The first one is a must see presentation by John W. Bush of MIT, proposing a novel TrajectoryBased Description of QuantumDynamics, inspired by the HydroDynamics of Walking Droplets:
Replace his 'Walking Droplets' with spiralling Torus Knots (spinors), et voilà, we have selfpropelling/walking 'particles' (QM) ...
... that also curve space thanks to the compression at their centers (Gravity),
So this is what the internal dynamics of the Dynamic Foam kind looks like.
Pulsating bubbles driven by the fluid in the edges:
There is a model that seems to resemble this (by MiMo):
Let's assume that the number of bubbles tends to infinity and and the state of the foam can be approximated by average pressure and flow intensity(with no direction, since the edges have arbitrary directions in average)
So we have scalar fields P(x,y,z,t) and I(x,y,z,t)
If we assume that the dynamic interaction between P and I resembles a wave (pressure induces flow > flow induces pressure) and are out of phase by 90 degrees(sin / cos) we can describe the foam state like a complex field Psi
Psi(x,y,z,t) = a*P(x,y,z,t) + imaginary_unit*b*I(x,y,z,t). a and b are some arbitrary constants that define how strong pressure induces flow and flow pressure;
The simplest equation for a wave like that is the Schrodinger Equation
For a special function of Psi, that basically defines how pressure interacts with the flow in this current bubble, we can get quantized vortices, the smallest stable of which are exactly torus vortices(!)
Wyatt has already made a simulation of that equation in 2d and 3d.
The last thing left to do is just to rewrite the equation from average bubble flow and average bubble pressure for each bubble. And that's basically it. Its not that hard, but there may be some instabilities related to the fact that the foam is not completely uniform(as in the assumption of the averaged out foam from above).

LG uses a ‘probe field’ as a trick to get these vortices:
'The modern study of knots grew out an attempt by three 19thcentury Scottish physicists to apply knot theory to fundamental questions about the universe’
"The way spin things hook up to each other... if there were a macroscopic model that corresponded to the matrices of the Dirac equation that would be cool." (By Dubs)
The general idea of the beginning of the Big Bang is a fast inflation model, which is a kind of hot soup of energy/matter that explodes, expands and wherein 'magically' forces appear and particles start to form.
That is a fine and dandy but let's philosophise a bit deeper into the matter, and look at what the options and necessities are of that first stage/state:
Starting with a red hot blob of energy, this is where we already have our first actingforce that should bound the blob together preventing it from spreading out (exploding).
The second thing we need to look at is the expansion for which we need space. Without space to move into there is no expansion possible, think of a sliding puzzle.
So on the other hand we could also say that no actingforce is needed because there was in the beginning no space to move into.
Chicken or the egg?
¯\_(ツ)_/¯
One thing in nature that resembles this situation is the breaking of tempered glass.
In the clip above it was the hand of a Goddess that ignited the effect, but there are other possibilities such as small defaults in the structure or heat, as explained in this clip:
The same goes for how Chalk cracks:
An other example is the dried out soil of a riverbed where heat evaporates the water and bakes the soil, breaking bonds and cracks appears.
An inverse example is the expansion of bread, like in a croissant (crescent: growing, increasing, developing) and the formation of a Voronoi pattern structure.
TL;DR imo it is more logic that the beginning of the BB was just the appearance of cracks / foamstructure (Voronoi) in an existing tight substance; instead of matter 'loosely flying around', like in typical explosions, and starting to bond.
Seen from this perspective the formation of elementary particles is a mere selforganisational process of the volumes (bubbles), where knotted rhythmic pathways appear, a dynamic network, and out of which all the forces can selfemerge based on basic fluiddynamic rules.
This dynamic foam (Voronoi) moves somewhat like Worley noise,
but regulated by currents that run through the edges that make the volumes contract or expand by heating them up or cooling them down.
As a result of these selforganising currents, closed circuit loops can emerge, and rhythmic volumetric patterns can popup within the foam.
These rhythmic fluctuations can align and form a dynamic string/wave that fold on itself and turn into a knot: Spiralling Torus.
A Spiralling Torus can be seen as an Elementaryparticle acting on 'the next level'.
Here it generates the Four Fundamental Forces of Nature:
The global propellermotion of the particle generates Spin, and produces vortexlike repulsion and suction, ...
... the internal propellermotion of the ring, that produces a current through the centre, also produces repulsion and attraction, together they give rise the Strong and Weak forces (I, II). The linear trust gives it the polar Magnetic force (III).
(S) in =(O)=> out (N)
While spiralling forward a Torus compresses the cells of the dynamic foam and generates a Gravitational force (IV). The more Toruses in one area the stronger the compression of Space.
Since I have been looking (again) at ReactionDiffusion and Grid simulations, I was pointed to the www.shadertoy.com community with its incredible WebGL simulations.
The first simulation on the ShaderToy platform that really struck me was this 'Cool Accident' sim by the CSartist Wyatt, which has the 'dynamic foam' vibe that I have in mind. (But with no currents between the bubbles.)
If you aren't familiar with Shadertoy, you should definitely check them out. You can run them yourself in your browser, best in Google's Chrome and you need to activate WebGL.
An other amazing computerscientist on the Shadertoy platform is Michael Moroz who made this dynamic 'Pilot Wave System' Voronoi simulation, that comes close to my Dynamic Foam.
I reached out to them and asked to add a HalfEdge structure to his sim, that distributes the currents between the cells, transporting energy; so the dynamics of pressure going from left to right, that you see in the animated gif and which are done manually, would all happen automatically.
Note, HalfEdges are way to add graphs to the edges of a Mesh.
The Dynamic Foam needs to be a ‘dryfoam' rather than a ‘wetfoam'. Tightly packed is key, otherwise we won’t get a selforganising flow circuit. There would be too much leeway. So thin edges and enough pressure from the volumes
Depending on the angles flow can easily be split up ...
… or be blocked when the corners are too sharp for a ‘fluent’ passage.
A bit like this example of an aortic valve in a pig's heart that opens and shuts depending on the angles:
———
Continuous flow.
When the angle reaches 90°'s the flow is blocked and pressure drops at the center.
The flow stops, inverses and moves in the opposite direction.
Think of the Bernoulli Principle where fast flow generates lower pressure and suction. When the angle of the pipes are larger than 90° then the air would be blown directly into the tank.
Changes in the dynamic foam will happen percentage wise. Smaller cooler bubbles have less intense surrounding flows. Relatively the interaction stay the same.

For the intensity of the currents you could think of siphoning where flow can move uphill, thanks to the pressure differences further down the line.
Or how flow can close a valve, something that isn’t possible with heattransfer.
All in all it might like the crazy M.C. Escher’s waterfall design : )
The underlying mechanism of my approach is that of a Dynamicfoam wherein knots can selfemerge. The uniqueness of this foam is that there are currents running between the bubbles. These currents are very energetic and selforganising like in Conway’s Game of Life: flows can block, merge or split. The second key element is that these currents transport heat around making some bubbles cool down and shrink, while others heat up and expand.
So I have been looking for a way to transforming my Bubbling mockup model into a mesh model, but with an energy exchange between the ‘temperature' of the Nodes and that of the surrounding Cells. A second feature would be a flow system where the temperature moves between the nodes from warm to cold.
Basics:
• Mesh with Cells and Nodes
• Each Cell has a temperature based on its size
• The global temperature of each Node is based on the sum of its surrounding Cells
• Heat is diffused between the Nodes; from hot to cold Nodes, along the Halfedges
• The new temperatures at the Nodes is updated after diffusion and fed back to the surrounding Cells.
Extras:
• Flow vectors have a force value
• Connection angles at the Nodes have a regulating factor
Angles:
• Currents form a circuit that affects the sizes of the Volumes
• Angles of the connected edges can change and flows can be cut off > Red
• This gives the flow circuit some LogicCircuitlike properties.
Some thoughts on the underlying mechanisms of the dynamic foam:
A. It began with a medium filled with tiny oscillations [white: gasphase]; herein ‘hotspots' appear where oscillations harmonise [red: solidphase]; these hotspots expand and increase the overall temperature in the gas, now bounded between these hotspots. At the sharp edges where these expanding hotspots collide, there the squeezed gas starts to flow [blue: fluidphase].
It is comparable to the crystallisation of water into ice. Ice has a lower density, which increases the global water pressure within a closed system. When the expanding icevolumes spread out and clash into a Voronoipattern, the pressurised water between the iceblocks can no longer freeze. Think of how pressure makes iceskating possible.
B. When freezing happens randomly throughout the medium we get a Voronoinetwork of connected canals.
C. The novelty to this model is that these fluidedges can form a circuit of currents and rules, similar to those of Game of Life, emerge. Currents can block each other and cells die; or currents can merge and cells grow. Heat is transported through the network making some volumes expand while others shrink > the foam becomes dynamic:
D. Finally rolling waves emerge. For instance we can focus on the one red cell bottom right, that fluctuates in size but keeps its position, while it looks as if the ensemble of cells rotates. What is rotating is the change in size, not the bubbles themselves. What is being transported around, is the heat within the edges.
The mechanics are similar to normal waves, drive, by external forces; but in dynamic foam model the drive comes from the energy that runs internally through the circuit/edges between the bubbles, heating up some bubbles and making them expand while others cool down and shrink.
This blog is to present a Scifi Aether concept of how knots (Torus, Trefoil and fig. 8) can self emerge in a dynamic foam and interact.
I have come to realise that some posts on my blog are too far out and completely wrong; but I guess there are still some fun ideas that might work. Who knows!? Anyway, I'm trying to get a good simulation going, so it all becomes more clear.
Here is a clip of the fig. 8knot propelling upwards: movie (40Mb)