rand_eca

A function like Matlabs built-in rand, but with elementary cellular automata rule 30 -> rand_eca.

Created as part of the final project for MTH 321 Intro to Math Software class at Oregon State University taught by Dr. Torrey Johnson.

• Paper Report detailing implementation and examples
• paper_figures.mlx Matlab live script to reproduce the figures and statistical tests from the paper

Usage

See paper_figures.mlx for some real examples. Or keep reading for some basic usage:

Create a 5 by 5 matrix of random numbers with

>>> rand_eca(5, 5)

ans =

    0.4503    0.5751    0.3367    0.0591    0.5269
    0.3175    0.2145    0.8160    0.4702    0.4904
    0.8158    0.9244    0.7169    0.8429    0.1620
    0.6902    0.5453    0.6776    0.0731    0.1528
    0.5684    0.4788    0.3795    0.9459    0.3949

Create a 10 by 1 vector of random numbers with

>>> rand_eca(10, 1)

ans =

    0.0090
    0.2432
    0.4174
    0.7878
    0.7194
    0.6636
    0.3868
    0.0585
    0.4775
    0.7587

Generating 10 numbers sampled from exponential with $\lambda=1$

>>> uniform_to_pdf(rand_eca(10, 1), @(x) exp(-x), 0, 6, 10000)

ans =

    1.6578
    1.2984
    0.7098
    0.2778
    2.4618
    0.0378
    3.5736
    0.3924
    0.3666
    1.5510

Resetting the seed, as you can see genereates the same numbers after subsequent calls

>>> rng_eca(0)
>>> rand_eca(5,5)

ans =

    0.4503    0.5751    0.3367    0.0591    0.5269
    0.3175    0.2145    0.8160    0.4702    0.4904
    0.8158    0.9244    0.7169    0.8429    0.1620
    0.6902    0.5453    0.6776    0.0731    0.1528
    0.5684    0.4788    0.3795    0.9459    0.3949

>>> rng_eca(0)
>>> rand_eca(5,5)

ans =

    0.4503    0.5751    0.3367    0.0591    0.5269
    0.3175    0.2145    0.8160    0.4702    0.4904
    0.8158    0.9244    0.7169    0.8429    0.1620
    0.6902    0.5453    0.6776    0.0731    0.1528
    0.5684    0.4788    0.3795    0.9459    0.3949

Visualize 512 iterations of ECA rule 30 starting from a single black cell

>>> visualize_rule30([zeros(1, 256) 1 zeros(1, 256)], 512, 1)