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| #include <complex>
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| #define z_type std::complex<double>
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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 "sqrt2f21e.cin"
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| #include "conto.cin"
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| | |
| int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
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| int M=601,M1=M+1;
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| int N=461,N1=N+1;
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| DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1];
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| char v[M1*N1]; // v is working array
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| FILE *o;o=fopen("tetqma.eps","w");ado(o,602,202);
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| fprintf(o,"301 101 translate\n 10 10 scale\n");
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| DO(m,M1)X[m]=-30.+.1*(m);
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| DO(n,200)Y[n]=-10.+.05*n;
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| Y[200]=-.01;
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| Y[201]= .01;
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| for(n=202;n<N1;n++) Y[n]=-10.+.05*(n-1.);
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| for(m=-30;m<31;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}
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| for(n=-10;n<11;n++){ M( -30,n)L(30,n)}
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| fprintf(o,".008 W 0 0 0 RGB S\n");
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| DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
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| DO(n,N1){y=Y[n];
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| for(m=295;m<305;m++)
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| {x=X[m]; //printf("%5.2f\n",x);
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| z=z_type(x,y);
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| c=F21E(z);
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| p=Re(c);q=Im(c);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
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| d=c;
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| for(k=1;k<31;k++)
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| { m1=m+k*10; if(m1>M) break;
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| d=exp(d*(.5*log(2.)));
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| p=Re(d);q=Im(d);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
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| }
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| d=c;
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| for(k=1;k<31;k++)
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| { m1=m-k*10; if(m1<0) break;
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| d=log(d)*(2./log(2.));
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| p=Re(d);q=Im(d);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
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| }
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| }}
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| fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1;q=.5;
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| for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".02 W 0 .6 0 RGB S\n");
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| for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".02 W .9 0 0 RGB S\n");
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| for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".02 W 0 0 .9 RGB S\n");
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| for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".08 W .9 0 0 RGB S\n");
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| for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 .9 RGB S\n");
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| conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".08 W .6 0 .6 RGB S\n");
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| for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 0 RGB S\n");
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| fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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| system("epstopdf tetqma.eps");
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| system( "open tetqma.pdf");
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| getchar(); system("killall Preview");
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| }
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| </nowiki>
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| ==References==
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| http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html<br>
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| http://www.ils.uec.ac.jp/~dima/PAPERS/2010q2.pdf<br>
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| http://mizugadro.mydns.jp/PAPERS/2010q2.pdf
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| D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
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| https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
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| http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
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| http://mizugadro.mydns.jp/BOOK/202.pdf
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| Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014. (In Russian)
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| D.Kouznetsov. Holomorphic [[ackermann]]s. 2015, in preparation.
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| [[Category:Complex map]]
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| [[Category:Superfunction]]
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| [[Category:Tetration]]
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