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 ...
Saturday, March 16, 2024
Physics of the Dynamic Foam
• 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.
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.
Tuesday, July 11, 2023
Markov-Chains in VoroX
For VoroX.jl BenoĆ®t build a system that is similar to Google’s PageRank that uses Markov Chains, where web-crawlers are released onto the internet to measure the connections and generate rating of sites.