Algorithmic randomness treats a sequence as random when no substantially shorter program can reproduce it. This compression-based view was developed by Andrei Kolmogorov and, independently, Ray Solomonoff. It differs from Shannon entropy, which measures average uncertainty across a probability distribution or source. section 8.2
Repeating patterns and coin flips
A repeating sequence is not algorithmically random because a short description can specify its pattern. A sufficiently long sequence of fair coin flips is typically incompressible: with high probability, no much shorter program outputs it. section 8.2
