umm... Randomness is at the heart of quantum mechanics which, describes the material world to very high accuracy.
Suggested reading that is not mathematically painful: “The Quantum World,” by K. W. Ford.
The great problem of physics today, is the quantum mechanics and the general theory of relativity (gravity) are fundamentaly incompatible yet both are experimentally very accurate.
Your comment on the universe as one big blob of information is spot-on compatible with some descriptions of quantum mechanics which are, still fundamentally about random processes at their core.
C.W.
It’s all about defining random. Uncertainty and unpredictability do not necessarily mean there is no pattern. In fact, there is little evidence that “patternlessness” can even be.
On the other hand, everything that seems regular could cease to exist the next instant, in a purely random event.