i also read three categorical randomness in Wolfram's a new kind of science, which is notable here.
the first is randomness as in environmental given. the example is the movement of boat on the sea. the second is randomness by way of initial conditions. the example is the bumpiness of driving along a bumpy road, bumpy road is initial condition. the third is intrinsic randomness, wolfram's claimant. although he fully realises that as wrote by deborah bennet, any randomness created by algorithms is categorically unrandom; he tries to show that at least rule 30 of CA is a true randomness.