The tweaks that SW included are pretty common to similar simulations:
1) the attraction-repulsion pair is typical of "boids" simulations, and also features in the Lennard-Jones forces acting in atoms (albeit with different powers on the decay rate);
2) making the force drop to zero for particle-particle distances approaching zero is effectively treating each particle as a "cloud" and not a singular point, it's called "regularization" in vortex particle methods and "Plummer softening" in gravitational methods; it's primary benefit is with SIMD and parallelization by removing the need for a (i != j) conditional; and
3) slow contraction (multiplying each particles' position by (1-epsilon)) is a technique used by generative digital artists to ensure that visual activity does not stray too far from a directed point.
The unique component of this simulation is the (computationally-efficient) dependence of a very small number (N=2 here) of neighbor particles. The typical O(N^2) that limits real-time simulations to 10k-50k particles becomes O(N).
Now that it's not late at night I can see a mistake: the primary benefit of regularization in nbody methods (self-influence being zero and not infinity) is stabilization of the dynamics. A close pass will not send one or both particles shooting out into the void with excessive energy.
The second advantage is removing the conditional in the inner loop.
I find it fascinating how (in the new version) the further away clumps stay separate, until something small from the larger swarm reaches them, then they all merge back to it
The tweaks that SW included are pretty common to similar simulations:
1) the attraction-repulsion pair is typical of "boids" simulations, and also features in the Lennard-Jones forces acting in atoms (albeit with different powers on the decay rate);
2) making the force drop to zero for particle-particle distances approaching zero is effectively treating each particle as a "cloud" and not a singular point, it's called "regularization" in vortex particle methods and "Plummer softening" in gravitational methods; it's primary benefit is with SIMD and parallelization by removing the need for a (i != j) conditional; and
3) slow contraction (multiplying each particles' position by (1-epsilon)) is a technique used by generative digital artists to ensure that visual activity does not stray too far from a directed point.
The unique component of this simulation is the (computationally-efficient) dependence of a very small number (N=2 here) of neighbor particles. The typical O(N^2) that limits real-time simulations to 10k-50k particles becomes O(N).
Now that it's not late at night I can see a mistake: the primary benefit of regularization in nbody methods (self-influence being zero and not infinity) is stabilization of the dynamics. A close pass will not send one or both particles shooting out into the void with excessive energy.
The second advantage is removing the conditional in the inner loop.
I find it fascinating how (in the new version) the further away clumps stay separate, until something small from the larger swarm reaches them, then they all merge back to it
What I like here is that the interesting behavior survives after throwing away one of the main assumptions behind boids: locality
Brings me back to when there were boids applets.
(2012)