Summary

File:Jungreis.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.Category:Vector version available File:Jung200.png → File:Jungreis.svg For more information, see Help:SVG. In other languages Alemannisch ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ မြန်မာဘာသာ ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ +/−

 

Maxima source code

 /*  batch file for maxima 
 uses :
 - symmetry around horizontal ( 0X ) axis
 - Psi_M function to map conjugate plane to parameter plane
 - jungreis algorithm to 
 time :
 263 sec for jMax:100; and iMax:800;
 4000 sec for jMax:400
 
 */ 
 start:elapsed_run_time ();
 
 jMax:300; /* precision  = proportional to details and time of computations  */
 iMax:800; /* number of points to draw */
 
/* ------------ computes b coefficient of Jungreis function ----------------*/
 betaF[n,m]:=block
 (
 [nnn:2^(n+1)-1],
 if m=0
 then 1.0
 else if ((n>0) and (m < nnn)) 
  then 0.0
  else (betaF[n+1,m]- sum(betaF[n,k]*betaF[n,m-k],k,nnn,m-nnn)-betaF[0,m-nnn])/2.0
 )$
 b[m]:=betaF[0,m+1]$
 /* -------------------------------*/
 /* Power of w to j */
 wn[w,j]:= if j=0 then 1 else w*wn[w,j-1]$
 

/* ---------Jungreis function ;  c = Psi_M(w) ----------------------------- */
 Psi_M(w):=w + sum(b[j]/wn[w,j],j,0,jMax)$

 /* exponential for of complex number with angle in turns */
 GiveCirclePoint(t):=R*%e^(%i*t*2*%pi)$ /* gives point of unit circle for angle t in turns */
 
/* -------------------------------------- w-plane -----------------------------------------*/
 

/*-------------- unit circle ------------*/
 R:1;
 circle_angles:makelist(i/iMax,i,0,iMax/2)$
 CirclePoints:map(GiveCirclePoint,circle_angles)$
 
/* -------------------------parameter plane = c plane -----------------------------------*/
 MPoints:map(Psi_M,CirclePoints); /* Mandelbrot set points */
 /* add points below horizontal axis */
 for w in CirclePoints do CirclePoints:cons(conjugate(w),CirclePoints);
 for c in MPoints do MPoints:cons(conjugate(c),MPoints);
 
/* time */
 stop:elapsed_run_time ();
 time:fix(stop-start); 
 
/* ---------------- draw *--------------------------------------------------------------------------*/
 load(draw); /* Mario Rodríguez Riotorto   http://www.telefonica.net/web2/biomates/maxima/gpdraw/index.html */
 draw(file_name = "jung300",
  dimensions=[1000, 500],
  terminal  = 'png,
  columns  = 2,
  gr2d(title = " unit circle {w:abs(w)=1} ",
  point_type = filled_circle,
  points_joined =true,
  point_size    =  0.34,
  color         = red,
  points(map(realpart, CirclePoints),map(imagpart, CirclePoints))
  ),
  gr2d(title      = " Image of circle under Psi_M(w) ",
  points_joined =true,
  point_type = filled_circle,
  point_size    =0.34,
  color         = blue,
  points(map(realpart, MPoints),map(imagpart, MPoints))
  ) 
 );

References

1. ↑ Drawing Mc by Jungreis Algorithm

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Category:CC-BY-SA-3.0#Jung200.png

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

Category:License migration redundant#Jung200.pngCategory:GFDL#Jung200.png

You may select the license of your choice.