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An infinite word  x  over an alphabet with  b  letters has full complexity if for each    all the  b m   words of length  m  are factors of  x . We prove that the periods of    in the 2-adic expansion approach full complexity for increasing  k : For any   , the periods for    have complexity   . Amazingly, these    words occur in the period almost the same number of times. On the way, first we prove the same for the binary period. We get a similar result for the decimal period of 1/3  k  .

The 2-Adic, Binary and Decimal Periods of 1/3 k Approach Full Complexity for Increasing k