Processing.js particle system
Interesting question,

there are few things that could be improved:


Read up on the revealing module pattern, it would be excellent to 


Reduce your usage of this
Make your class look like 1 piece of code


Something like this:

// main particle constructor class
function Particle(position) {

  var velocity = new PVector(random(-0.1, 0.1), random(-0.1, 0.1)),
      acceleration = new PVector(random(-0.01, 0.01), random(-0.01, 0.01)),
      lifeTime = 300,
      position = position.get();

  function update() {
    velocity.add(acceleration);
    position.add(velocity);
    lifeTime--;
  }

  function render() {
    strokeWeight(2);
    stroke(161, 153, 153, lifeTime);
    fill(140, 135, 140, lifeTime);
    ellipse(position.x,position.y, 15, 15);
  };

  return {
    update : update,
    render: render;
  }     
};


I obviously did not rewrite the whole thing, but you should catch my drift.
You keep using random(-0.1, 0.1), I would create a helper function for this
fill(140, 135, 140, lifeTime); &lt;- I would put a comment as to what color this should be
Do not use an if statement to determine true or false like you do :

// check if the particle is dead
Particle.prototype.particleDead = function() {
    if(this.lifeTime &gt; 0) {
        return false;
    } else {
        return true;
    }
};                


do this instead:

// check if the particle is dead
Particle.prototype.particleDead = function() {
    return this.lifeTime &gt; 0
};     


If you have time, read up on falsy values, you could also simply do return !this.lifetime
I am still playing with the code, I managed to fix the right hand side bounce with this:

if(this.position.x &gt;= 385) {
  this.acceleration.x = random(-0.02, -0.01);
  this.velocity.x = random(-0.1, -0.01);
}


In essence you have to solve both the acceleration and the velocity.


I have to wonder, how do you access random? I can only access random as a function under the instance of Processing.

It is too bad that the snippets will now allow for localStorage access, so I can only give you a link to jsbin with my refactored version and the source code here in case jsbin ever dies:

var canvas = document.getElementById('partikals'),
    pjs = new Processing(canvas),
    width = 400,
    height = 400,
    padding = 15;

function Particle2(position) {

    var velocity = new PVector(pjs.random(-0.1, 0.1), pjs.random(-0.1, 0.1)),
        acceleration = new PVector(pjs.random(-0.01, 0.01), pjs.random(-0.01, 0.01)),
        lifeTime = 300;

    position = position.get();

    function update() {
        velocity.add(acceleration);
        position.add(velocity);
        lifeTime--;
    }

    function render() {
        pjs.strokeWeight(2);
        //Each particle is grey
        pjs.stroke(161, 153, 153, lifeTime);
        pjs.fill(140, 135, 140, lifeTime);
        pjs.ellipse(position.x, position.y, 15, 15);
    }

    function isDead() {
        return !lifeTime;
    }

    //I wonder if just *= -1 would work
    function bounce() {
        if (position.x &gt; width - padding) {
            acceleration.x = -Math.abs(acceleration.x);
            velocity.x = -Math.abs(velocity.x);
        }
        if (position.x &lt; padding) {
            acceleration.x = Math.abs(acceleration.x);
            velocity.x = Math.abs(velocity.x);
        }
        if (position.y &gt; height - padding) {
            acceleration.y = -Math.abs(acceleration.y);
            velocity.y = -Math.abs(velocity.y);
        }
        if (position.y &lt; padding) {
            acceleration.y = Math.abs(acceleration.y);
            velocity.y = Math.abs(velocity.y);
        }
    }

    return {
        update: update,
        render: render,
        isDead: isDead,
        bounce: bounce
    };
}

// array containing particles
var particles = [];

pjs.setup = function() {
    pjs.size(width, height);
    pjs.frameRate(24);
};

pjs.draw = function() {

    //Clear by drawing the background and push a new particle
    pjs.background(11, 100, 209);
    particles.push(new Particle2(new PVector(pjs.mouseX, pjs.mouseY)));

    // iterate through particles and run their methods
    for (var p = particles.length - 1; p &gt;= 0; p--) {
        var particle = particles[p];
        particle.bounce();
        particle.update();
        particle.render();
        if (particle.isDead()) {
            particles.splice(p, 1);
        }
    }
};

pjs.setup();