- A “mixed-upness” of results (for example, the digits 1, 2, 3, 4, 5, and 6 are all equally likely on a die).
- Laws which constrain this “mixed-upness” (for example, that a die has no “memory,” that numbers are not “due to come up,” and that the sum of many dice is very close to normally distributed).
- The fact that, apart from those laws, the results are unknown to us.
A random walk in 2 dimensions (image by “Zweistein”). Given enough time, a return to the start will almost certainly occur. This is not true in 3 dimensions.
Chaos theory is famous for displaying randomness constrained by rules:
Two random trajectories on the shape called the Lorenz attractor (image by “Hellisp”). Both trajectories trace out the same general shape, but the details of the two paths differ unpredictably.