I have discussed how the evolution of self by BSFRs could correspond to a transition to chaos as iteration of the polynomial defining the space-time surface. The proposed picture was that the evolution by SSFRs corresponds to iteration of a polynomial P assignable to the active boundary of CD. This would predict a continual increase of the degree of the polynomial involved. This is however only one possibility to interpret the evolution of self as iteration leading to chaos.
See the chapter Could quantum randomness have something to do with classical chaos? or the article When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?.
- One could argue that the polynomial Pnk= Pn∘....∘ Pn associated with the active boundary remains the same during SSFRs as long as possible. This because the increase of degree from nk to n(k+1) in Pnk→ Pnk∘ Pn increases heff by factor (k+1)/k so that the metabolic feed needed to preserve the value of heff increases.
Rather, when all roots of the polynomials P assignable to the active boundary of CD are revealed in the gradual increase of CD preserving Pnk, the transition Pnk→ Pnk∘ Pn could occur provided the metabolic resources allow this. Otherwise BSFR occurs and self dies and re-incarnates. The idea that BSFR occurs when metabolic resources are not available is very natural for this option.
- Could Pnk→ Pnk∘ Pn occur only in BSFRs so that the degree n of P would be preserved during single life cycle of self - that n can increase only in BSFRs was indeed the original guess.