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CONFIGURATIONS IN A TWO DIMENSIONAL  RANDOM FIELD
FIELD GENERATION OF THE SPIRAL CONFIGURATION

        Consider these conditions: (a) a normal field of normal density and isotropic, (b) within this greater field, a field whose surfaces happen to be arranged radially and (c) a small and fast moving wave entering this radial zone.
    If the speed of this wave is very fast relative to the field surfaces in general, such that they appear "frozen in time" as it approaches the radial center, its orthogonal passage will cause it to curve around the radial center. If its speed is sufficiently fast so that it can make it around one time before the radial order changes (all surfaces are in motion), it will stabilize the radial field as such. Of course everything must be right for this to happen, such as its speed, size and angle of approach. It is a matter of chance. The mechanism allowing this stabilization directly relates to IDDI and the associated geometry.
    What we have, given ideal conditions which are purely a matter of chance, the possibility of a single wave finding passage around this imaginary radial core, also a matter of chance, but, if the wave manages to complete one full transit around, surfaces associated with this radial order will be trapped, thus remaining part of it. At this stage, the radial order is called a radial array; albeit, only briefly, does it remain as such.
    A radial array is a radial order of the field confined to a flat plane of indeterminate finite thickness.  It happens by chance.
    Once a single wave spiral progressive to this stage of radial array, it winds up the radial surfaces into into a spiral.  At this stage, it is called a spiral configuration, eventually becoming stable.  [For more on spiral configuration, go here.]

FIELD GENERATION OF THE RADIAL CONFIGURATION

    Another class of configurations, called a radial configuration or dual-wave radial, evolves from a purely radial array consisting of two waves, rather than one, traveling in opposing orbits.  Because two waves must enter a radial field virtually simultaneously, the odds of occurrence of this configuration must be substantially less than for a spiral configuration, where only one wave is required for its formation.
        Besides one having one wave, and the other two waves, there are several other significant differences between these two configurations.
    In the case of two waves orbiting around a common radial center, no winding of the field occurs; each wave nicely offsetting the forward displacement of radials caused by the opposing wave. Just as with the spiral configuration, field surfaces are caught and trapped by the same mechanism as before, causing the density of field surfaces within the configuration to rise above the normal ambient field density, until a certain maximum is reached. As mentioned before, this mechanism is called radial restoration.
     Another difference between a spiral configuration and a radial configuration is that a radial configuration is not permanent, eventually decaying, because, unlike the spiral configuration, no standing wave conditions develop. Instead, because of the radial field, both counter rotating waves follow a gradually enlarging spiral path, ultimately causing dissipation of the radial configuration.
    The waves forming a radial configuration do not need to be exactly alike, but may vary in wave size and speed, as well as angle of entry into the radial field, nor do both need to arrive at exactly the same moment. Once engaged in mutual counter rotation, despite speed variation, the faster moving wave will tend to twist the field, since it gets around more times in the same time.
    By so doing, the faster moving wave will wrap the field in the direction of its passage. The slower and opposite moving wave encountering these slightly spiraled radials, because orthogonal redirection, will take a tack inward. Because it is now traveling along a smaller orbital radius, the slower wave, though not moving any faster than before, is now completing its revolution a little bit more quickly. If its period matches the faster wave, each wave will perfectly offset the forward advancement of radials caused by the other wave, and no further spiraling of radials will occur.
    Besides undergoing change in its orbital radius, the slower wave, as it moves closer to center, will face a predominance of convex radials, and thus become smaller, allowing it to move closer to center than it otherwise would be able if its wave size had not diminished.
    The reverse of this process also occurs. If the outermost wave's period is too long, allowing the innermost wave to wrap radials, the innermost wave will tend to move away from center.
    This process which is not purported to be perfect, probably does not allow perfectly stable orbits, but instead a yo-yoing so-to-speak, or weaving of wave orbits, of the two waves.
    The radial configuration, also called a dual wave configuration, is formed much in the same way as an outside-shelled spiral, except in its case, two waves, rather than only one, are involved; moving in counter rotation. Though both waves do not need to be exactly alike, they should at least be sufficiently similar in order to provide identical, or nearly identical periods of rotation as they orbit around the radial center. If this happens, spiraling cannot occur, because the counter rotational passage of each wave will neutralize the field spiraling caused by the other wave. In other words, though one wave in its passage will start to wrap the field into a spiral, the other wave, coming from the opposite direction will unwrap the field, and vice versa.  As is suggested, the field surrounding a radial configuration, by virtue of its mutually restorative counter rotating waves, remains radial.
    As a direct consequence of this, no shell is formed, and standing waves will not develop. Instead, both waves will continue to orbit around the radial center with progressively larger and larger orbits. This is true by virtue of the nature of orthogonal wave propagation from surface to surface; each wave describing a segmented path from one radial to the next, until eventually the waves begin to encroach upon the ambient, random field which surrounds the configuration.
    Once reaching this portion of the field containing fewer and fewer radials belonging to the configuration itself, the waves dissociate from the radial configuration, causing it to decay.  [For more on radial configuration, go here.]
 
 

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