This document discusses pseudo-randomness and statistical tests used to analyze random number generators. It explains an algorithm that takes a digit number, squares it, and uses the middle digits as the random number for the next iteration. It also lists several popular statistical tests used to analyze randomness, including normality, compressibility, linear complexity, autocorrelation, and Fourier coefficient tests.

1. Pseudo-
Randomness
Dr. Hector Zenil

2. Pseudo-Randomness
● Take any n-digit number
● Square it
● Take the middle n digits of the resulting number as the "random
number"
● Use that number as the seed for the next iteration

3. Pseudo-Randomness
http://reference.wolfram.com/mathematica/tutorial/RandomNumberGeneration.html

4. Pseudo-Randomness
Among the most popular statistical tests are the following:
● Normality
● Compressibility
● Linear complexity
● Autocorrelation
● Fourier coefficients
● Run and gap tests
● Partitioning the set of m-bit strings and counting hits in subsets
● Serial tests
● Rank of a binary matrix
● Longest run of 1's
● Hamming weights
● Random walk tests
● Close pairs

5. Pseudo-Randomness