It's been a fairly busy few months at my "proper" job, so my recreational Houdini tinkering has taken a bit of a back seat. However, when I saw my Swarm Chemistry hero, Hiroki Sayama tweeting a link to How a life-like system emerges from a simple particle motion law, I thought I'd dust off Houdini to see if I could implement this model in VEX.

The paper discusses a simple particle system, named Primordial Particle Systems (PPS), that leads to life-like structures through morphogenesis. Each particle in the system is defined by its position and heading and, with each step in the simulation, alters its heading based on the PPS rule and moves forward at a defined speed. The heading is updated based on the number of neighbors to the particle's left and right. 

The project set up is super simple: 



Inside a geometry node, I create a grid, and randomly scatter 19,000 points across it. An attribute wrangle node assigns a random value to @angle:
@angle = $PI * 2 * rand(@ptnum); 
The real magic happens inside another attribute wrangle inside the solver.

In a nutshell, my VEX code iterates over each point's neighbors and sums the neighbor count to its left and right. To figure out the chirality, I use some simple trigonometry to rotate the vector defined by the current particle and the neighbor by the current particle's angle, then calculate the angle of the rotated vector. 
while(pciterate(pointCloud)) {

    vector otherPosition;
    pcimport(pointCloud, "P", otherPosition);

    vector2 offsetPosition = set(otherPosition.x - @P.x, otherPosition.z - @P.z);
    float xx = offsetPosition.x * cos(-@angle) - offsetPosition.y * sin(-@angle);
    float yy = offsetPosition.x * sin(-@angle) + offsetPosition.y * cos(-@angle);
    
    float otherAngle = atan2(yy, xx); 

    if (otherAngle >= 0) {
        L++;
    } 
    else {
        R++;
    }   
}
After iterating over the nearby particles, I update the angle based on the PPS rule:
float N = float(L + R);
@angle += alpha + beta * N * sign(R - L);
...and, finally, I can update the particle's position based on its angle and speed:
vector velocity = set(cos(@angle) * @speed, 0.0, sin(@angle) * @speed);  
@P += velocity ;
Not quite finally, because to make things pretty, I update the color using the number of neighbors to control hue:
@Cd = hsvtorgb(N / maxParticles, 1.0, 1.0); 
Easy!

Solitons Emerging from Tweaked Model



I couldn't help tinkering with the published PPS math by making the speed a function of the number of local neighbors:
@speed = 1.5 * (N / maxParticles);
In the video above, alpha is 182° and beta is -13°.

References

Schmickl, T. et al. How a life-like system emerges from a simple particle motion law. Sci. Rep. 6, 37969; doi: 10.1038/srep37969 (2016).


5

View comments

Loading