A question concerning algorithmic randomness and the Second Law of Thermodynamics

According to the theory of algorithmic randomness, there is no algorithm that can express a totally random sequence that is shorter than the sequence itself.

But, in fact, there are an infinite number of such algorithms for any totally random sequence, because any totally random sequence is duplicated by an infinite number of totally nonrandom sequences.

For example, any totally random N-digit sequence of zeros and ones (or dots and dashes) has an infinite number of totally nonrandom duplicates consisting of the N digits beginning with the Mth digit after the binary point of the base-2 expression of π (or any other irrational number). Regardless of how large M and N are, the minimum-length algorithm required to construct any such duplicate is only A