If the current travels at the boundary of the circles, bearing CW or CCW, from circle to circle, it would seem that the progress averaged along the overall path of a straight chain of circles would be pi/2 times slower than as measured along the full length around the circles (pi/2 being half the circumference, when 1 is the diameter).

However, consider the paths consisting of the top and bottom "staight-edge" boundaries in the above picture.

It turns out that all the circles that touch the same boundaries (either top or bottom) are an even number of hops away. This means that if you rotated all these circles, as if they were gears, then all the circles touching the bottom boundary would move the bottom area together in the same direction. Ditto for the top boundary. However, the bottom and the top boundaries would actually be pulled in opposite directions, as circles touching opposite boundaries are an odd number of steps away.

So, if we could imagine a situation where two seemingly touching circles must rotate together (sharing the same spin orientation), they could in fact do so if they were separated by a bar like this one, however thin such a bar were (even perhaps as thin as the Schwarzschild radius of a much larger orbitsphere that it is a part of). In fact, it would appear that such bars must exist between the circles touching the two edges of the above bar (i.e. the top and bottom boundaries mentioned previously). This relationship would appear to be infinitely recursive if all the space in the bar were to be filled with circles. In a sense, we have could have "bars within bars".

It would be clear that any speed of energy transfer from "border-to-border" would be reduced by a factor of pi/2 averaged over the length of the chain, assuming a straight chain. However, given that these chains are not straight, the border-to-border energy transfer would propagate significantly slower. One could imagine that properties such as material permittivity, refractive index, resistivity, and emissivity, all of which are frequency and/or wavelength dependent, might only be explained at a fundamental level if understanding about them is obtained from some geometric pattern embodying the properties themselves. Otherwise, they may remain as solely empirically-determined properties that evade an accurate classical, first-principles explanation.

Given the arrangement of the circles, it would also be possible to stack these "bars" layer by layer, while still allowing all the circles to rotate in "unison", in the sense I mentioned above. To the extent that such layers do not line up, the extent to which such layers may have difference in "bar curvature" to make up for the offset. The result would be an alternating pattern of "left"-oriented and "right"-oriented motions with a variable overall orientation. Thus, any energy moving across layers, particularly along paths such as those "vertical" chains highlighted in red, would have a characteristic alternation about them, perhaps identifiable as a TEM wave, or transverse electromagnetic mode wave, with the ability to have interactions with surrounding media.

A connection can be made here with the alleged "longitudinal [aether] waves" that some, such as Konstantin Meyl (Konstantin Meyl Scalar Wave Interview with William Alek - YouTube) and Eric Dollard (Eric Dollard 2007 Presentation - Misconceptions of Electricity and More - YouTube) have supposed as being capable of traveling at pi/2 times the speed of light (https://www.google.com/search?q="pi%2F2+times+the+speed+of+light"). [This notion in fact became a catalyst for my development of a geometrical hypothesis that longitudinal waves might travel in spherical surfaces, which I later compared to Mills' orbitsphere concept.] If we were to take the above image as a guide, then the likely place that such "longitudinal waves" would travel along would be the relatively straight path at the top and bottom boundaries, in opposite directions, perpendicular to what maybe analogous to a TEM wave (the red "vertical" chains).

Beyond this point, there is too much to speculate at this time. The patterns remain very interesting and suggestive, however.