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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 src code

/*
batch file for Maxima CAS program
save it as a file with mac extension and open in Maxima 
It creates l6.svg file in the directory path ( see below)
change the path directory if you save mac file in the different location 

https://commons.wikimedia.org/wiki/File:Lyapunov_exponent_of_real_quadratic_map.png

http://fy.chalmers.se/~f99krgu/CompBioA/CompBioLecture2.pdf

log(c - cf)

log(-c_f) = 0.3372970313844768
log(0.25-c_f) = 0.5014751574920848

---------------
Transform is c←ec+c0 with c0=−1.401155189092051.

https://fractalforums.org/fractal-image-gallery/18/feigenbaum-stretch/2112
--------------


*/
kill(all);
remvalue(all);


/* real quadratic  diagram based on the code by Mario Rodriguez Riotorto using Maxima CAS draw packag  */



pts:[]; /* points of the orbit */

ls:[];
kMax1:200;
kMax2:500;
cF:-1.4011551890; /* The Feigenbaum Point of period doubling cascade */ 

cMax:  0.25;
xMax : log(cMax - cF); /* from c to x  */


/* width of component is about 1.5 */
NoOfComponents : 8 ; /*  (xMax-xMin)/1.5; */
xMin : xMax - NoOfComponents*1.5; /* from NoOfComponents to x  */
cMin: cF +exp(xMin); /* from x to c = -1.3996312;  */


 
n:500;
dx:(xMax-xMin)/n;


/* ------------- compute -----------------------------------*/

for x:xMin while x <= xMax step dx do 
    (
    
       c: cF + exp(x),
       z: 0.0,
       l:0, /* Lyapunov exponent */
       for k:1 thru kMax1 do 
         (    
           z: z * z+c, /* to remove points from image compute and do not draw it */
           l:l+log(abs(2*z))
         ),
       
        for k:1 thru kMax2  do 
          ( 
           z:  z * z+c, /* compute and draw it */
           pts: cons([x,z], pts),/* save points to draw it later */
	   l:l+log(abs(2*z))	
          ),
       ls:cons([x,l/(kMax1+kMax2)],ls)   /* save points to draw it later */         
                   
    ); 


/* =================  draw ======================================*/

 path:"~/maxima/batch/logistic/log/m2/"$ /* result of pwd; to save image in the same directory as mac file  */
 FileName:concat("n_",string(NoOfComponents), "_", string(n),"_", string(kMax1),"_",string(kMax2))$ /* without extension which is the terminal name */

load(draw);

 
 draw(
  terminal  = 'svg,
  file_name = concat(path,FileName),
  dimensions=[1900,2600], /*  y = x*rows  */
  
  
  
  gr2d(
  	title      = "Bifurcation diagram, z[i+1] = z[i]*z[i] +c",
  	font_size = 30,
  	font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */
    	points_joined =false,
   	xlabel     = "log(c - cF)",
        ylabel     = "z ",
        point_type = filled_circle,
        point_size = 0.2,
        color = black,
        points(pts) 
   ),

  gr2d(
  	title = " Lyapunov exponent ",
  	font_size = 30,
  	font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */
   	points_joined =true,
    	yaxis       = true,
   	xaxis 	= true,
   	xlabel     = "log(c - cF)",
   	ylabel     = " lyapunov exponent ",
   	yrange = [-0.5,0.1],
   	color         = red,
   	point_size    = 0.5,
   	point_type = filled_circle,
   	points(ls))

 );
 
 

Image Mafic / Bash src code

 convert n_8_500_200_500.svg n.png

1. ↑ how to make multiplots with the draw package by Mario Rodríguez Riotorto