Dynamic Foam Emerging from a Gas of Vibrating Particles

 The hypothesis is that the Dynamic Foam ...

... can emerge out of a gas of particles that have an attraction-repulsion force that's in-sync with their vibrational rhythm. 

The particles are spherical solitons going back and forth in size: 1 <---> 10

Their colour changes depending on their state:  Red (1) <---> Yellow (10)

They repel their neighbours while expanding (+) vs attract when contracting (-)

• Two neighbours with different timing can be contracting and attracting each other, but when one starts to expand again before the other, it will push that neighbour away -> chaos

• Two neighbours with the same timing are in harmony and bounce together -> spherical or linear group

• Random --> Voronoi

Linear formation and pulsing edges.

Spherical groups (credit to Rawdy):

The initial condition of the gas are particles with a random timing where some are expanding while others are contracting:

Think of this distribution model in Unity: 

https://github.com/przemyslawzaworski/Unity-Million-Spheres

https://x.com/pzaworski90/status/1641518112087367680 (Clip)

The idea is similar to these Spin Wheels: 

https://www.complexity-explorables.org/explorables/spin-wheels/

That is related to the Kuramoto model:

https://en.wikipedia.org/wiki/Kuramoto_model

https://youtu.be/FO3mYe8zkrM

But those particles synchronise, losing their fixed period, like metronomes placed on a rolling table:

https://en.wikipedia.org/wiki/File:Wesphysdemo_-_Synchronized_Metronomes.webm

While the ‘unique' thing of my model is that all the particles keep their fixed period, and as a result we 'might' get pulses in the edges of the Voronoi mesh.

Mockups in Midjourney

So long story short I haven't been able to make any significant leap forward to boost up the simulator to a large scale, so I've switched now to make an animation of the whole concept and made some mockups in Midjourney. To be continued ...

Physics of the Dynamic Foam

• In the beginning Space was a dense medium wherein vibrations appeared (Black -> white).

• The tiny vibrations are like gas-particles and Space became a dense misty cloud.

• At random points in this cloud the vibrations started to align and harmonise (blue).

• The expanding harmonious dots collided and form a pressure regions (red).

• A Voronoi pattern (foam) formed and the edges distributed the intense pressure.

• The pressure distribution can’t make <90°-turns and is cut-off at certain junctions.

• The strength of the currents in the edges affect the size of the cells: heating up vs. cooling down. Changing cells-sizes change consequentially the angles … and the mesh becomes dynamic.

• Stable fluctuations emerge that form strings that can turn into knots.

• Gradual pathways 'pinch' Space. 

It's like the idea of a Quantum Foam where particles pop into existence.

 Proposed by John Wheeler:

Flow regulated by Local Tree Network:

 The idea was to simplifying the Monte-Carlo-Marcov-Chain method to just a small Local Tree Network.

a. It’s still the same starting idea of junctions are open ( > 90°) or closed ( < 90°)

b. The simplification was to calculate the weight of each edge based on the number of connections with only small local percolation-tree, that should do:

c. The total weight of the edges of around a cell defines its pressure. 

d. The pressure changes between cells pushes them further or closer together.

Here’s a small test by Markus Rawdy who came up with this sim in Houdini:

The Fabric of Space

 The Fabric of Space is a Semi-Solid like a Foam .

Think of this Truchet FBM Lace toy by Fenix to get a feeling:

1. Currents in the edges.

2. When a junction is open current can pass.

3. Depending on the Force of the current a Bubble/Field can Expend or Shrink.

We can model this foam with a tri/tet mesh.

4. When there is a lot of current in ‘voronoi’ edge Y between A,B than the ‘delaunay’ edge between A-B contracts, otherwise it expands.

The diagram below shows the different parts of calculating the Gates, using a Graph Network to calculate the flow in all the Edges, and finally how the mesh contracts or expands at different parts.

Note, the idea is that by using a small local tree this whole Graph-Network is no longer necessary, see next Local Tree Network post. 

Processing Schemes & Diagrams II

 1. A tri/tet (Delaunay) mesh is the physical backbone.

2. Via the Barycenters we can check if ‘gates’ of it’s dual (virtual) Voronoi mesh are open or closed.

3. The results form a Graph Network.

4. With Monte Carlo Markov Chains (MCMC) walks we measure the currents.

5. The value of these currents defines the deformation of the dual tri/tet-edges.

6. Loop back to 2.

BTW when doing walks gates could be bridged and loops can emerge, therefore the need for 'Valves' that prevent U-turns in the Gates. Note, these diagrams are just a suggestion maybe there’s a better solution.

Little extra: Delaunay triangulation with Hilbert curve