Coding Assignment – Week #3

For this week’s assignment, I was inspired by the Planar Choreographies, especially this simulation: https://personalpages.manchester.ac.uk/staff/j.montaldi/Choreographies/

The concept of planar symmetry was utterly new to me, however, I found it really fascinating (and a bit addictive even). Here is my own attempt and my sketch:

Apparently, what turned out of the sketch is a system of particles with mutual gravitational attraction. This type of system is chaotic and sensitive to initial conditions, that is why I set all the parameters manually in the code (the positions and velocities of movers and attractors). Even small changes in the starting positions or velocities of the particles lead to significant differences in the long-term behavior of the system. That is how I got to learn that the sensitivity to initial conditions is a characteristic of chaotic systems.

What seemed really interesting to me is that in the beginning the system appears organized, or in more official terms – symmetrical. However, after a while, the system becomes imbalanced and progresses to develop more chaotic qualities. The reason for that is the design of the system. As time progresses, the particles continuously influence each other due to gravity. Small disruptions in their positions or velocities accumulate over time and lead to significant deviations from the initial state.

An additional upgrade that I added was the force of repulsion. Here is how I implemented it in code:

for (let other of movers) {
      // Checking if the current 'mover' (outer loop) is different from the       current 'other' (inner loop)
      if (mover !== other) {
        // Calculating the vector pointing from 'other' to 'mover' and its           distance
        let repulsion = p5.Vector.sub(mover.pos, other.pos); 
        let distance = repulsion.mag();
        // Defining a minimum distance for repulsion and a maximum repulsion           force
        let minDistance = 50; 
        let maxForce = 0.5; 

        // Apply repulsion force if particles are too close
        if (distance < minDistance) {
          repulsion.setMag(map(distance, 0, minDistance, 0, maxForce));
          mover.applyForce(repulsion);
        }
        mover.attract(other);

To calculate the repulsion force, I subtracted the position of ‘other’ from the ‘mover’ to obtain a vector pointing from ‘other’ to ‘mover’, and then  computed the distance between them. I then set a minimum distance that determines when repulsion should occur and a maximum repulsion force to control the strength of the repulsion effect.If the distance between ‘mover’ and ‘other’ falls below the specified minimum distance,  I mapped the repulsion force by scaling the ‘repulsion’ vector based on the distance and the maximum force. This ensures that particles t experience a repulsive force based on the distance at which they encounter each other. Finally, I applied this repulsion force to the ‘mover. This force counteracts the gravitational attraction, preventing particles from getting too close and adding a repulsive behavior to the simulation.

For further improvements, I would be interested to experiment with more movers and attractors placed in various positions. It would be exciting to attempt to create a more stable choreography, make it appear 3D or perhaps to add some additional visual effects, like color changes or to play around with connecting lines.