The Period(w) command computes the period of a string (word) w. A positive integer p is said to be a period of a string s if, for all integers i with $1<=i<=\mathrm{length}\left(s\right)-p$, one has $s_i=s_{i+p}$. The least period of the string s is called the period of s.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

with(StringTools):

Period( "aaa" );

$1$

Period( "abcde" );

$5$

Period( "abcabc" );

$3$

Period( "abcabcab" );

$3$

seq( Period( Fibonacci( n ) ), n = 1 .. 10 );

$1,2,2,3,5,8,13,21,34,55$

seq( combinat[ 'fibonacci' ]( n ), n = 1 .. 10 );

$1,1,2,3,5,8,13,21,34,55$

seq( Period( ThueMorse( n ) ), n = 1 .. 10 );

$1,2,3,3,3,5,6,6,6,6$

Periodic? := w -> evalb( Period( w ) <= floor( length( w ) / 2 ) );

$\mathrm{Periodic?}≔w\mapsto \mathrm{evalb}\left(\mathrm{StringTools}:-\mathrm{Period}\left(w\right)\le ⌊\frac{\mathrm{length}\left(w\right)}{2}⌋\right)$

( Period, length, Periodic? )( "ababababababababa" );

$2,17,\mathrm{true}$

( Period, length, Periodic? )( "abcdeab" );

$5,7,\mathrm{false}$