How computers fake randomness: a maths EPQ idea
A title to start from
How can a computer, which follows rules, produce random numbers, and how random are they?
Why it works as an EPQ
Simple generators can be analysed exactly and tested statistically, with clear failures to find.
Scope and difficulty
Solid. Solid. Linear congruential generators in depth; modern generators described.
The maths
Builds on these A Level topics: Sequences and series · Hypothesis testing · Proof.
You would learn:
- Modular arithmetic
- Period of a generator
- Statistical tests of randomness
One possible plan
- Analyse linear congruential generators and their period.
- Find a poor generator and show its pattern graphically.
- Run statistical tests on several generators.
- Judge what 'random enough' means for games, simulation and security.
Pitfalls
- One test treated as proof of randomness.
- Using a library generator for cryptographic claims.
Where to start reading
- Search for: linear congruential generator full period conditions
- Search for: RANDU flaw planes
Making something? Read the artefact guide first: an artefact still needs a research-based written report.
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