REQUIREMENTS

The requirements listed below are in the order of their importance.

1.

Random. The generated sequence should have as much the appearance of randomness as is possible, and as many of the statistical properties as are required of it; e.g., independence, stationarity, distribution characteristics, &c. Since the generator will, in fact, be deterministic, it should be simple enough that its shortcomings are well-known. In the case of linear congruential sequences, for example, it is their periodicity and Marsaglia's complaint that points lie mainly in the planes.

2.

Repeatable. Although we seek to model indeterminate effects, our schemes must not themselves involve indeterminacy. Reproducibility is of the essence in any scientific experiment.

3.

Portable. In the case of integer sequences, we can insist on identity of results across platforms. For floating-point sequences this is impractical, but individual numbers should differ by no more than round-off dictates.

4.

Fast. All the schemes I have in mind are now so fast that speed is no longer an issue. The only problem might be with real-time generators for VHF acoustic signals in laboratory work with rock samples.