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Mathematics Forum
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| cramwit Quote | Reply | | Chaos engineering Blather posted on: 6/5/2007 9:05:10 AM I am just going to blather a bit about vague ideas of chaos. Chaos must be essentially bounded. Without a boundary all the vector elements go asymtotic/entropic. The logistical function is bounded mathematically by the two terms which manage to juxtapose one another within certain parameters of coefficients & powers of the two terms. By nesting the output back into the function it creates a 'noise' of outcomes. Certain initial values have flat/linear recursive [or asymtotic?] outcomes, but if you start with various fractions or floating point values of sufficient[infinite?] granularity then it goes on seemingly indefinitely cranking out noise [indeterminate outcomes within the outer boundaries]. I am going to talk more in layperson geometry [engineering] rather than in pure math, but perhaps there are pure math descriptions/correlations. Generally in physics the chaos we deal with is numerous particulate elements on vector paths that either encounter the greater bounds of chaos or the other elements of the chaos, changing/altering the vector movement & creating a context of [what i will call] noise. Extraneous thought: As a general principle i will guess, without any mathematical basis, but from observations of wind speeds of super frigid wind/atmosphere speeds on the outer, coldest planets that the colder [slower vector speed] of the particulate elements the more organized patterns that 'naturally'/readily occur. I was thinking about structures floating in ambient chaos. If a line segment floats in chaos it has a sort of stability perpendicular to its length, but almost zero resistance to movement parallel to its axis. A circle floating has a more generalized stability but not the degree of stability as the segment does on the perpendicular to it. A circle also isolates a region of chaos from another region of chaos. Allowing potentially, if it is a rigid tension holding structure, to have a region of lower or higher pressure/noise. On a purely passive basis that would be a function of element population to area. I thought a possibly more interesting structure is a spiral. It creates a sort of calmer interior(s) yet is still accessible to the external chaos. I was thinking you could have a sort of infinite inward spiral [nautilus] or you could have a sort of 'screw' circle with sort of a few nested circles & a large circular interior. I was thinking if you have a spiral & it spins then depending on which way it spun it would tend to create in its interior an environment of compression or decompression. If you put burrs on the outermost cycle of the spiral the noise would tend to drive the spiral [albeit slowly] in the direction of the burrs. I don't know if purely passively driven by noise it would create a very distinct region/interior of altered pressure or not. I wonder if you had several nested screw circles that were all oriented the same way if that would create a significant pressure alteration? As an ancillary thought a screw circle has less overall structure so presumably less 'mass' so it might make any passive environment alterations more efficient. I suppose you also might have some naturally occurring spring closing teardrop/arrowhead shape. It would tend to be driven in the direction of its point. As it was the density of elements at the back end would build up, increasing pressure & tending to push out the back. With a spring tension type closing it is easy to imagine that cumulatively creating a region of reduced compression within the teardrop/arrowhead. External burrs would probably assist increasing it. I can't offhand think of a seemingly imaginarily easily occurring shape that created an internal region of increased pressure. Maybe some kind of burred closed cylinder type shape? With an inward double flap valve, much like a heart valve. So pressure tended to hold the valve closed. |
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