In this talk I discuss the relationship between discrete randomness (Chaitin's Algorithmic Information Theory) and something which seemingly represents continuous randomness; specifically, Brownian motion. Surprisingly, one can recursively exchange one for the other, once a suitably effective description for Brownian motion is found. Taking this concept further, we introduce the idea of Hausdorff dimension into the mix, something which has not been fully explored yet. The consequences for AIT are unknown, but may be fruitful (or not)!