The   Fibonacci Word   may be created in a manner analogous to the   Fibonacci Sequence   as described here:

    Define   F_Word1   as   1
    Define   F_Word2   as   0
    Form     F_Word3   as   F_Word2     concatenated with   F_Word1    i.e.:   01
    Form     F_Wordn   as   F_Wordn-1   concatenated with   F_wordn-2



Task

Perform the above steps for     n = 37.

You may display the first few but not the larger values of   n.

{Doing so will get the task's author into trouble with them what be (again!).} 

Instead, create a table for   F_Words   1   to   37   which shows:

   The number of characters in the word
   The word's Entropy


Related tasks
 
   Fibonacci word/fractal
   Entropy
   Entropy/Narcissist


fcn entropy(bs){ //binary String-->Float
   len:=bs.len(); num1s:=(bs-"0").len();
   T(num1s,len-num1s).filter().apply('wrap(p){ p=p.toFloat()/len; -p*p.log() })
   .sum(0.0) / (2.0).log();
}
 
"  N     Length      Entropy Fibword".println();
ws:=L("1","0");
foreach n in ([1..37]){
   if(n>2) ws.append(ws[-1]+ws[-2]);
   w:=ws[-1];
   "%3d %10d %2.10f %s".fmt(n,w.len(),entropy(w),
      w.len()<50 and w or "<too long>").println();
}