Planets, Fractal, Phi and Stockmarkets

Following up on the Ouroboros stuff from ages ago, which is related to the SRH thread, and through an article on Alchemy I came upon the presence of Phi in the planetary orbits. Odd I think and am trying to explain that becauise it is also used in charting stock markets. It is commented already that stock markets show fractal geometry, and Phi is the limit of the relationship between adjacent numbers in the Fibonnaci Sequence - a sequence that is gained by recursion i.e. fractal! Consider two systems A and B which proceed by adding the value of the other system - this is the Fib sequence. A and B can start at any value (as long at they are different).

A 10 24 etc
B 14 38

They will come into Phi relationship ... why? Algebraically it is obvious:

B(n) / A(n) = [ B(n-1) + A(n) ] / A(n) = B(n-1)/A(n) + 1 (ok not quite I've got this in notes will update)

Anyway looking further this is interesting and I note it for reading later:
http://www.cyberalley.com/G-Home/R&D/R&D5/FofL12.html

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http://www.ermanometry.com/

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Funny how everything appears to fit together ... or is this an illusion because I want it so? Actually I don't want it so because if Phi is this fundamantal then it will end up explaining things rather than being explained!

http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html

So it seems that in iterative processes the repeating units come into Phi relationship *for some reason*. This link describes it as "self-reference" - I don't call it self reference because it isn't. A large structure being composed of structures "similar" at many scales is only "self" in the sense of "similar". Altho I must conceed that a set which is made of copies of that set at a smaller scale is more extraordinary than one that is made from dissimilar material. This really questions what we mean by "self". What we don't mean (a la Buddha) is a material existing thing called self. Fractals actually illustrate this "self" that is built from "copies" of "itself", and so not self and self at the same time.

But why Phi?

Web site here were the writer seems a little carried away with the patterns. If there was no pattern that itself would be amazing. It is Wolfram versus Caitin on whether the universe is full of information or whether the apparent diversity has underlying rules. I part company on ths page and this statement "There is no natural explanation for these unusual relationships" [http://solargeometry.com/34power.htm]. I reckon there is a very good reason. 2 options. Either:

(1) the planets formed in this relationship and it is a feature of the fractal collison and amassing of dust in the emryonic nebula + the expulsion of massive rocks that were too excentric and out of phase with the system. OR

(2) over time the planets have evolved into this relationship. Evidence for this would be that the inner planets (with more revolutions and periods of evolution) have tighter relationships.

Some things to note. All the planets bar Earth are in a 2*Phi relationship. Mars is the most deviant. And there is a missing planet (from the pattern) between Mars and Jupiter, where instead is the asteroid belt.

Jupiter, Saturn and Uranus are massive and it seems likely to me that the planet that formed immediately inside jupiter's orbit suffered some catastrophe and either never formed properly, was broken up by the gravity of Jupiter or there was some massive early collision creating the asteroid belt. Mars, which is incredibly light, will be hugely affected by Jupiter and aided by early collisons from the drama in the asteroid belt has a distorted orbit.

However such speculation leads no closer to why Phi.

The inner planets are in almost circular orbits. This is most likely the influence of Jupiter which I understand would accentuate any eccentric orbits and eventually fling the planet from the system. By simple evolution only circular orbits exist. Given radius from the Sun, and assuming nearly circular orbits, the possible velocity and therefore orbit period are hugely constrained for the planets. I need develop my calculus a bit before describing that in detail.

Then it remains only to find out why only certain radiuses from the Sun are favoured for planet formation and stability.

I expect the iterative dynamics to be something of the form Sqrt(x+1) = x or x = 1/(x-1) both of which converge on Phi...

Then I have a demonstration of my hunch that a similar iteration exists in the Stock Market game mentioned a few posts ago. After all the stock price is what speculators base there trading on, and their trading affects the stock price so there is an iterative system and ergo it will show fractal geometry (with patterns feeding back through the system at scale) with stable points existing at solutions to these interations ... like Phi.