The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. If you'd like to use the PCG generation scheme, head to the download page.Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The PCG paper describes permutation functions on tuples in depth, as well as the output functions used by different members of the PCG family. PCG's output functions are what gives it its excellent statistical performance and makes it hard predict from its output (and thus more secure).
PCG's Output Function PCG uses a new technique called permutation functions on tuples to produce output that is much more random than the RNG's internal state. Moreover, LCGs have number of very useful properties that make them a good choice. Linear congruential generators are known to be statistically weak, but PCG's state transition function only does half the work, so it doesn't need to be perfect. PCG's State-Transition Function The PCG family uses a linear congruential generator as the state-transition function-the “CG” of PCG stands for “congruential generator”. The PCG family takes a more balanced approach. The observation that underlies the PCG family is that these approaches are unbalanced, they put too much weight on one side or the other. For example, the Fortuna RNG has a trivial state transition function (it just increments a counter), but uses a cryptographic block cypher as the output function. Again, this is a very simple output function.Ī few RNGs adopt the opposite approach. Some RNGs combine multiple simple RNGs and thus have an output function that just merges them together (e.g., with addition or xor). Many RNGs just use the identity function! They just return the state as is (making them easily predicted). Most RNGs use a very simple output function. We can see them as two functions: The State-Transition Function Governs how the RNG's internal state changes every time you ask for a random number The Output Function Turns the RNG's internal state into the actual random number
There are two parts to a random number generator. To explain why the PCG family is better, we need to get a little bit technical.
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