Sorting hexagons by size

This simulation uses the same set-up as seen in the video • A "molecular sieve": s... to sort particles according to their size, but with hexagons instead of squares. The set-up consists in three grids of obstacles with decreasing space between them, acting as particle sieves. The obstacles rotate and exert a tangential force on the particles, in order to decrease clogging of the sieves.
The conveyor belt effect results from the segments forming the belt exerting a tangential force on the polygons, in addition to the normal force. The tangential force is proportional to the difference between the tangential speed of the polygon and the speed of the belt.
To compute the force and torque of polygon j on polygon i, the code computes the distance of each vertex of polygon j to the faces of polygon i. If this distance is smaller than a threshold, the force increases linearly with a large spring constant. In addition, radial forces between the vertices of the polygons have been added, whenever a vertex of polygon j is not on a perpendicular to a face of polygon i. This is important, because otherwise triangles can approach each other from the vertices, and when one vertex moves sideways, it is suddenly strongly accelerated, causing numerical instability. A weak Lennard-Jones interaction between polygons has been added, as it seems to increase numerical stability.
Unlike in some previous videos involving interacting polygons, there is no thermostat in this simulation. Instead, friction forces (both linear and angular) have been added for numerical stability. In addition, the particles are subject to a gravitational force directed downwards.
The color of the polygons depends on their size.
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle.
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see en.wikipedia.o...
Render time: 50 minutes 6 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.co...
Music: "Crystal" by Vibe Tracks
Current version of the C code used to make these animations:
github.com/nil...
www.idpoisson....
Some outreach articles on mathematics:
images.math.cn...
(in French, some with a Spanish translation)
#molecular_dynamics #polygons #conveyor

[@idoben-yair429]

Lots of errors in the rightmost bin because the bigger hexagons end up forming a mini-conveyor that sends smaller ones that land on top, to the right. Maybe try some kind of tumbler-like setup and just keep the biggest objects inside the tumbler?

[@omegahaxors9-11]

The spinner's ability to antigrav causes a lot of mistakes, you'll see a small piece start to fall through but then it gets sucked back up. There's also the problem of bigger ones getting stuck between the spinners, but that design flaw is pretty accurate to the real world.

[@NilsBerglund]

Here is an improved design: ua-cam.com/video/-k5cxxNL2po/v-deo.html , in which a longer stretch of the sieves is used, and the discs spin sometimes faster, and sometimes more slowly. It may be possible to improve it even more, by making the centers of the discs move.

[@josephbolger]

Beautiful as ever

[@jac6255]

I can relate to some of these hexagons

[@zTown09]

Hexagons are the bestagons

[@ProSureString]

Hexa GONE

[@KitagumaIgen]

Nice as per expected, what was the biggest shift from the expected/designed target? To me it seems some of the light blue-green ends up in the three leftmost, maybe a more practical one than the sorting Galton designed?
It also reminded me of a line in an old song from home: '... sålla agnarna från vetet och föra var och en till hans rätta fålla'

[@NilsBerglund]

It seems that the main imperfection is that too many small hexagons land in the rightmost bin, due to clogging of the sieve. A forthcoming simulation will improve on that.