same solution set as before, but the details of the chaotic function are enhanced.

what is particularly obvious here is that the numbers appear to be “interacting” with each other.  this is one of the primary conditions of any chaotic system. 

the very odd thing about this type of chaotic system is that the numbers are generated linearly (generated from point A to point B to point C, sequentially), but this “interactivity” is occurring non-linearly (point A and Point C are mutually generated, non sequential).

it is akin to saying that, not only does the Past affect the Future, but the Future affects the Past.

indeed, this is a brilliant illustration of the role of Time in quantum physics.

control group: spin-field numbers only. not under the influence of the chaotic attractor.

glyph-like analysis of the spin-field numbers in the chaotic attractor. the color effect is applied to enhance details. the regularity of these forms is due (almost exclusively -> please compare to control group plot) to the inherent nature of the attractor function. THIS REGULARITY is what i am attempting to discern in the course of my research. although we have seen other manifestations of this regularity in many of my fractal plots, this is a particularly compelling depiction. almost language-like, no? (Taken with picplz.)

spin-field #4 (Taken with picplz.)

spin-field #3 (Taken with picplz.)

spin-field #2 (Taken with picplz.)

spin-field #1 (Taken with picplz.)

this may help with the 3D “seashell” visualization. explanation: these are the “spin-field” numbers (plotted as points in the four graphs following this post), plugged in to my chaos-generating strange attractor function. you will notice that, while there is a definite regularity to the form, there is no distinct symmetry in any dimension. (Taken with picplz.)

the Real and Imaginary solutions diverge. if you plot these points as polar coordinates, projecting the Imaginary solutions into the page, these points in three dimensions would look like a series of nested (rotationally increasing in size) spirals….sorta like a fancy seashell. (Taken with picplz.)

the chaotic system in “3D” (with glasses).

a “3D” rendering of the chaotic system i am studying.

a “3D” rendering of the chaotic system i am studying (magenta/green glasses are best).

lattice,circle @ 3D-2 (Taken with picplz.)

lattice,circle @ 3D-1 (Taken with picplz.)

lattice,circle @ scale=100 (Taken with picplz.)