File:Ack3b600.jpg: Difference between revisions

Latest revision as of 19:53, 11 March 2022

Summary

Importing file

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	19:53, 11 March 2022		5,130 × 1,776 (1 MB)	Maintenance script (talk \| contribs)	== Summary == Importing file

You cannot overwrite this file.

File usage

The following page uses this file:

Maps of tetration

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Horizontal resolution	600 dpi
Vertical resolution	600 dpi

@@ Line 1: / Line 1: @@
 == Summary ==
-{{Image_Details|user
+Importing file
-|description  = [[Complex map]] of [[tetration]] to base <math>b=\exp(1/\mathrm e)</math>
-|author       = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
-|date-created = August 2014
-|pub-country  = Japan
-|notes        = I plan to use this image in the article
-D.Kouznetsov. Holomorphic ackermann. 2015, in preparation.
-|versions     = http://mizugadro.mydns.jp/t/index.php/File:Ack3a600.jpg
-The real-real plot of this function is one of curves at http://en.citizendium.org/wiki/File:Tetreal10bx10d.png
-|versions     = http://mizugadro.mydns.jp/t/index.php/File:Ack3b600.jpg
-}}
-== Licensing ==
-{{CC|by|3.0}}
-==[[C++]] generator of map==
-Files
-[[ado.cin]],
-[[conto.cin]],
-[[e1etf.cin]]
-should be loaded to the working directory in order to compile the code below.
-<nowiki>
-#include <math.h>
-#include <stdio.h>
-#include <stdlib.h>
-#define DB double
-#define DO(x,y) for(x=0;x<y;x++)
-#include <complex>
-#define z_type std::complex<double>
-#define Re(x) x.real()
-#define Im(x) x.imag()
-#define I z_type(0.,1.)
-#include "e1etf.cin"
-#include "conto.cin"
-int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
- int M=601,M1=M+1;
- int N=461,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("tet1ma.eps","w");ado(o,602,202);
- fprintf(o,"301 101 translate\n 10 10 scale\n");
- DO(m,M1)X[m]=-30.+.1*(m);
- DO(n,200)Y[n]=-10.+.05*n;
-         Y[200]=-.01;
-         Y[201]= .01;
- for(n=202;n<N1;n++) Y[n]=-10.+.05*(n-1.);
- for(m=-30;m<31;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}
- for(n=-10;n<11;n++){ M( -30,n)L(30,n)}
- fprintf(o,".008 W 0 0 0 RGB S\n");
- DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
- DO(n,N1){y=Y[n];
- DO(m,M1)
-          {x=X[m]; //printf("%5.2f\n",x);
-           z=z_type(x,y);
-           c=E1ETF(z);
-           p=Re(c);q=Im(c);
-           if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
-        }}
- fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1;q=.5;
- 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");
- 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");
- 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");
- 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");
- 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");
-                    conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".08 W .6 0 .6 RGB S\n");
- 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");
-fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
-system("epstopdf tet1ma.eps");
-system(  "open tet1ma.pdf");
-getchar(); system("killall Preview");
-}
-</nowiki>
-==[[Latex]] generator of labels==
-<nowiki>
-\documentclass{amsproc}
-\usepackage{graphicx}	% Use pdf, png, jpg, or eps§ with pdflatex; use eps in DVI mode\usepackage{amssymb}
-\usepackage{rotating}
-\usepackage{hyperref}
-\newcommand \be {\begin{eqnarray}}
-\newcommand \ee {\end{eqnarray} }
-\newcommand \sx {\scalebox}
-\newcommand \ds {\displaystyle}
-\newcommand \bN {\mathbb{N}}
-\newcommand \bC {\mathbb{C}}
-\newcommand \bR {\mathbb{R}}
-\newcommand \cO {\mathcal{O}}
-\newcommand \cF {\mathcal{F}}
-\newcommand \rot {\begin{rotate}}
-\newcommand \ero {\end{rotate}}
-\newcommand \ing \includegraphics
-\newcommand \tet {\mathrm{tet}}
-\usepackage{geometry}
-\topmargin -97pt
-\oddsidemargin -87pt
-\paperwidth 618pt
-%\paperheight 216pt
-\paperheight 214pt
-\begin{document} %\title{AMS Proceedings Series Sample}
-\newcommand \mapax {
-\put(2,206){\sx{1.2}{$y$}}
-\put(2,188){\sx{1.2}{$8$}}
-\put(2,168){\sx{1.2}{$6$}}
-\put(2,148){\sx{1.2}{$4$}}
-\put(2,128){\sx{1.2}{$2$}}
-\put(2,108){\sx{1.2}{$0$}}
-\put(-6,88){\sx{1.2}{$-2$}}
-\put(-6,68){\sx{1.2}{$-4$}}
-\put(-6,48){\sx{1.2}{$-6$}}
-\put(-6,28){\sx{1.2}{$-8$}}
-\put(-1,1){\sx{1.2}{$-30$}}
-\put( 49,1){\sx{1.2}{$-25$}}
-\put( 99,1){\sx{1.2}{$-20$}}
-\put(149,1){\sx{1.2}{$-15$}}
-\put(199,1){\sx{1.2}{$-10$}}
-\put(252,1){\sx{1.2}{$-5$}}
-\put(309,1){\sx{1.2}{$0$}}
-\put(329,1){\sx{1.2}{$2$}}
-\put(349,1){\sx{1.2}{$4$}}
-\put(369,1){\sx{1.2}{$6$}}
-\put(389,1){\sx{1.2}{$8$}}
-\put(407,1){\sx{1.2}{$10$}}
-\put(457,1){\sx{1.2}{$15$}}
-\put(507,1){\sx{1.2}{$20$}}
-\put(557,1){\sx{1.2}{$25$}}
-\put(607,1){\sx{1.2}{$x$}}
-}
-{\begin{picture}(620,216) \mapax \put(10,10){\ing{tet1ma}} %%%%%%%%
-\put(25,108.4){\sx{1.4}{\bf cut}}			\put(502,108.4){\sx{1.4}{$v\!=\!0$}}
-\put(262,192){\sx{1.4}{$v\!=\!0.2$}}
-\put(260,170){\sx{1.4}{$v\!=\!0.4$}}
-\put(266,156){\sx{1.4}{$v\!=\!1$}}
-\put(263,60){\sx{1.4}{$v\!=\!-1$}}
-\put(100,156){\sx{1.4}{\rot{45}$u\!=\!3$\ero}}
-\put(102,55){\sx{1.4}{\rot{-44}$u\!=\!3$\ero}}
-\put(356,96){\sx{1.4}{\rot{90}$u\!=\!2$\ero}}
-\put(385,96){\sx{1.4}{\rot{90}$u\!=\!2.2$\ero}}
-\put(449,96){\sx{1.4}{\rot{90}$u\!=\!2.4$\ero}}
-\put(375,146){\sx{1.4}{\rot{51}$v\!=\!0.2$\ero}}
-\put(367,76){\sx{1.4}{\rot{-56}$v\!=\!-0.2$\ero}}
-\end{picture}}
-\end{document}
-</nowiki>
-==Refrences==
-http://mizugadro.mydns.jp/t/index.php/File:Ack3b600.jpg
-http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2012-02590-7/S0025-5718-2012-02590-7.pdf <br>
-http://www.ils.uec.ac.jp/~dima/PAPERS/2011e1e.pdf <br>
-http://mizugadro.mydns.jp/PAPERS/2011e1e.pdf
-H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). Mathematics of computation, 2012 February 8. ISSN 1088-6842(e) ISSN 0025-5718(p)
-https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
-http://mizugadro.mydns.jp/BOOK/202.pdf
-Д.Кузнецов. [[Суперфункции]]. [[Lambert Academic Publishing]], 2014. (In Russian)
-[[Category:Book]]
-[[Category:BookPlot]]
-[[Category:Tetration]]
-[[Category:e1e]]
-[[Category:Complex map]]
-[[Category:AMS]]
-[[Category:TORI]]