群動

群動指一大群個體一齊移動，並且喺途大致守三條規則：
分隔－唔好撞到隔離嘅其他個體；
順向－將自己方向對準周圍其他個體嘅平均；
凝聚－將自己置於周圍其他個體嘅平均嘅位置。

實驗表明咗，上述嘅法則能夠令到一大群個體就算冇中央指揮都做到有組織性嘅移動；群動演算法喺動物學上可以攞嚟模擬雀鳥同魚等嘅大規模群體移動。

例子碼 

Flock flock;

void setup() {
  size(640, 360);
  flock = new Flock();
  // Add an initial set of boids into the system
  for (int i = 0; i < 150; i++) {
    flock.addBoid(new Boid(width/2,height/2));
  }
}

void draw() {
  background(50);
  flock.run();
}

// Add a new boid into the System
void mousePressed() {
  flock.addBoid(new Boid(mouseX,mouseY));
}

// The Flock (a list of Boid objects)
class Flock {
  ArrayList<Boid> boids; // An ArrayList for all the boids
  Flock() {
    boids = new ArrayList<Boid>(); // Initialize the ArrayList
  }
  void run() {
    for (Boid b : boids) {
      b.run(boids);  // Passing the entire list of boids to each boid individually
    }
  }
  void addBoid(Boid b) {
    boids.add(b);
  }
}

// The Boid class
class Boid {
  PVector position;
  PVector velocity;
  PVector acceleration;
  float r;
  float maxforce;    // Maximum steering force
  float maxspeed;    // Maximum speed

Boid(float x, float y) {
    acceleration = new PVector(0, 0);
    // This is a new PVector method not yet implemented in JS
    // velocity = PVector.random2D();

// Leaving the code temporarily this way so that this example runs in JS
    float angle = random(TWO_PI);
    velocity = new PVector(cos(angle), sin(angle));
    position = new PVector(x, y);
    r = 2.0;
    maxspeed = 2;
    maxforce = 0.03;
  }

void run(ArrayList<Boid> boids) {
    flock(boids);
    update();
    borders();
    render();
  }

void applyForce(PVector force) {
    // We could add mass here if we want A = F / M
    acceleration.add(force);
  }

// We accumulate a new acceleration each time based on three rules
  void flock(ArrayList<Boid> boids) {
    PVector sep = separate(boids);   // Separation
    PVector ali = align(boids);      // Alignment
    PVector coh = cohesion(boids);   // Cohesion
    // Arbitrarily weight these forces
    sep.mult(1.5);
    ali.mult(1.0);
    coh.mult(1.0);
    // Add the force vectors to acceleration
    applyForce(sep);
    applyForce(ali);
    applyForce(coh);
  }
  // Method to update position
  void update() {
    // Update velocity
    velocity.add(acceleration);
    // Limit speed
    velocity.limit(maxspeed);
    position.add(velocity);
    // Reset accelertion to 0 each cycle
    acceleration.mult(0);
  }
  // A method that calculates and applies a steering force towards a target
  // STEER = DESIRED MINUS VELOCITY
  PVector seek(PVector target) {
    PVector desired = PVector.sub(target, position);  // A vector pointing from the position to the target
    // Scale to maximum speed
    desired.normalize();
    desired.mult(maxspeed);
    // Above two lines of code below could be condensed with new PVector setMag() method
    // Not using this method until Processing.js catches up
    // desired.setMag(maxspeed);
    // Steering = Desired minus Velocity
    PVector steer = PVector.sub(desired, velocity);
    steer.limit(maxforce);  // Limit to maximum steering force
    return steer;
  }

void render() {
    // Draw a triangle rotated in the direction of velocity
    float theta = velocity.heading2D() + radians(90);
    // heading2D() above is now heading() but leaving old syntax until Processing.js catches up
    fill(200, 100);
    stroke(255);
    pushMatrix();
    translate(position.x, position.y);
    rotate(theta);
    beginShape(TRIANGLES);
    vertex(0, -r*2);
    vertex(-r, r*2);
    vertex(r, r*2);
    endShape();
    popMatrix();
  }
  // Wraparound
  void borders() {
    if (position.x < -r) position.x = width+r;
    if (position.y < -r) position.y = height+r;
    if (position.x > width+r) position.x = -r;
    if (position.y > height+r) position.y = -r;
  }
  // Separation
  // Method checks for nearby boids and steers away
  PVector separate (ArrayList<Boid> boids) {
    float desiredseparation = 25.0f;
    PVector steer = new PVector(0, 0, 0);
    int count = 0;
    // For every boid in the system, check if it's too close
    for (Boid other : boids) {
      float d = PVector.dist(position, other.position);
      // If the distance is greater than 0 and less than an arbitrary amount (0 when you are yourself)
      if ((d > 0) && (d < desiredseparation)) {
        // Calculate vector pointing away from neighbor
        PVector diff = PVector.sub(position, other.position);
        diff.normalize();
        diff.div(d);        // Weight by distance
        steer.add(diff);
        count++;            // Keep track of how many
      }
    }
    // Average -- divide by how many
    if (count > 0) {
      steer.div((float)count);
    }
    // As long as the vector is greater than 0
    if (steer.mag() > 0) {
      // First two lines of code below could be condensed with new PVector setMag() method
      // Not using this method until Processing.js catches up
      // steer.setMag(maxspeed);

// Implement Reynolds: Steering = Desired - Velocity
      steer.normalize();
      steer.mult(maxspeed);
      steer.sub(velocity);
      steer.limit(maxforce);
    }
    return steer;
  }
  // Alignment
  // For every nearby boid in the system, calculate the average velocity
  PVector align (ArrayList<Boid> boids) {
    float neighbordist = 50;
    PVector sum = new PVector(0, 0);
    int count = 0;
    for (Boid other : boids) {
      float d = PVector.dist(position, other.position);
      if ((d > 0) && (d < neighbordist)) {
        sum.add(other.velocity);
        count++;
      }
    }
    if (count > 0) {
      sum.div((float)count);
      // First two lines of code below could be condensed with new PVector setMag() method
      // Not using this method until Processing.js catches up
      // sum.setMag(maxspeed);

// Implement Reynolds: Steering = Desired - Velocity
      sum.normalize();
      sum.mult(maxspeed);
      PVector steer = PVector.sub(sum, velocity);
      steer.limit(maxforce);
      return steer;
    } 
    else {
      return new PVector(0, 0);
    }
  }
  // Cohesion
  // For the average position (i.e. center) of all nearby boids, calculate steering vector towards that position
  PVector cohesion (ArrayList<Boid> boids) {
    float neighbordist = 50;
    PVector sum = new PVector(0, 0);   // Start with empty vector to accumulate all positions
    int count = 0;
    for (Boid other : boids) {
      float d = PVector.dist(position, other.position);
      if ((d > 0) && (d < neighbordist)) {
        sum.add(other.position); // Add position
        count++;
      }
    }
    if (count > 0) {
      sum.div(count);
      return seek(sum);  // Steer towards the position
    } 
    else {
      return new PVector(0, 0);
    }
  }
}

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