Koch snowflake is simple fractal. This fractal has fairly simple implementation. You just describe this recursive curve within recursive function. I will demonstrate this implementation in canvas element animation. You simply must love beauty of recursion implementations of any kind.

Code:
$(function() { var canvas = $("#mycanvas"); var context = canvas.get(0).getContext("2d"); context.fillStyle = "rgb(63, 169, 245)"; var x; var y; var angle; var level = 0; var animateKochSnowflake = function() { initialize(); save(); drawKochSnowflake(); flush(); level++; } //Create snowflake var drawKochSnowflake = function() { drawKochCurve(level, 150); angle += 120; drawKochCurve(level, 150); angle += 120; drawKochCurve(level, 150); }; //Recursive implementation var drawKochCurve = function(level, sideLength) { if (level < 1) { draw(sideLength); } else { drawKochCurve(level - 1, sideLength / 3); angle -= 45; drawKochCurve(level - 1, sideLength / 3); angle += 90; drawKochCurve(level - 1, sideLength / 3); angle -= 45; drawKochCurve(level - 1, sideLength / 3); } }; var draw = function(sideLength) { x += sideLength * Math.sin(angle * Math.PI/180); y -= sideLength * Math.cos(angle * Math.PI/180); context.lineTo(x, y); }; var initialize = function() { angle = 90; x = 170; y = 100; if (level > 5) { level = 0; } }; var save = function() { context.save(); context.beginPath(); context.clearRect(0, 0, 640, 480); context.translate(-level*10, 0); context.moveTo(x, y); }; var flush = function() { context.closePath(); context.fill(); context.restore(); }; var animate = function() { setInterval(animateKochSnowflake, 1000); }; animate(); });