For Voronoi-pattern networks we can look at two different approaches with similar results:
A. The first one is a solid medium that shrinks and loses volume and where packed matter is converted into particles that can move freely in and out the space that is emerges. Think of the cracks in a soil where water is vaporised, steam is produced, and canals are formed.
B. The second are compressed grains where force chains show up, increase the pressure and these tense grains start to crumble and form smaller particles; or think of a grinder where juices are squeezed out of fruits by compressing them.
In both cases we end up with fields and moving particles in between.
The graph below shows 'heated' fields that expand, overlapping each other and creating regions where solid matter is converted into lose particles; or look the other way around, as regions where fields cools down, retract, and generate empty space for steam to be released.
The lose particles can start line up and form currents, pathways, canals, edges between the fields. The amount of current passing the fields can make the fields shrink or expand; adding or taking away pressure. Condensation vs. Vaporisation.
Some flows will be able to line up and form closed circuits, forming steady formations. In 2D these structures are simple loops; in 3D these loops can form tubes (strings); at a next step these strings form again closed-circuits -> knots.
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One way to get this idea working is by using boids and fields. So recently I have developed with the help of The Guru a Particles - Fields Simulator in Processing.
A. The first one is a solid medium that shrinks and loses volume and where packed matter is converted into particles that can move freely in and out the space that is emerges. Think of the cracks in a soil where water is vaporised, steam is produced, and canals are formed.
B. The second are compressed grains where force chains show up, increase the pressure and these tense grains start to crumble and form smaller particles; or think of a grinder where juices are squeezed out of fruits by compressing them.
In both cases we end up with fields and moving particles in between.
The graph below shows 'heated' fields that expand, overlapping each other and creating regions where solid matter is converted into lose particles; or look the other way around, as regions where fields cools down, retract, and generate empty space for steam to be released.
The lose particles can start line up and form currents, pathways, canals, edges between the fields. The amount of current passing the fields can make the fields shrink or expand; adding or taking away pressure. Condensation vs. Vaporisation.
Some flows will be able to line up and form closed circuits, forming steady formations. In 2D these structures are simple loops; in 3D these loops can form tubes (strings); at a next step these strings form again closed-circuits -> knots.
-
One way to get this idea working is by using boids and fields. So recently I have developed with the help of The Guru a Particles - Fields Simulator in Processing.
Here is a link to download a Mac OS X version (turn down your security settings)
and/or use the Processing files that are included:
and/or use the Processing files that are included:
The cool thing about this method is that it resembles Maxwell's model for:
'A Mechanical dynamical theory of the electromagnetic field'
http://rsta.royalsocietypublishing.org/content/373/2039/20140473
The next step for this concept is to add a detector that computes a local density field of the particle flow within each field, causing them to shrink or expand accordingly. So the Fields can start to tumble over each other as currents of particle are being pushed around … getting the curling effect that Maxwell mentioned in his work.
A change in field-size due to the flowing currents, will change the 'normally' steady pathways. Steady horizontal paths == are bend into diagonal ones X redirecting flow while cutting it off at some intersections, having some fields shrink rapidly while others can quickly expand.
So the medium with particles and fields is like an elastic 'bouncy' foam.
