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


go =>
  foreach(N in 1..37)
     F = fib(N),
     E = entropy(F),
     if N <= 10 then
       printf("%3d %10d %0.16f %w\n",N,length(F),E,F)
     else
       printf("%3d %10d %0.16f\n",N,length(F),E)     
     end
  end,
  nl.
 
table
fib(1) = "1".
fib(2) = "0".
fib(N) = fib(N-1) ++ fib(N-2).
 
entropy(L) = Entropy => 
  Len = L.len,
  Occ = new_map(),
  foreach(E in L)
    Occ.put(E, Occ.get(E,0) + 1)
  end,
  Entropy = -sum([P2*log2(P2) : _C=P in Occ, P2 = P/Len]).