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Random Number Generators

By: Sid Iyer

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Why is randomness useful?

Heavily used in statistics to determine outliers and out-of-ordinary data values
Modeling and Simulation

Financial Modeling of random occurrences or hidden variables (Monte Carlo Integration)
Weather prediction

Astronomy is basically finding deviations from the normal given massive data
Casinos
Cryptography (determining padding in asymmetric encryption)
English teachers grading my essays

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How can you determine if something is random?

You can use a Gaussian Distribution aka Normal Distribution!
You can also use Chi square Test - yall remember your chi square from bio right?

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True Randomness

Ideal Gases have atoms/molecules that move randomly
Vibrations of elementary particles are random
Double pendulum (chaotic motion really)
Fluid Turbulence

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Wait...that’s illegal

But computers can’t generate that…

Why? Because we don’t know how to generate something random...and it’s annoying to calculate the motion of a particle every time you need random numbers

So we use very good approximations

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Fake Randomness (Pseudorandomness)

One common algorithm - it uses cyclic division so it will repeat

True random

Pseudo random (bad)

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Other algorithms for randomness

Middle-square method (one of the oldest ones) - code from Wikipedia

seed_number = int(input("Please enter a four digit number:\n[####] "))�number = seed_number�already_seen = set()�counter = 0��while number not in already_seen:� counter += 1� already_seen.add(number)� number = int(str(number * number).zfill(8)[2:6])� print(f"#{counter}: {number}")��print(f"We began with {seed_number}, and"� f" have repeated ourselves after {counter} steps"� f" with {number}.")

Xoroshiro128+: one of the fastest today

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Deterministic vs Nondeterministic randomness

Deterministic: this basically means that given a certain starting value (or seed value), the random numbers generated are always going to be the same

Nani? How is this random then?! - It’s not

Nondeterministic: input seed doesn’t give same random list every time