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Bo Atkinson's Blog page ...
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Quadrantal and semi toroidal visualizations and construction experiments of 2014 are provided as an open source thought experiment. First photo shows the rolling up of a flat coil segment.
The nature of winding flat coils cylindrically, tends to curl the windings as if to nearly form a ball coil! I was immediately excited by this physical effect. Second photo shows coil placed inside a food container.
The curling nature is entirely natural and relaxed. This same attribute is felt when held in hand:
Next came the cognition that forcing flat coil sections into quadrantal shaped sections provided a natural means of distributing turns in a flat coil, to more nearly space out the windings. Thus to densify the electrical field surface geometry- To reduce the 'holes' between windings.
This work demands long sections of flat coil windings. I will add photos of my efforts to build a productive, very-long, coil winder, in due course.
A very simplistic example of flat coil formation is demonstrated in this photo:
Quadrant coil sections can be force-shaped with a common iron pipe bender, but here used to shape just one quadrant:
I tend to physically test visualizations for deeper reflections on what effects may be had, such as sharper curls:
Next are array concepts. Concentric, quadrantal arrays are next suggested to explore magnetic field shaping. Such arrays might require molding of concrete, using a potters wheel, (to build shapers). Or the iron bender above might satisfactorily provide a quarter curl, while a flexible spacer might be used to create successively enlarged tori sections (and to secure the otherwise loose quadrants in a concentric array).
These concentric arrays might usefully apply to my orbital magnetic field experiments.
The nature of the nautilus shaped spiral path evokes a sense of "slinging off" a tangential force effect.
In yet another assembly concept, next photo, matched quadrantal sections may assemble to form a torus or a novel toroid:
More details on methods are planned to be added in future.
I cannot afford user posted comments on this low cost website. Comments are welcome: 
All visualization and construction art work is by Bo Atkinson in Maine, USA.
Here are some of my coil visualization pages with additional links within each web page:
InductiveCouplingGeometry.html
Reflex-Vortex-Interleaved.html
HelicalWaveTransverseCoil.html
My index page is mostly pictorial, linking to decades of my varied occupations.