I’ll try to explain it as I understand it (ie very basically). If I make any terrible errors, I hope someone will step in to correct me.
The results are similar to seeded random, in that they are deterministic - ie. you get the same output(s) for the same input. But, they are more useful than seeded random in several ways.
There are 4 different types of CHAOS algorithms.
CHAOS.ALG 0, the Logistic algorithm has low variance, in the output, for low values of “r” (which you can imagine as a seed value for now) and high variance for higher values of r.
See this diagram from the Chaos topic:
In the diagram r is the “seed” along the x-axis and x, on the y-axis is the value that will be returned.
With the exception of CHAOS.ALG 3, the value of r that you set always ranges from 0-10000 - so there are 10,000 “seeds”. This number from 0-10000 is then mapped to the interesting portion of the graph - in this case, for CHAOS ALG 0, it is between r=3.2 (where small changes in r result in an output which is one of two potential values) to r=4.0 (where small changes in r produce a practically random output).
So to use CHAOS, we choose an algorithm, set an “r” value (along the x-axis of the function) and then the output is read from CHAOS which is a number between -10000-10000 mapped from the -1 to 1 on the y-axis.
For example:
CHAOS.ALG 0 - set algorithm to 0, Logistic
CHAOS.R 5000 - set the r value (“seed”) to half-way along the x-axis
CHAOS - read the value there, which is oscillating between 4 values
…from there you would map CHAOS to a useful number and use it to set a Pitch or Length of a gate, or whatever you want to do with your chaotic number.
As I say, the term “seed” isn’t really correct for “r” but the value of r which you input does dictate the possible outputs.
This post shows the graph for CHAOS.ALG 1, the Cubic algorithm - and @zebra explains why it is even more useful, musically, than the Logistic algorithm:
CHAOS.ALG 3, is the Cellular Automata Ruleset - these are binary arrays rather than floating point numbers. I believe it is the same ruleset developed by Stephen Wolfram in his incredible, if not humble book “A New Kind of Science” (https://www.amazon.co.uk/New-Kind-Science-Stephen-Wolfram/dp/1579550088). I highly recommend it!
@zebra goes into more detail on that here:
And check this excellent post from @sliderule on using Cellular Automata rules to generate 4 percussion parts: