SOURCE

var linkLength = 10, initCount = 12;
var createEvery = 10; // milliseconds
var growTime = 3000; // ms too
var accuracy = 3; // Repeat the "constraints solving" part this many times per frame (reduce if slow)
var repulsionRadius = 15, repulsionForce = 50; // Fun with 100,200 (keep radius > linkLength to avoid overlappings)
var outRad = 100;
var growFactor = 2, backFactor = 3; // >= 1
var showFps = false;

var c = document.getElementById('c'),
	ctx = c.getContext('2d');

// Background
(function(){
	var bg = document.createElement('canvas'),
		ctx = bg.getContext('2d');
	bg.width = 1; bg.height = 7;
	var gradient = ctx.createLinearGradient(0,0,0,bg.height);
	var colors = ['#8c58b7', '#8352ab'];
	gradient.addColorStop(0, colors[0]);
	gradient.addColorStop(.5,colors[1]);
	gradient.addColorStop(1, colors[0]);
	ctx.fillStyle = gradient;
	ctx.fillRect(0,0,bg.width,bg.height);
	c.style.background = 'url('+bg.toDataURL()+')';
})();

(window.onresize = function() {
	c.width = c.offsetWidth;
	c.height = c.offsetHeight;
	ctx.strokeStyle = 'rgba(255,255,255,1)';
	ctx.lineWidth = 2.2;
	ctx.lineJoin = 'bevel';
	ctx.lineCap = 'round';
	// Glow (can be slow)
	ctx.shadowColor = 'rgba(255,255,255,1)';
	ctx.shadowBlur = 15;
	ctx.textBaseline = 'top';
})();

function comeCloser(n, goal, factor, limit)
{
	return (limit && Math.abs(goal - n) < limit) ? goal : n + (goal - n) / (factor || 10);
}
function Point(x, y, init)
{
	this._x = this.x = x;
	this._y = this.y = y;
}
function Link(p1, p2, length)
{
	this.p1 = p1;
	this.p2 = p2;
	this._length = this.length = this.goal = length;
	p1.next = p2;
}
var points = [], links = [];
var init = function()
{
	points = []; links = [];
	for(var i = 0; i < initCount; i++)
	{
		points.push(new Point(0, linkLength * (i - initCount * .5 + .5)));
		if(i)
			links.push(new Link(points[i-1], points[i], linkLength));
	}
};
init();

function draw()
{
	ctx.clearRect(0,0,c.width,c.height);
	ctx.save();
	ctx.translate(c.width * .5, c.height * .5);
	ctx.beginPath();
	var p = points[0];
	ctx.moveTo(p.x, p.y);
	while((p = p.next))
		ctx.lineTo(p.x, p.y);
	ctx.stroke();
	ctx.restore();
}

function normVector(v, d)
{
	if(d === undefined)
		d = Math.sqrt(v[0] * v[0] + v[1] * v[1]);
	if(d < 1e-6)
	{
		var a = Math.random() * 2 * Math.PI;
		return [Math.cos(a), Math.sin(a)];
	}
	return [v[0] / d, v[1] / d];
}

var counter = 0, total = 0;
var sqOutRad = outRad * outRad, sqRepRad = repulsionRadius * repulsionRadius;
var retracting = false;
function compute(dt)
{
	if(dt > 100) dt = 100;
	if(retracting)
	{
		var done = true;
		for(var i = points.length; i--;)
		{
			var p = points[i], src = p.source || p;
			p.x = comeCloser(p.x, src._x, backFactor, .001);
			p.y = comeCloser(p.y, src._y, backFactor, .001);
			if(p.x != src._x || p.y != src._y) done = false;
		}
		if(done)
		{
			counter = total = 0;
			init();
			retracting = false;
		}
		return;
	}
	total += dt;
	if(total > growTime)
		retracting = true;
	counter += dt;
	while(counter > createEvery) // Insert new point
	{
		var link = links[~~(Math.random() * (links.length - 1) + 1)];
		var p = link.p1;
		var np = new Point(p.x + Math.random() * .001, p.y + Math.random() * .001);
		np.source = p.source || p;
		link.p1 = np;
		np.next = link.p2;
		var nl = new Link(p, np, 0);
		//nl.goal = Math.random() * 4 + 8;
		nl.goal = linkLength;
		points.push(np);
		links.push(nl);
		counter -= createEvery;
	}
	for(var i = links.length; i--;)
		links[i].length = comeCloser(links[i].length, links[i].goal, growFactor);
	for(var s = 0; s < accuracy; s++)
	{
		for(var i = 0, l = points.length; i < l; i++)
		{
			var a = points[i];
			var sqcd = a.x * a.x + a.y * a.y;
			if(sqcd > sqOutRad) // Force the thing to stay inside a disc
			{
				var cd = Math.sqrt(sqcd);
				var f = cd - outRad;
				if(f < 0) f = 0;
				f = 1 - f * .1 / cd;
				a.x *= f;
				a.y *= f;
			}
			for(var j = i + 1; j < l; j++) // Point-point repulsion
			{
				var b = points[j];
				if(a.next == b || b.next == a) continue;
				var d = [b.x - a.x, b.y - a.y], sqd = d[0] * d[0] + d[1] * d[1];
				if(sqd > sqRepRad) continue;
				d = normVector(d, Math.sqrt(sqd));
				var f = repulsionForce / (sqd + 1);
				a.x -= f * d[0];
				a.y -= f * d[1];
				b.x += f * d[0];
				b.y += f * d[1];
			}
		}
		for(var i = links.length; i--;) // Force links distance
		{
			var link = links[i], from = link.p1, to = link.p2;
			var dist = [to.x - from.x, to.y - from.y], l = Math.sqrt(dist[0] * dist[0] + dist[1] * dist[1]);
			dist = normVector(dist, l);
			var delta = (l - link.length) * .5;
			from.x += delta * dist[0];
			from.y += delta * dist[1];
			to.x -= delta * dist[0];
			to.y -= delta * dist[1];
		}
	}
}

var pt, fps = 0, frameCount = 0, prevFps, fpsInterval = 100;
function loop(t)
{
	if(!pt) pt = t;
	var dt = t - pt;
	pt = t;
	compute(dt);
	draw();
	if(showFps)
	{
		if(!prevFps) prevFps = t;
		frameCount++;
		if(t - prevFps >= fpsInterval)
		{
			fps = 1000 * frameCount / (t - prevFps);
			frameCount = 0;
			prevFps = t;
		}
		ctx.fillText(fps, 0, 0);
	}
	requestAnimationFrame(loop);
}
requestAnimationFrame(loop);

<canvas id="c"></canvas>

#c
{
	position: absolute;
	left: 0; top: 0;
	width: 100%; height: 100%;
}