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


SetFormat, FloatFast, 0.15
SetBatchLines, -1
OutPut := "N`tLength`t`tEntropy`n"
        . "1`t" 1 "`t`t" Entropy(FW1 := "1") "`n"
        . "2`t" 1 "`t`t" Entropy(FW2 := "0") "`n"
Loop, 35
{
    FW3 := FW2 FW1, FW1 := FW2, FW2 := FW3
    Output .= A_Index + 2 "`t" StrLen(FW3) (A_Index > 33 ? "" : "`t") "`t" Entropy(FW3) "`n"
}
MsgBox, % Output
 
Entropy(n)
{
    a := [], len:= StrLen(n), m := n
    while StrLen(m)
    {
        s := SubStr(m, 1, 1)
        m := RegExReplace(m, s, "", c)
        a[s] := c
    }
    for key, val in a
    {
        m := Log(p := val / len)
        e -= p * m / Log(2)
    }
    return, e
}