File:Golden mean.png

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/* 
golden ratio conjugate 
= ((sqrt(5)-1)/2 = 0.618033988749895
It is approximated by finite continued  fractions :

[0;1,1,1,....]



*/

kill(all);

iMax : 10;



/* continuead fraction - goldem mean */
f(i_Max):=
(
[a,i],
i:1,
a:[0,1,1],
while i<i_Max do 
(a:endcons(1,a),
 i:i+1),
float(cfdisrep(a))
)$



/* save the values to 2 lists */
xx:makelist (1, i, 1, 1); /* list of positive integers  */
yy:makelist (f(1), i, 1, 1); /* list of cf  */

for i:2 thru iMax step 1 do 
(  
   xx:cons(i,xx), 
   y:float(f(i)),
   yy:cons(y,yy)

);

load(draw);
draw2d(
   file_name = "golden_mean",
   terminal  = 'png,
  
  
   dimensions  = [1000,1000],
   title= "Finite continued fraction aproximation for golden mean",
   key = "n-fraction",
   xlabel     = "n",
   ylabel     = "n-continued fractions",
   point_type    = filled_circle,
   point_size    = 1.0,
   points_joined = true,

   color         = red,
   points(xx,yy),
   color = blue,
   key = "golden mean",
   explicit((sqrt(5)-1)/2,x,1,iMax)

  );