Thursday, December 18, 2014

Extended Fibonacci and the 60 End Digit Fibonacci Pattern

(I've included the Extended Fibonacci graphic for reference)
The color coding denotes the Sequence that arise from the individual number, not the number itself.
The 4 odd numbers (1, 3, 7, 9), the exception being number 5, have the pattern sequences of itself and the other 3 occurring every 15 Fibonacci steps.
The 4 even numbers (2, 4, 6, 8) have the pattern sequences of itself and the other 3 occurring every 5 Fibonacci steps, the full set of which recur every 20 Fibonacci Steps.
The number 5 and its multiples seems to be the fulcrum.
- Chad Adams


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  2. taking into consideration your research, can't one say and prove that systems displaying fractal properties/behavior, like when using calculus or surface integrals and one of the system's component becomes infinitesimal while at the same time another becomes infinite, then one can consider what constitutes fractal behaviour, which comes down to non-linearity and iteration, separating thus noise and information? because likewise digital roots and modular math with cross-additions one can down-project higher dimensional objects onto lower dimensional surfaces since the latter operation shows that for example a totalizing of positions in the spirals exists and each power implies an additional dimension of spiraling? and so we arrive at the beginning of what I'm trying to say, which is in favor of the fractal approach to (ungainly) systems that high orders of complexity can often be collapsed to simple models mimicing the overall characteristics, and again perceiving noise fron information. .
    however this approach needs in every case ak practical application in reality, or else we can't make direct use of it..5 seems to fit here as you put it very naturally.