You talk about cells. Concerning cells, I would imagine areas of space with borders between, and that the set of cells completely covers the space. But the cuboids in your picture do not, there is empty space between them. So, is there empty space between them or not?
There is, indeed, space between the cells: Each cell may be moved, rotated and stretched, independent of the others. If there would be no space between them, this would not be possible. (But the border regions between the cells should not be necessarily large. Their size restricts the possible deformations of the cells. But these should not be large at all. If these rotations, shifts, and deformations are only very small, then a very thin border is sufficient.)
On the other hand, the space between the cells is not necessarily empty. It may be occupied by some other material, for example, some amorphous material or a liquid. As well, the cells and the material between them may be different phases of the same material.
How particles emerge?
How emerge fermions from cells? Is a fermion a cell flying around in space?
No, the cells remain on their places. They oscillate around them, like atoms in a crystallic lattice, but they don't move freely.
This gives a lot of different types of sound waves. (Every degree of freedom of a cell defines another type of wave. And there are even more waves — almost continuous waves and oscillatory waves.)
Particles appear only as quantum effects of the sound waves.
This is similar to the electromagnetic field: It is, in the classical limit, not a collection of photons, but a single classical field, defined by four functions A_{μ}(x,t). The photons — the particles of light — appear only as quantum effects.
The same happens even for sound waves. If we have some crystal, we have some sound waves in it. These sound waves are created by oscillations of the atoms of the crystallic lattice. These are, as obvious as possible, waves, not particles. But even for these waves, quantum theory leads to effects that may be described in terms of particles. These quasi-particles are named phonons.
In a similar way, all particles of the SM appear as quasi-particles caused by quantum effects. In a classical world, there would be no particles at all, only waves.
(There is one objection against this approach: These quantum quasi-particles, like phonons or photons, are bosons, not fermions. It was a quite difficult task to solve this problem, but I have found a solution. So, fermions can appear as quantum quasi-particles too, but only together with a boson. Thus, there is also some type of supersymmetry in our approach: For every fermionic degree of freedom there is also a corresponding bosonic degree of freedom. Fortunately, these bosonic partners obtain large masses, and this happens without any conspiracy, almost automatically. I see no way, yet, to obtain an upper bound for their mass.)
This approach has very much in common with the old ether concept. The most important differences are:
Based on modern physics: The old ether theories have tried to find models for the electromagnetic field. Today we know much more about the fundamental fields: We have the so-called standard model of particle physics, which describes all known particles and fields except gravity, and general relativity as the theory of gravity. The aim of our ether theory is not to obtain the EM field, as in the old ether theories, but these modern physical theories. These theories are much more complex — they contain about 250 real field components, in comparison with four fields A_{μ}(x) of the EM field. But this makes the job, in some sense, easier: False models can be easily seen to be false — they will be unable to give the whole picture.
Quantization: Quantum theory has been developed at a time when the old ether concept was already abandoned. Thus, it was not part of the old ether idea. But quantization is a natural and important part of our ether concept: We need it to obtain the elementary particles from the waves of the ether. And, especially, we are free to use all the interesting results about quantum effects in condensed matter theory.
Universality: The old ether was a medium for the electromagnetic field. It was assumed, that, except the ether, there are also other things in the universe, like usual matter and gravity. Today, we describe all fields, including gravity and the fermion fields, with wave equations which have the same fundamental speed as the electromagnetric field. Of course, it would be strange to have an ether for the EM field, but to explain other fields, which have the same "speed of light" c in their equations, without an ether. The new ether is, therefore, the medium for all fields which have the same characteristic speed c in their equations — that means, for all fields we know: Gravity, the gauge fields of the standard model (which includes electromagnetism, weak and strong forces), and all fermions of the standard model — quarks, leptons (like the electron) and neutrinos. Thus, the new ether has to be (and is) universal — it describes all fields of our universe. There is nothing in our world except the ether.
On the other hands, there is a long list of concepts shared with the old ether idea:
Absolute space: We have a classical, Euclidean space R^{3}, with the classical (global) Euclidean symmetry group E(3), generated by translations and rotations in space.
Absolute time: We have a classical, Newtonian concept of absolute, true time.
Time dilation caused by the ether: The time measured by clocks is distorted by effects of the ether: Moving clocks are slower.
Length contraction caused by the ether: As well, ether effects lead to a contraction of moving rulers. Thus, relativistic effects are described in a way similar to the Lorentz ether.
Medium fills space: The space is filled with some medium — the ether. This medium has parts, and these parts have a well-defined (even if unobservable) velocity.
Speed of light as the speed of sound of the medium: The speed of light in the vacuum is the characteristic speed of waves in this medium, similar to the speed of sound.