File:Number smaller then one after repetitive squaring.svg

Summary[edit]

Licensing[edit]

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

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You are free:

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• to remix – to adapt the work

Under the following conditions:

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https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

Maxima CAS code[edit]

 /*  
batch file for Maxima CAS
 */ 



kill(all);
remvalue(all);





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


compile(all);

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


l:GiveList(9.9999999999999956e-01);



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

path:"~/maxima/batch/julia/hyperbolic/0/"$ /*  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,"p"),
  user_preamble="set size square;set key top right",
  title= "Radius r<1.0 after iterations using function f(r)=r*r",
  dimensions = [1000, 1000],
  yrange = [-0.01,1.01],
  /*xrange = [ZxMin,ZyMax],*/
  xlabel     = "iteration ",
  ylabel     = "radius",
  point_type = filled_circle,
  points_joined =true,
  point_size    =  0.5,
  color         = red,
    
  
  key = "radius",
  points(l)
 
 );

C src code[edit]

/* 


gcc i.c -Wall

./a.out
*/


#include <stdio.h>
#include <float.h> // DBL_EPSILON
 
 int main()
 {
    
    double r = 1.0 - DBL_EPSILON; // maximal double value < 1.0
    double i = 0.0; // iteration number
         
    //check r value 
    if ( r != 1.0 )
     printf("initial r = %.16f and is good \n", r);
     else printf("r is not good, increase epsilon!!! \n");


     do 
     {
        r*=r; // r*r = r^2
        i+=1.0; // increase iteration number
	printf("r = %.16e after i = %.0f iterations   \n", r,i);
      }
     while ( r > DBL_MIN); // isnormal


     printf("final r = %.16e after i = %.0f iterations   \n", r,i);

    return 0;
 }