Thinking like a bubble in 3D is hard

I am just now starting to train my brain, but being a bi-symmetric being, it is hard. I have five fingers, but that is DNA and only gives me a fifth root decoder.  Not enough CPU units in me.

But, so far.  The bubbles have thing called r which adjust the unit sphere.  Each r must be place one noise unit away from any other r, so it becomes an r+1 thing. In 3D, any other r will be one volume away, so I have, r^3 = 1+r. So  am training myself to place little spheres just inside the unit sphere, tangent to its surface and tangent to each other.

The separation by one unit, by the way, is minimum redundancy, or optimum noise separation; entropy theory. What I mean is that this thing is already encoded, I need the decoder. So, I know the form of values will be (1+r)^(1/3), which gives me r. When the decoder is orthogonal to noise then its decoding graph is given by: log3((1+r)^(1/3)). That gives me a counting system that counts three things for each digit and has the quant log3(1+r).

What happened to pi?
Good question, I have not gotten that far! They are likely ellipsoids. Wait, won't Markov give me ellipsoids? Likely, and I might discover that with a little work. Are Markov sum of squares really the differential of ellipsoids? Good point, maybe.

 What about this equation? Does not this give me what I want?  The hyperbolic function tanh is a solution to this, likely a good spot to look. But I wonder, what are the ellipsoids that correspond to the Markov triples, do they follow some form like this?

Wiki has a section on hyperbolic differential equations and says:

The solutions of hyperbolic equations are "wave-like." If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point of space feels the disturbance at once. Relative to a fixed time coordinate, disturbances have a finite propagation speed. 

These sound like fixed bandwidth solutions to me. They have a finite propagation bandwidth. I always eliminate the t thing.

The tanh gives the slope of the unit circle where the conic has touched. When that value changes, it point in the direction of minimum phase, toward some other point on the unit circle. There is only one quantized solution in that direction because we are at maximum entropy in a fixed bandwidth system. The motion will be a rotation about some center radial of symmetry.