ABSTRACT 2: The Period 3 Window:
A New (and Very Old) Key to Nonlinear Dynamics

The horizontal period 3 window (hp3) in a bifurcation tree signifies chaos patterning—as proved mathematically in 1975 by James Yorke and Tien-Yien Li in their seminal paper "Period Three Implies Chaos." The vertical period 3 window in a polarized bifurcation tree signifies co-chaos patterning.  It can lead us into finding co-chaos patterning in the master code that generates our Double Bubble universe. 

This paper and slide presentation will examine the horizontal and vertical period 3 windows (hp3 and vp3) in two very different systems - (1) the genetic code found by Watson and Crick in 1953, and (2) the 5,000-year-old Chinese mathematical system of the I Ching.

DNA is physical; the I Ching is metaphysical. Genetics is new knowledge; the I Ching is very old wisdom. DNA codes for organic matter; the the ancient Chinese claimed that the I Ching showed the way of the Tao as world mind.  How can two such unrelated topics—matter and mind—studied in two cultural heritages so far apart in space and time—echo each other in their math, and even in their meaning?

Here is the answer. Both systems are variants of the same fractal master code. It is based on co-chaos patterning. This shared code uses vertical and horizontal period 3 windows (hp3 and vp3) to develop nonlinear equations that structure both systems. This math is seen in both the ancient I Ching hexagrams and the more recently found genetic code. This meeting of East and West is due to their shared fractal paradigm. It is based on co-chaos patterning. This is what provides the genetic code with its fail-safe supersystem. It assures basic stability plus enough leeway for the evolutionary change that is evident in every species. It provides this kind of stability plus flexibility for the universe itself, too.

This theory also speculates on further possible applications for this distinctive co-chaos paradigm, including the elucidation of string theory and developing a unique hybrid computer that utilizes both binary and analog processing.

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ABSTRACT 1: Could the Arrow of Time reveal a Strange Attractor?

The butterfly-like, two-domain shape of the Lorenz oscillator is well-known in deterministic chaos. It indicates a specific kind of strange attractor. This paper and slide presentation suggest the possibility that our universe is itself a double bubble oscillator in a dynamical system, and thus a specific kind of strange attractor. In some ways, our universe is like a giant Lorenz system, for it oscillates between two polarized domains on a path iterated by what amounts to three coupled, ordinary differential equations (ODEs). On the other hand, in some ways it is more like a Mandelbrot set, for it contains a whole set of ever-iterating fractals that evolve their contents within the basic form. Call our universe a DB attractor.

Regard the two domains of this DB attractor. They are the huge twins of our Double Bubble universe. The upper bubble holds spacetime with the properties of 3D space and arrow of time, plus matter, energy, and our known gravity pole. But the lower bubble is a flip-flop mirror domain. Its timespace has the counterbalancing properties of 3D time and arrow of space, plus antimatter, tachyonic energy, and the lost pole of gravitation.

(It's important to note for later: this TOE proposes that each bubble’s arrow of dimensionality, either space or time, is really only ½D, since it goes in only one direction—ahead. The omnipresent arrows are really only vectors on the curving, re-polarizing infinity
path that oscillates between both bubbles from each cell of the membrane interface, repolarizing as it shifts between bubbles. )

The two bubbles interface in a mobic membrane that can exist only at the mactor scale. Each mactor “pore” or cell at this interface combines attributes of a Mobius band and a Lorenz attractor, hence the name. Gravitons drum dimensionality into existence here, knitting the smooth fabric of space and time at a scale far smaller than the Planck scale where lumpy particle-waves of matter and energy emerge.

Three graviton beats in a pore create the dimensional tension of a triangle with opposing faces of 2D space and 2D time. It is a 2DD triangle. A fourth beat in that sub-quantum topology develops a polarized tetrahedron made of four such triangles. It thus becomes a 3DD tetrahedron with two volumes, inner and outer. Both volumes project far out beyond that scale, extraverting 3D space with three stress vectors of ½D time far above the mactor scale…and likewise, introverting 3D time with three stress vectors of ½D space far below it.

So many projections by so many pores of mobic membrane interface merge into the holographic Double Bubble universe extending far above and below the mactor scale. This holographic merger renders smoothly contiguous the two bubbles of 3D space and 3D time. It also consolidates the many vectors of ½D time above and those of ½D space below. They merge into each bubble's arrow of only now or only here. Those arrows are really vectors along the oscillating infinity ∞ path that repolarizes  into either ½D time or ½D space at the border crossing between each 360° circuit of a bubble.

How many dimensions are there in all? With 3D space above and 3D time below, with ½D time above and ½D space below, along with those tiny 2D space x 2D time mobic bands in the pores of the membrane interface, this gives a total of 11 dimensions for the Double Bubble universe.

Thus the Double Bubble’s working dynamic recalls a Lorenz attractor, for its two domains are the upper and lower bubbles. Its 3D space and 3D time act together as the three coupled, ordinary differential equations (ODEs) that allow both bubbles to iterate along the oscillating infinity 
 path the evolving nonlinear solution of emergent, ongoing reality. 

If we track the arrow of time back to its origin as a vector on the endless path oscillating between the two bubbles, we find that it can indeed reveal a strange attractor—the one we live in. This proposal of a fractal Double Bubble universe could account for the continually emerging chaotic flow of events that is subject to abrupt, seemingly random changes, yet that has somehow also managed to evolve from hot plasma gas to ever-diversifying matter and energy in particles, atoms, molecules, stars, planets, people. Our universe acts deterministic in its basic fractal space and time forms, yet its matter and energy contents will iterate the ever-evolving specific details, including our lives, in its ongoing nonlinear solution.





Dr. Katya Walter presented two papers at the 20th annual international conference of the Society for Chaos Theory in Psychology & Life Sciences. Their two abstracts are below:


Abstracts