Refinements to the next stages of my model.
A type #2 universe can look and evolve like our universe.
Justification: Stage 1
Designate the succession of states for universe "j" as Sj(i) and its
representative binary bit string as Uj(i) where "i" runs over some range of
integers from 1 to n.
If we restrict the discussion to universes of type #2 as proposed and make
the additional cut of restricting discussion to type #2 universes in which
the true noise monotonically accumulates [i.e. make the Second Law of
Thermodynamics an axiom for the universe globally, but not necessarily
always so locally] then the "complexity" of Sj(i) and Uj(i) must
monotonically increase as i counts up.
If we measure the complexity of Uj(i) in the manner of Algorithmic
Information Theory i.e by the length of the shortest self delimited program
able to compute Uj(i) which generally increases in length as the degree of
internal de-correlation and the length of string Uj(i) increase then:
1) To maintain a degree of internal correlation as its complexity increases
Uj(i) must locally increase correlation while it is also locally
2) Finite strings can easily increase local correlation by appending or
inserting finite correlated strings and they can also progressively
internally de-correlate as information is added so they can satisfy the
requirements for Uj(i) given in (1).
Thus it may be simplest to represent states of some type #2 universes with
finite strings Uj(i). Finite strings have limited resolution potential,
but nevertheless can describe the location of discrete points within a 3D
space on a grid with finite non zero pitch.
An additional cut is now made to restrict examination to type #2 universes
that can be modeled as finite face centered cubic 3D grid multi state
cellular automata subject to true noise.
Notice that an increase in length of Uj(i) can be identified as the
addition of a new cell i.e. the expansion of the universe's space.
Further if the rules of state succession for a universe have an
appropriately constructed "Do not care" component then their repeated
application to the data of each successive state will lead to an
accelerating increase in the complexity of the finite Uj(i) [i.e. despite
the true noise the rules are such that each successive shortest program
Pj(i) that computes Uj(i) effectively contains the previous state's
shortest program Pj(i -1) plus the noise as data plus the rules acting on
the data plus its own delimiter] and so the length of Uj(i) must increase
in an accelerating manner to contain this complexity increase i.e. the
universe's space expands at an accelerating pace.