Cosmological Cycles

The Nature and Patterns of Chaos

Chaotic Patterns
Chaos, Galaxies and Stellar Systems
References and Recommended Reading

Chaos - The Basic Pattern of the Universe

The dictionary contains definitions for the word "chaos" that have little to do with the actuality of chaos. Various definitions found are

1. complete disorder and confusion.
2. the formless matter supposed to have existed before the creation of the universe.

or even more elaborately,

1. (obsolete) chasm, abyss.
2. (often capitalized) a state of things in which chance is supreme; especially the confused unorganized state of primordial matter before the creation of distinct forms.
3. the inherent unpredictability in the behavior of a complex natural system (as the atmosphere, boiling water, or the beating heart).
4. a state of utter confusion.
5. a confused mass or mixture.

Only certain of these ideas fit with the modern mathematical and scientific definition of chaos. Our definition utilizes the concepts of unpredictability, statistical behavior, but not necessarily of disorganization or formlessness. It also relies upon a notion of some underlying pattern that is being followed though not in a strictly cause-and-effect mechanical fashion. It is better developed in the formalized subject known as Chaos Theory, first put forth in that version by Henri Poincaré in 1890 and later more fully developed under the label "ergodic theory". Numerous contributors followed over the next three quarters of a century until Benoit Mandelbrot successfully characterized all such phenomena in terms of geometric patterns that were closely reproduced at all scales of size. This characteristic, called statistical "self-sameness", was caused by the occurrence of fractional dimensionality in the equations describing the phenomena. Such patterns were ultimately labeled "fractals". When viewing a fractal pattern, one can change the scale to either smaller increments or larger magnitudes and continue to find the same or very similar patterns of plotted functions geometrically repeating over and over.

This property is also found in the real world and is present when one looks at dynamic natural systems ranging from clusters of galaxies all the way down to atoms and below. Such self-sameness implies that in the real universe, there can always be something smaller as well as larger than anything we presently think is a final definition of physical reality and the matter it contains. This suggests that we will find smaller particles than the current crop of elementary particles as well as even larger interacting structures besides galactic clusters. It is the author's conclusion that all such structures are behaving this way because of a basic set of physical elements they have in common.

If one could find the master equation that would fully describe all dynamic behavior within the universe at any scale of size, virtually all of the mathematical development of different scientific disciplines would literally become unified. It is anticipated that when these master equations are finally discovered, each of the current scientific descriptions will be seen as special cases, limits or boundary conditions of the master equations. Further, these master equations will incorporate all of the known types of force and particle property characteristics or determinants.

A more detailed elaboration of the etymology of the word "chaos"

Search for the Master Universal Chaotic Equations
2 Dimensional Polar Plot

Created with GraphNow Equation Grapher v. 2.0
The use of either a polar or preferably a cylindrical coordinate system allows any spinning, rotating or revolving object or ensemble to create a definite orientation in 3 space. Like a spinning gyroscope, the rotational axis becomes a fixed-position reference line that the position of all other bodies being considered can be related to through two additional angular variables. Such a frame of reference would be expected to allow all types of measurements while remaining relative to the spinning object and follow all known physical laws of motion and energy within the context of a cylindrical frame of reference. Positions in one cylindrical coordinate system can be related and translated into any other cylindrical coordinate system created by other nearby rotating objects. The advantage of this coordinate system behavior is that there may also be definable forces that can interact between two or more rotating coordinate systems that would in effect link them to one another. An example could be two oppositely spinning free electrons that approach each other and begin to exert an ever-increasing repulsion as they fly towards each other plus a magnetic torque that attempts to flip their spins to an antiparallel condition.

The function whose graph is pictured here was created by the author using polar coordinates and fractal construction. It represents the path that most interactive bodies follow at all scales of the universe. It is an early test function in the search for the universal chaotic equations.

(C) Copyrighted 2008 by Joseph H. Guth, Ph.D.