In the category of energy transport, multiplicative exponential effects, which span a huge number of interactions, we can identify “spirals” as the energy interactions “curl” the resultant additive CIE xy projection flights.
If we combine the idea that luminance to chrominance are orthogonal dimensions, and expand the latter to be momentum-like, it makes me wonder if there’s a more basic “ideal” spiral for any given mixture.
As energy approaches infinity zero, orbit-like flights emerge.
Binet's work "simplifies" the orbit calculations by using the reciprocal of the radius to remove the nonlinear effect of the squaring of distance in the inverse square law.
Interestingly, it at least seems plausible the MacAdam's moment calculation employs a *similar* mechanism. MacAdam takes the Euclidean distance from a point, and applies a 1/normalized_luminance scaling. This seems similar to the Binet trick.
Binet's work seems to conserve "angular momentum". That is, they take a small amount of radial distance as a rate of angle change. A sort of "acceleration to angle acceleration" relationship.
In MacAdam's work, there is a similar "conservation" at work. As we move away from the relative frame of reference, our luminance *always* decreases at equivalent energy, and our chrominance *always* increases.
Consider MacAdam's ellipsoidal "equal energy" relationships as slices of a conic!
While this tends toward the rather obfuscating idea that we always are relative to some global centroid, we don't need to abide by this misunderstanding.
We can reframe *any* coordinate as a relative frame of reference, and compute the MacAdam fields for it.
If we imagine a complete conservation of energy at work, we'd expect an infinite orbiting around a given centre of mass. A slice through a conic for any given point.
When we think about multiplicative stimuli transport, we remain in an energy conserved system arguably, it's just that our energy is being transformed into heat via absorption etc.
Thankfully, in terms of visual cognition, this "decrease in energy" is not nearly as complex, and instead is partitioned into decrement signals.
TL;DR: As the luminous energy per unit angle of stimuli decreases, the chrominous energy increases. This is the reciprocal relationship as our Riemann-like sum "thins".
At risk of a gross oversimplification, given some stimuli level S, we can roughly suggest that our retinal ganglion cells partition the S into luminance and chrominance signals, where the chrominance signals are two dimensional. One along the L-M direction, and one along the (L+M)-S direction.
But in this constrained case, where S is fixed... as we *remove* S energy, the L+M drops, and our L-M to (L+M)-S increases in the vector magnitude sense.
In terms of multiplicative effects, such as if we imagine a "red" diffuse sphere next to a "green" diffuse sphere, the energy that bounces between them reduces our total stimuli S level with every indirect hop.
However, given the multiplicative nature, the excitation purity increases at every hop. This is what happens when we peer into a flower, where the sunlight might be filtering through the petals, *and* there's indirect bouncing within the flower core itself.
We end up with incredibly
high excitation purity.
Fun experiment: Grab a set of coloured filters and look at these cases such as a plastic toy being illuminated from the outside. Through the gaze of the filter, the rates of change become far more apparent, appearing almost surreal if one combines the right filter against these indirect exponential effects.
It helps us to visualize how the exponential gradients are decomposed in our visual systems.
As these multiplicative effects scale our energy toward zero infinitely, we can imagine a sort of "orbit-like" spiral as the "gravity" of the mixture collapses toward the "mass".
The way these pigment mixtures curl hints at this sort of a framing, they do not reveal the complete spirals of course, as the energy drops exponentially, making it incredibly challenging to measure.
I suppose we could emulate this using a model and amplify the results to see if there's a spiral-like flight.
troy_s 