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


func entropy(s) {
    [0] + (s.chars.freq.values »/» s.len) -> reduce { |a,b|
        a - b*b.log2
    }
}
 
var n_max = 37
var words = ['1', '0']
 
{
    words.append(words[-1] + words[-2])
} * (n_max - words.len)
 
say ('%3s %10s %15s  %s' % <N Length Entropy Fibword>...)
 
for i in ^words {
    var word = words[i]
    say ('%3i %10i %15.12f  %s' % (i+1,
                                   word.len,
                                   entropy(word),
                                   word.len<30 ? word : '<too long>'))
}