Difference between revisions of "File:Tetma.jpg"

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[[Complex map]] of the [[natural tetration]] without labels.
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Importing image file
  
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This image is loaded to the ingrampublishing.com
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In order to use it in the book [[Суперфункции]],
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https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
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\url{http://mizugadro.mydns.jp/BOOK/201.pdf}
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The low resolution draft also had been loaded at the site of ingrampublishing
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==[[C++]] generator==
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Files
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[[ado.cin]]
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[[conto.cin]]
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[[fsexp.cin]]
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[[fslog.cin]]
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should be loaded in order to compile the code below
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<poem><nomathjax><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></nomathjax></poem>
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==References==
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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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  +
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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[[Category:Complex map]]
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[[Category:Tetration]]
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[[Category:Natural tetration]]
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[[Category:Book]]
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[[Category:BookMap]]
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[[Category:Lambert Publishing]]
  +
[[Category:Ingimage]]

Latest revision as of 08:53, 1 December 2018

Complex map of the natural tetration without labels.

This image is loaded to the ingrampublishing.com

In order to use it in the book Суперфункции,

https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0

\url{http://mizugadro.mydns.jp/BOOK/201.pdf}

The low resolution draft also had been loaded at the site of ingrampublishing


C++ generator

Files ado.cin conto.cin fsexp.cin fslog.cin should be loaded in order to compile the 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 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

References

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.

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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