Complexogenesis is the emergence of complexity. In order to understand this phenomenon, we have to ask ourselves: What even is complexity?
Complexity is the multiple combinations of merely simple functions/principles.
But to understand which role complexogenesis plays in the creation of diversity and life itself, we have to take an important detour into chaos theory and define entropy as factor of complexity increase and emergence as factor of relative complexity decrease.
Chaos, to be more concrete,deterministic chaos shouldn't be confused with randomness; Whereas randomness is merely a primarily manmade thing, nature's laws always have a hidden underlying principle; Chaos is merely defined by probabilistic determinism, and is still deterministic in that sense, that it follows logical rules. The only difference between probabilistic determinism and strict probabilism, that is common for linear binary logic, probabilistic determinism adds a tolerance interval of deviation to the strict deterministic prediction.
Emergence can be observed in everrepeating patterns, resulting in probabilistic determined systems turn into merely strict deterministic ones after uncountable renditions; The tolerance interval shrinks more and more, until the deviation is so minimal that its formerly nonbinary nature vanishes entirely.
Hence, chaos can be regarded as a more complex form of order:
And this chaos/ order can be classified into complexity levels.
The complexity levels depend on three main factors:
The interaction coefficient is embedded in quantity of recursion levels and metamathematical dimensionality, the two "mediums"
The two mediums are synonymous to spacetime, which relate very intertwinedly to gravity, a curvation of the medium.
The interaction coefficient is synonymous to matter in this analogy, which can be regarded as a highly knotted and interwoven form of spacetime itself as we will discuss in following chapters The structureprocesscomplex and Cosmic weaving.
For all factors an increase of their value also means an increase in complexity.
Entropy, from an utterly minimalistic/reductionistic point of view, works like an intrinsic force leading to interaction;
Say, elements/entities don't want to "sit still", and therefor entropy can also be regarded as an intrinsic force to move or oscillate, which then leads inevitable to interactions.
Entropy thus produces an increase of complexity.
In some system there arises a principle called emergence, which means that a system develops patterns its entities don't have themselves.
Emergence is a result of entropy, which is a process of complexification. On the other hand, emergence is a form of selfsimplification, produced by a given amount of complexity.
In the upshot, emergence is nothing more but the process of a system that becomes so complex that it simplifies itself.
As emergence works as a kind of reversecomplexifier, say, a form of simplifier, emergence is a kind of antagonist or inversion of entropy itself.
If the ratio is larger on the emergence side, the system's relative complexity decreases.
If the ratio is larger on the entropy side, the system's relative complexity increases
Complexity can be grouped into 5 main categories; Level 0, 1, 2, 3 and 4: The higher the level the bigger the metamathematical dimensionality, say the "intertwinedness".
A level 0 complexity is marked by having no combinations and mixtures of different entities, it is a strict separation of different elements/ entities. No diversity can be found. This is a rather unnatural state in nature because the law of entropy is a kind of intrinsic force for interaction.
Whereas the simplest form of order (Level 0) is strict separation of different entities, level 1 complexity starts to combine the different entities in a linear way.
If you make a very simple mixture in form of a simple sequence its complexity increases in form of an additional complexity.
It has a fixed structure and is created by a fixed process.
If you let a system with level 1 complexity interfere/ knot with itself, you get a level 2 complexity, which is like multiplicated complexity.
This level is marked by systems that are selfreferent, but are not selfinterfering, and thus don't change their processes. It is a rigid selfreplicating process that doesn't change.
This is a main principle that can be found in the sequences of DNA.
It has a flexible structure and is created by a fixed process (like F_{n} = F_{n1} + F_{n2}/ Fibonacci sequence)
Fixed process = repeating pattern of the process that changes the structure.
If you let a system with a level 2 complexity interfere/ knot with itself, you get a level 3 complexity; which is like powered complexity.
This level is marked by recyclingloops that interfere with its own processes, they "reprogram/ rewrite themselves", say they get selfinterfering, additional to selfreferent. Hence it is an adaptable selfreplicating process.
This is the main principle of deep learning mechanisms in AI.
Systems with level 3 complexity have a highly nested nature; Each entity interacts with all other entities, including parents/ superordinated branches, siblings/ parallel branches, and also children/ subordinated branches.
It has a flexible structure and is created by a flexible process (Both the equation/ rules of processes can change as well as its structures, but gradually, so no abrupt changes that have utterly no relation to the previous equations/ rules of processes)
Level 4 and above have complexity like level 3 complexity, but are nested even more.
There is an overview of the aspects and attributes of each complexity level:
Complexity level  Zero  1  2  3  4 

synony  mous number system 
  ima  ginary 
real  complex  hypercomplex 
dimen  sions 
0D  1D  1D/2D  2D/3D  ≥3D 
structure    fixed  flexible  flexible  flexible 
process    fixed  fixed  flexible  flexible 
synony  mous to operations 
  addition  multi  plica tion 
poten  tiation 
poten  tiation of poten tiation 
selfreferent  no  yes  yes  yes  yes 
rigid selfreplication  no  yes  yes  yes  yes 
linear selfinter  ference 
no  no  yes  yes  yes 
adaptable selfrepli  cation 
no  no  no  yes  yes 
selfsimplifi  cation/ multidimen sional selfinter ference 
no  no  no  no  yes 
Absolute complexity increase  0  1+  2+  4+  8+ 
Relative complexity increase _{complexity increase relative to the entropyemergenceratio} 
0  0  *x / +x  ±0  :x / x; (decrease through selfsimpli  fication) 
Entropyemergence ratio _{larger emergence leads to reduction in the entropic degree of complexity/ decreases relative complexity} 
0  0  Entropy > Emergence  Entropy ≅ Emergence  Entropy < Emergence 
row in Pascal's triangle      1 for 1D  2 for 2D  3 for 4D 4 for 8D 5 for 16D 
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