chaos theory was my first tattoo.
the first actual theory which changed my life.
my question for you is what is the value of variance and is there a way to predict the variability or the patterns which may form in chaotic systems?
i love your work, it is true art for me
Ohh that is a lovely tattoo!
And I am glad you like my stuff. 👌
I agree, chaos theory has had also a large impact on my -or our, in a way- life.
It is deeply satisfying to see order in chaos, to find elegant simplicity in complexity.
And somehow, for us it has also ensured a feeling of safety and certainty in times of utter lack thereof.
Finding certainty in uncertainty - this brings us closer to your question on variance:
For introduction concepts to answering I can recommend Hermann Haken's stuff on synergetics: self-organization and emergence, which describes that patterns in a system emerge which its elements don't offer themselves. But which patterns, well, my concept about information weaving could explain how information can re-distribute iitself, which might be a part of the answer to your question. Emergence is like a form of "gravity"; quantum gravity, a re-distribution of information density, equivalent in their interpretation to the concept of probabilty intensity distributions in quantum theory. Given that elementary particles are a collection of certain "information geometries" I regard as "complex information weaving sequences", this quantum gravity interpretation is about the distribution of information density in its weaving patterns, and, this is a major leap of thought: The other side of quantum gravity brings us straight to the issue of Navier-Stokes and turbulences, which are, per my interpretation, complex interference patterns, still obeying given 'symmetries' I regard as "butterfly clones" - pairs of possible anthitetic states. (Could also be related to virtual pairs in Feynman diagrams) In a way these turbulences are feedback-loops. The conversation of energy, as in Netwon's second law, "Every action creates a reaction", becomes non-linear, and hence probabilistic and chaotic. And well, this brings us to non-linear causal networks and quantum logic.
And additionally, currently I develop an algorithm that tries to do that - how to 'tackle chaos to unravel itself' - it's a recursive iterative combinatorial approach and highly adaptable to the input you feed it with.
So, to summarize my answer: Predictions might be possible, but I can't say to which degree of exactness and accuracy. Yet, I "sense" a way, and it is primarily "imitating the chaos you want to unravel" - and letting these, the object of study and your imitation of it, interact - somehow you also use self-reference as tool. It's like you throw that chaos in a view between mirrors and it dissects itself.
That is literally what happens in LASERs - they are a result of self-organization.
