Yup. You got it. It's the same principles that drive them to look at CBR. I am not a physicist. However, I share a language with them - the language of mathematics. I also shared a ton of coursework with 'em, 'cause I'm an *applied" maths type of guy. Alas, I graduated in 1991 - and so much has changed in the world of physics since then. I've tried to keep up, but so much has change since then! It's more than I can possibly devote the time to. I'd say my physics understanding is not much better than the average academic layperson. But, that's my understanding. From examining the CBR, they were able to observe the similitude across the visible universe and infer things like the big bang wasn't really a bang but a giant inflation. I think... Again, not a physicist.
It should also be noted that lots of people mistakenly believe Lorenz was the originator of chaos theory. He was not. That had been around for something like 100 years before his work with it began. My memory is a little fuzzy and I'm too lazy to Google, but I believe it was inferred from the 'three body problem.' (Which also has quite a bit to do with astronomy/astrophysics.)
It was Lorenz that made me interested in seeing where else we could apply the theory. Mass. DOT just happened to have free ('cause students like free) traffic data that they'd been collecting. And it's that simple twist of fate that got me started. Yup. That's the reason.
I don't pretend to comprehend (or understand the significance of) different degrees of infinity or randomness, but I think it makes sense conceptually. The chaos theory bit does makes sense though.
Is this why physicists are so interested in cosmic background radiation? Are they trying to infer things about the initial state of the universe for the purpose of predicting the future of the cosmos?