Robin and Jed recently elaborated on the unpredictable nature of weather patterns attributed to Global Warming where it might seem for brief spells as if the exact opposite of global warming is occurring. A branch of computer simulations for which I have immersed myself in for several months now would tend agree with these conclusions.
Let me endeavor to clarify. For several months now I have been researching a specific branch of computer simulations based on the simple rules of Celestial Mechanics. I'm sure they are associated with an obscure branch of chaos theory. I basically plot the path of an orbiting satellite as it makes its way around an attractor in a 2D (x,y) plane. Chaos theory employs similar algorithms where the computed results are fed back into the system to generate the next iteration. Certain simulations need to be iterated fifty million times or more in order to build visual patterns. Certain observations where initially the orbital path of the satellite appears to be in a stable orbit reveal how the system eventually becomes unstable, where the satellite eventually breaks free of the attractor's influence. I have explored two unique factors that can cause initially stable orbits to eventually destabilize. FACTOR ONE: Increase the positive attractive force of the attractor while all other factors remain fixed. (This would be the equivalent to raising the temperature, as in Global Warming.) The introduction of instability is primarily due to larger sampling step rates brought about by increasing the force attributed to the attractor. As in Chaos theory the computed (x,y) values are fed back into the system as the "seed" to the next iteration. Eventually the generated values become too great for the closed system to manage in its current configuration. The satellite's orbital period is forced to reorganize into a different pattern to accommodate the additional "forces." Often the reorganization process is unpredictable and abrupt. For brief spells islands or reorganized stability can temporarily reassert themselves between rivers of chaotic instability. Eventually, however, the entire system breaks down utterly and completely. FACTOR TWO: Introduce an outside/external force such as an infinite/parallel force "beam." Eventually, if the external force's influence becomes too great it essentially knocks the satellite out of its stable orbit. However, before that happens, as the strength of the external force "beam" slowly increases, the satellite's orbital path tries to reorganize into new patterns of stability. Some of the patterns generated as the satellite searches for stability are, IMO, visually striking and totally unexpected. Depending on the combination of celestial mechanical algorithms used patterns of precise order and ordered chaos can occasionally find ways to work in seeming harmony in unique dances. Some of the visual patterns generated in fact seem reminiscent, to my POV, of the Van Allen radiation belts, including the bow shock. What my mathematical orbital explorations seem to have revealed so far is that, if given a chance, these systems seem to prefer stable patterns that often involve predictable periodic oscillations. If the initial pattern of stability is disturbed either internally and/or externally the system will attempt to reorganize or reconfigure into a revised pattern of stability – again, if at all possible. However, as additional influences or forces are fed into the system in increasing amounts the ability for the system of having the capacity to find a new level of stability steadily diminishes. Increased chaotic behavior becomes the norm. Increased chaotic fluctuations are also observed. Eventually the system "breaks". * * * * * * * I'm seriously toying with the idea of showing, visually, the evolution of some of the more interesting chaotic patterns through a series of computer animations. However, it's also clear to me that it would be an ambitious project, one that I'm not yet sure I want to commit to. There is still a ton of work left to do on just the computer programming side. There remain countless unexplored rocks that I would like to turn over. Each completed simulation seems to generate brand new questions that beg to be explored in greater detail. I would need to create a new subdirectory out on my OrionWorks web site devoted to personal research in this obscure branch of study, where interested parties could drop by and download graphics, animations and accompanying text. Alas, I don't know how much outside interest truly exist in what I'm currently researching. It seems likely to me that previous explorers have already walked through significant portions of this chaotic forest - the famous Mandlebrot set and it's many siblings being the most obvious example. Perhaps they have already mapped, sufficiently, the chaotic domains of Celestial Mechanics as well. I have no desire to embark on a project that promises to be a ton of work, one that is nothing more than the reinvention of someone else's wheel. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
