I showed this before, but let's assume for a second that there exists some being capable of perceiving all possible universes, though all these observations are synchronized in time with observer. Other than being perceived as a unified structure by that being, these universes are otherwise independent and need not actually be synchronized in time with the observations - the requirement I place on this is simply that the being observe a sequence of arbitrarily long "symbols", similar to either the presence or not of some consciously detected quality.
Now we have a few possible classes of "universes", but it appears they compress down to just 2 types - finite and infinite.
If the observations are of a finite system, then the observations of it ultimately repeat and the primary characteristic is the period or wavelength of this repetition.
If the observations of it do not repeat then there's really nothing predictable about it and all the influences of all of the infinite universes can be described as the single influence of a single infinite universe but with multiple properties it displays (which isn't particularly relevant for this example).
For all the finite universes we have a repeating sequence of observations and similar to the infinite sequence, 2 such universes that share the same period of repetition, or wavelength can be compressed into the observation of a single universe determining multiple perceived qualities simultaineously.
So we so far have the equivalent of an infinite spectrum of wavelengths and each "step" of time within each wavelength determines some perceived quality of an experience at that time (as an example, the quality of seeing red and green simultaineously could be the same as just seeing yellow and not red and green independently).
Now if this being begins with no knowledge but learns structures from recurrences in these perceptions, then we need to look at what novel information can be observed over time.
If we begin at time 1, every observation of every universe is entirely unique and has no previous history. There are not yet any relationships in memory to construct and so the first observation could be anything.
At time 2, we have all the systems that are not constant changing, whereas all "universes" that simply remain at a constant state (with a period or wavelength of 1 ) are observed to remain unchanged.
At time 3, we still have all the period one systems repeat identically (forever) and we now see a second split of the original "indescribable" remainder into both the remaining period 3 and larger components as well as the first repetition of all the period 2 systems (which should oscillate back and forth between 2 states forever).
Notice that we no longer need to observe the period 1 systems anymore as they provide no new information on "what time it is". If each phase of the period 2 system contains the same information information as the period 1s, then informationally we only need to know what state the period 2 systems are at to determine what state the period 1 systems are at (they remain constant).
As a quick example of this, imagine that all trees have leaves. If there was never a tree without a leaf then simply knowing something was a tree would tell you that it also had leaves and the "tree perception" overrides the perceptions of the leaves. There may have been an initial moment that either the branches or the leaves may have been noticed, but after that "it's all trees" (except for what else comes along later).
So in this sense, the observation of the period 2 system informationally "obscures" the period 1 systems.
From a subjective perspective, this should appear similar to a split - you have an initial event that's indescribable and from there it splits into a component that remains indescribable and then comes an oscillating component that proceeds to obscure the observation of the constant components.
At time 4 we see the repetitions of length 3 systems and this is just a new construction that doesn't synchronize with the length 2 systems. So it simply splits out of the "indescribable" component on its own.
At time 5 we find once again an that the period 4 systems informationally overwrite the period 2 systems, so the bipolar oscillation could be seen to split into a an object with a period of 4 (though it could also be interpreted as a pair of binary oscillation an octave apart).
At time 6 we have another new class of length 5.
At time 7 we have a class of length 6 which creates a different form of transformation as it can describe both the length 2 and length 3 systems simultaineously, but we've already had the length 4 system overwrite the length 2 system, so we could have the interpretation of the "smaller/faster" component of a binary pair describing the length 4 system splitting off and combining with the length 3 system in order to construct the length 6 system.
To show this better as a graphical timeline, imagine these sequences being observed over time.
Time goes from left to right and all the properties of an observation are shown vertically with the shortest wavelengths at the top:
Code:
AAAAAAAAAAAAAA...
BCBCBCBCBCBCBC...
DEFDEFDEFDEFDE...
GHIJGHIJGHIJGH...
KLMNOKLMNOKLMN...
PQRSTUPQRSTUPQ...
...
At the initial time, the observation was of the composite of A, B, D, G, K and P.
Because none of these have ever been seen before and potentially each one of these symbols is also an infinite combination of various perceived qualities. The "ensemble" could simply be described like a single symbol itself.
At the second moment of time, the A is the only property that repeats and so, if we assume each of these universes possesses some form of rules by which they operate, then going from A to A leaves the system unchanged and it would remain at A forever.
The remain C,E,H,L,Q observations are once again unique, so the initial perception of the A, B, D, G, K and P could now be interpreted as having split into a constant A component and the remaining transformation from B, D, G, K and P to C, E, H, L and Q.
At the third step we have the C component change back to B and once again, if we assume we're seeing the entirety of some "universe" operating by a specific set of rules, then we already know that B will then become C, so we can now, after seeing the repetition predict the BCBCBCBCB... continues.
Again, notice that whenever B or C was observed, there was always A present and because of this, we can remove the perception of A as something independent because it was already present in both the B and C observations and so by knowing BCBCBCBC... we also know AAAAAA...
So the constant component, A, could be seen as having "left" or become obstructed etc. because it no longer conveys information (it's now "timeless").
When we encounter the repetition of the DEFDEFDEF... this can't be combined or simplified in any way, so we'd now have two oscillations - the BCBCBCBCBC... and the separate DEFDEFDEF...
When we see the repetition of the GHIJGHIJGHIJ, the BCBCBCBC... now becomes redundant as every G and I contains a B and every H and J contains a C, so this could interpreted as a splitting of the BCBCBCBC.... into two pairs (though this splitting isn't symmetrical and it contains two components an octave apart - one could be considered the smaller/faster/inner pair and the slower/larger/outer pair).
Anyway, the progression ends up having correlations with lots of areas but the most direct correlation is with the properties of prime numbers and factoring and there are ways of remapping this similar to a vortex with rings of various wavelengths interacting between themselves over time.
There are also many musical, geometric, and mathematical relationships that arise from this (for example, a "chord" appears as a single static structure that's the composite of multiple wavelengths and it could appear to have various loops like a lissajous image to describe the ratios of the frequencies - if we compare two frequencies of similar but not identical wavelengths there can appear to be relative motion between them and the appearance of an orbital).
I mostly like the fact that you can begin with something as basic as conscious perceptions of information over time and find a naturally arising "common landscape" shared by these.