Rational fractions have repeatable remainders, that is what these generators do is generate the sequences when fed by a uniform counting index. Or make the finite index reordered, we get the repeatable sequence.
Tradebook uncertainty makes the implicit sequence irrational, so our approximations generate a chaotic bit error. One rational approximation will begin to diverge and the the pit requantizes to another rational approximation.
This is exactly what S&L pit do, they find rational loan/deposit matches that minimize the error in the approximation. Sort of at the heart of most new AI, these days.
The Markov numbers are restrictions on the indices, each x,y,z in the Diophantine equation is an integer, and the equation defines a relationship between a surface and a volume, in terms of the finite size of sequences. Why? Dunno, something about sphere packing,the need to count by threes.
These integer indices are the window sizes brigade theory deals with.
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