DescriptionDistance between repetitive squaring of point smaller then one.svg	English: Distance between repetive iteration of point smaller then one
Date	23 November 2015
Source	Own work
Author	Adam majewski
SVG development InfoField	The SVG code is valid.  This plot was created with gnuplot.   This plot uses embedded text that can be easily translated using a text editor.

==Compare with ==

• 
  Number ( real, positive and smaller then one ) after repetive squaring

 /*  
batch file for Maxima CAS


see also : 
http://fraktal.republika.pl/julia_equi.html
https://commons.wikimedia.org/wiki/File:NUmber_smaller_then_one_after_repetive_squaring.svg

 */ 



kill(all);
remvalue(all);





GiveList(r0):=
   /*  computes forward orbit of point r0
   and saves it to the list for draw package */
block(
 [r,rtemp,l,i, distance],
 r:r0, /* first point  */
 rtemp:r*r,
 distance :r-rtemp, 
 r:rtemp,
 l:[[0,distance]], 
 for i:1 thru 65 step 1 do
        ( rtemp:r*r,
          distance : r-rtemp,
          l:endcons([i,distance], l),
          r : rtemp),
         
 return(l) 
)$


compile(all);

/* ----------------- computations -------------------------------*/


l:GiveList(9.9999999999999956e-01);



/* ---------------- draw ------------------------------- */

path:"~/maxima/batch/julia/hyperbolic/distance/"$ /*  if empty then file is in a home dir */
/* draw it using draw package by */
 load(draw); 
/* if graphic  file is empty (= 0 bytes) then run draw2d command again */
 draw2d(
  terminal  = 'svg,
  file_name = sconcat(path,"pzoom2"),
  user_preamble="set size square;set key top right",
  title= "distance between r(n) and r(n+1) after iterations r(0) < 1.0 using function f(r)=r*r",
  dimensions = [1000, 1000],
  yrange = [-0.001,0.001],
  /*xrange = [ZxMin,ZyMax],*/
  xlabel     = "iteration ",
  ylabel     = "radius",
   xaxis       = true,
  point_type = filled_circle,
  points_joined =true,
  point_size    =  0.5,
  color         = red,
    
  
  key = "radius",
  points(l)
 
 );

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