There’s another possible explanation: Collatz-type recurrences are the most complex behaviors that can be encoded using a tiny number of Turing machine states,

There’s another possible explanation: Collatz-type recurrences are the most complex behaviors that can be encoded using a tiny number of Turing machine states, due to the way TMs access memory. From another comment, it turns out you can apply similar busy-beaver definitions to the lambda calculus, but you get very different results for small structures due to the innate recursive structure of the lambda calculus. Of course, if you have enough states in your Turing machine, or enough terms in your lambda expression, you can express any computation. The interesting thing is what happens when you look at small instances of each.