Some of the things that looking at the graphics has shown me are:
1) There may only be primary spirals and the opposite spirals may be represented by the overlap of sequential primary spirals. This would not "eliminate" the intersecting spiral model, it would however change the basic structure of the intersecting spirals. It would also introduce quantum spacing into the separation which might provide a mechanism for stacking spirals, the capacitance part of the model.
2) pi prime is a solvable derivative of pi for each value of x based on the number of places to which pi must be solved in the model. The factors involved in this are immensely complicated: 1) do all the spirals, i.e. x spirals or x! spirals or e^x spirals go into the equation. there may be several pis to solve for in different places in the universe. 2) This requires a better understanding of the F-series applied to spiral growth. It appears at this point in time, based on historical perspectives (F(N) where n is n, n-1,n-2) that each subsequent spiral embodies all the spirals in the prior two spirals plus one more value of x. This one value of x is a change in every data point, however, so it comes out to be an enormous change for each quantum change in x. The change in every point in the universe, if it were the only change, would mean that the total amount of data remains fixed but this may not be the case. If it is the case, it would require that the initial universe has all of the data of this one and that seems too unlikely in a self generating universe. The growth factor has to be determined.
3) There are many ways to approach the graphic and one of them must accommodate the model 4/1-4/3+4/5... This derivation works and is relatively simple, but there are other, more intriguing method of getting to the result quicker which may have value in the analysis:
http://mathworld.wolfram.com/RiemannZetaFunction.html
http://mathworld.wolfram.com/PiFormulas.html
http://mathworld.wolfram.com/GammaFunction.html
The prior mathematics are intriguing and worth studying but just as the study of pi in AuT discloses the basic defect in space curvature, so also do we need to eliminate non-finite curvature (i.e. all curvature must be a function of pi prime and not pi which requires an infinite series) in the analysis. Since the goal of the graphics generated are to provide models which explain observed phenomena, what we currently have are rough models of the universe, the equivalent of pre-relativistic newtonian mathematics. The graphics only approximate the true results and rely on observations for the modifications. That is, they are not pure mathematical plots as they need to be. Instead, observations are used to come up with possible models that would reflect them. The models then suggest other answers. For example, the spiral is the direction of movement of gravitational acceleration, so it works well with the transition from linearity to non-linearity. The overlapping spirals provides a model for compression and linear models provide for the type of continuous expansion and even accelerated expansion we see after the big bang and this model, in turn, especially when combined with the F(N) and F(series) functions for spontaneous growth of information teaches that the big bang is nothing more than one in a long series of compression/expansion cycles. However instructive, this brings us back to the fundamental problem of fully defining the growth algorithm, the fundamental algorithm that defines the universe in response to a single variable which is not as illusive as it might seem since the underlying parameters are necessarily not complex.
4) The conclusion is that while the graphic analysis has been helpful, at this point in time, it has to take a second place to plotting out the various methodologies for coming to the observed and predicted results experienced to show: 1) building using the F-series, 2) compression and expansion, 3) averaging intersections to get curvature 4) F(n), and the like.
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