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              html,
		body {
			font-family: 'Open Sans';
			margin: 0;
			padding: 0;
		}

		canvas {
			display: block;
		}

		.controls {
			left: 0;
			padding: 0.5rem;
			position: fixed;
			right: 0;
			top: 0;
		}

		.btn {
			-webkit-appearance: none;
			background-color: purple;
			border: none;
			border-radius: 0.25rem;
			color: #fff;
			cursor: pointer;
			font-size: 0.875rem;
			margin: 0 0.25rem;
			padding: 0.5rem 1rem;
		}

		.btn:hover {
			background-color: dark-purple;
		}

		.btn--danger {
			background-color: red;
		}

		.input {
			margin-bottom: 1rem;
		}

		.input__label {
			display: block;
		}

		.input__value {
			background-color: #fff;
			border: 2px solid #9d4db8;
			border-radius: 0.25rem;
			margin: 0 0.5rem;
			padding: 0.25rem 0.5rem;
		}
            
          
!
            
              const PIXEL_RATIO = (() => {
    const ctx = document.createElement("canvas").getContext("2d"),
        dpr = window.devicePixelRatio || 1,
        bsr = ctx.webkitBackingStorePixelRatio ||
              ctx.mozBackingStorePixelRatio ||
              ctx.msBackingStorePixelRatio ||
              ctx.oBackingStorePixelRatio ||
              ctx.backingStorePixelRatio || 1;

    return dpr / bsr;
})();

class NormalDistribution {
		  constructor(mean = 0, standardDeviation = 1) {
		    this.mean = mean;
		    this.standardDeviation = standardDeviation;
		  }

		  zScore(value) {
		    return (value - this.mean) / this.standardDeviation;
		  }

		  pdf(value) {
		    const dividend = Math.pow(Math.E, -Math.pow(value - this.mean, 2) / (2 * Math.pow(this.standardDeviation, 2)));
		    const divisor = this.standardDeviation * Math.sqrt(2 * Math.PI);
		    return dividend / divisor;
		  }

		  cdf(value) {
		    let zScore = this.zScore(value);
		    zScore = this._round(zScore, 2);

		    if (zScore === 0) {
		      return 0.5;
		    } else if (zScore <= -3.5) {
		      return 0;
		    } else if (zScore >= 3.5) {
		      return 1;
		    }

		    const zTable = NormalDistribution.zTable;
		    const absZScore = Math.abs(zScore);
		    const zRow = Math.floor(absZScore * 10) / 10;
		    const zCol = this._round(Math.round(absZScore * 100) % 10 / 100, 2);
		    const zColIndex = zTable.z.indexOf(zCol);
		    const absPercentile = zTable[zRow.toString()][zColIndex];

		    return zScore < 0 ? 1 - absPercentile : absPercentile;
		  }

		  probabilityBetween(value1, value2) {
		    return Math.abs(this.cdf(value1) - this.cdf(value2));
		  }

		  static get zTable() {
		    return {
		      "z"  :  [0     , 0.01  , 0.02  , 0.03  , 0.04,   0.05  , 0.06  , 0.07  , 0.08  , 0.09  ],
		      "0"  :  [0.5000, 0.5040, 0.5080, 0.5120, 0.5160, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359],
		      "0.1":  [0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753],
		      "0.2":  [0.5793, 0.5832, 0.5871, 0.5910, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141],
		      "0.3":  [0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.6480, 0.6517],
		      "0.4":  [0.6554, 0.6591, 0.6628, 0.6664, 0.6700, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879],
		      "0.5":  [0.6915, 0.6950, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.7190, 0.7224],
		      "0.6":  [0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549],
		      "0.7":  [0.7580, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852],
		      "0.8":  [0.7881, 0.7910, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133],
		      "0.9":  [0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.8340, 0.8365, 0.8389],
		      "1"  :  [0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621],
		      "1.1":  [0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.8770, 0.8790, 0.8810, 0.8830],
		      "1.2":  [0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.8980, 0.8997, 0.9015],
		      "1.3":  [0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177],
		      "1.4":  [0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319],
		      "1.5":  [0.9332, 0.9345, 0.9357, 0.9370, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441],
		      "1.6":  [0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545],
		      "1.7":  [0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633],
		      "1.8":  [0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706],
		      "1.9":  [0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.9750, 0.9756, 0.9761, 0.9767],
		      "2"  :  [0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817],
		      "2.1":  [0.9821, 0.9826, 0.9830, 0.9834, 0.9838, 0.9842, 0.9846, 0.9850, 0.9854, 0.9857],
		      "2.2":  [0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.9890],
		      "2.3":  [0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916],
		      "2.4":  [0.9918, 0.9920, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936],
		      "2.5":  [0.9938, 0.9940, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952],
		      "2.6":  [0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.9960, 0.9961, 0.9962, 0.9963, 0.9964],
		      "2.7":  [0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.9970, 0.9971, 0.9972, 0.9973, 0.9974],
		      "2.8":  [0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.9980, 0.9981],
		      "2.9":  [0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986],
		      "3"  :  [0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.9990, 0.9990],
		      "3.1":  [0.9990, 0.9991, 0.9991, 0.9991, 0.9992, 0.9992, 0.9992, 0.9992, 0.9993, 0.9993],
		      "3.2":  [0.9993, 0.9993, 0.9994, 0.9994, 0.9994, 0.9994, 0.9994, 0.9995, 0.9995, 0.9995],
		      "3.3":  [0.9995, 0.9995, 0.9995, 0.9996, 0.9996, 0.9996, 0.9996, 0.9996, 0.9996, 0.9997],
		      "3.4":  [0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9998]
		    }
		  }

		  /**
		   * Rounds a value to a specified amount of decimal places
		   * @param {number} value - the value to be rounded
		   * @param {number} decimalPlaces - the amount of decimal places to round to
		   * @return {number} the rounded number
		   */
		  _round(value, decimalPlaces) {
		    const factor = Math.pow(10, decimalPlaces);
		    return Math.round(value * factor) / factor;
		  }
		}

		const lerp = (a, b, p) => a + ((b - a) * p);
		const B1 = t => (1 - t) * (1 - t) * (1 - t); //        (1 - t)^3
		const B2 = t => 3 * t * (1 - t) * (1 - t);   // 3t   * (1 - t)^2
		const B3 = t => 3 * t * t * (1 - t);         // 3t^2 * (1 - t)
		const B4 = t => t * t * t;                   //  t^3
		const getBezierComponent = (f, p1, c1, c2, p2) => p1 * B1(f) + c1 * B2(f) + c2 * B3(f) + p2 * B4(f);

		class QuincunxBall {
			constructor(born, height) {
				this.born = born;
				this.lifeSpan = 5000;

				this.height = height;
				this.path = this.generatePath(height);

				this.rAF = false;

				this.position = {
					row: 0,
					column: 0,
				};
			}

			generatePath(height) {
				const path = [0];

				for (let i = 1; i < height; i++) {
					path.push(path[i - 1] + (Math.random() < 0.5 ? 0 : 1));
				}

				return path;
			}

			updatePosition(clock) {
				const {born, height, lifeSpan} = this;
				const age = clock - born;

				if (age > lifeSpan) {
					return false;
				}

				const row = (height - 1) / lifeSpan * age;
				const column = this.getColumn(row);

				this.position = {
					row,
					column,
				};

				return true;
			}

			getColumn(rowFactor) {
				const prevRow = Math.floor(rowFactor);
				const currentRow = Math.ceil(rowFactor);
				const prevColumn = this.path[prevRow];
				const currentColumn = this.path[currentRow];
				const sign = currentColumn - prevColumn;
				return prevColumn + (rowFactor % 1) * sign;
			}

			get finalColumn() {
				return this.path[this.path.length - 1];
			}

			destroy() {
				this.destroyed = true;
			}
		}

		class Quincunx {
			constructor(height = 9) {
				this.height = height;

				this.startTime = Date.now();
				this.time = Date.now();
				this.clock = 0;
				this.speed = 1;
				this.paused = false;

				this.reset();

				this.tick = this.tick.bind(this);

				this.tick();
			}

			tick() {
				const now = Date.now();
				const delta = now - this.time;
				this.time = now;

				if (!this.paused) {
					this.clock += delta * this.speed;
				}

				const newBalls = []

				this.balls.forEach(ball => {
					const isAlive = ball.updatePosition(this.clock);

					if (isAlive) {
						newBalls.push(ball);
					} else {
						this.counters[ball.finalColumn] += 1;
						this.balls.splice(this.balls.indexOf(ball), 1);
					}
				});

				window.requestAnimationFrame(this.tick);
			}

			generateCounters() {
				const counters = [];

				for (let i = 0; i < this.height; i++) {
					counters[i] = 0;
				}

				return counters;
			}

			drop() {
				if (!this.paused) {
					const ball = new QuincunxBall(this.clock, this.height);
					this.balls.push(ball);
				}
			}

			reset() {
				if (this.balls) {
					this.balls.forEach(ball => ball.destroy());
				}

				this.balls = [];
				this.counters = this.generateCounters();
			}

			pause() {
				this.paused = true;
			}

			resume() {
				this.paused = false;
			}

			setHeight(height) {
				this.height = height;
				this.reset();
				if (this.onHeightUpdate) {
					this.onHeightUpdate(this);
				}
			}

			onHeightUpdate(func) {
				this.onHeightUpdate = func;
			}

			get maxCounter() {
				return this.counters.reduce((a, b) => Math.max(a, b));
			}
		}

		class QuincunxRenderer {
			constructor(quincunx) {
				this.quincunx = quincunx;

				this.canvas = document.createElement('canvas');
				this.ctx    = this.canvas.getContext('2d');

				this.updateDimensions();
				this.addListeners();

				this.draw = this.draw.bind(this);

				document.body.appendChild(this.canvas);

				this.draw();
			}

			addListeners() {
				window.addEventListener('resize', () => {
					this.updateDimensions();
				});

				this.quincunx.onHeightUpdate(() => {
					this.updateDimensions();
				})
			}

			updateDimensions() {
				const {quincunx} = this;

				this.padding = 50;
				this.graphHeight = Math.max(window.innerHeight / 4, 100);
				this.minGap = 25;
        this.maxGap = 40;
				this.gap = Math.max(
					this.minGap,
					Math.min(
            this.maxGap,
						(window.innerHeight - this.graphHeight - this.padding * 2) / (quincunx.height - 1),
						(window.innerWidth - this.padding * 2) / (quincunx.height - 1)
					)
				);

				this.height = this.canvas.height = Math.max(
					window.innerHeight,
					(this.gap * (quincunx.height - 1)) + (this.padding * 2) + this.graphHeight,
				);
				
				this.width = window.innerWidth;
        
        this.canvas.width = this.width * PIXEL_RATIO;
        this.canvas.height = this.height * PIXEL_RATIO;
        this.canvas.style.width = this.width + "px";
        this.canvas.style.height = this.height + "px";
        this.ctx.setTransform(PIXEL_RATIO, 0, 0, PIXEL_RATIO, 0, 0);

				this.center = this.width / 2;
			}

			clear() {
				const {ctx, canvas} = this;
				ctx.save();
				ctx.setTransform(PIXEL_RATIO, 0, 0, PIXEL_RATIO, 0, 0);
				ctx.clearRect(0, 0, canvas.width, canvas.height);
				ctx.restore();
			}

			draw() {
				const {height, balls, counters, maxCounter} = this.quincunx;

				this.clear();
				this.renderGraph(counters, maxCounter, height);
				this.renderNormal(counters, maxCounter, height);
				this.renderNodes(height);
				this.renderBalls(balls);
				this.renderBuckets(height);
				this.renderCounters(counters, height);

				window.requestAnimationFrame(this.draw);
			}

			getScreenPos(row, column) {
				const {center, gap, padding} = this;
				return {
					x: center - (gap * row / 2) + (gap * column),
					y: row * gap + padding,
				};
			}

			renderNodes(height) {
				for (let row = 0; row < height - 1; row++) {
					for (let column = 0; column <= row; column++) {
						const {x, y} = this.getScreenPos(row, column);
						this.renderNode(x, y);
					}
				}
			}

			renderNode(x, y) {
				const {ctx} = this;

				ctx.beginPath();
				ctx.moveTo(x, y)
				ctx.lineTo(x - 5, y + 5);
				ctx.moveTo(x, y);
				ctx.lineTo(x + 5, y + 5);

				ctx.strokeStyle = '#777';
				ctx.lineWidth = 2;
				ctx.stroke();
			}

			renderBuckets(height) {
				const row = height - 1;
				for (let column = 0; column <= row; column++) {
					const {x, y} = this.getScreenPos(row, column);
					this.renderBucket(x, y);
				}
			}

			renderBucket(x, y) {
				const {ctx} = this;

				ctx.beginPath();
				ctx.arc(x, y - 10, 10, 0, Math.PI);

				ctx.fillStyle = '#8cb65a';
				ctx.lineWidth = 2;
				ctx.fill();
			}

			renderBalls(balls) {
				balls.forEach(ball => {
					const {row, column} = ball.position;

					const prevRow = Math.floor(row);
					const nextRow = Math.ceil(row);
					const rowFactor = row % 1;

					const prevColumn = Math.floor(column);
					const nextColumn = Math.ceil(column);
					const columnFactor = row % 1;

					const pos1 = this.getScreenPos(prevRow, prevColumn);
					const pos2 = this.getScreenPos(nextRow, nextColumn);

					const x = lerp(pos1.x, pos2.x, columnFactor);
					const y = lerp(pos1.y, pos2.y, getBezierComponent(rowFactor, 0, -0.2, 0, 1));

					this.renderBall(x, y);
				});
			}

			renderBall(x, y) {
				const {ctx} = this;

				ctx.beginPath();
				ctx.arc(x, y - 5, 4, 0, Math.PI * 2, false);
				ctx.fillStyle = '#9d4db8';
				ctx.fill();
			}

			renderCounters(counters, height) {
				const {ctx} = this;

				for (let i = 0; i < height; i++) {
					const {x, y} = this.getScreenPos(height - 1, i);
					ctx.strokeStyle = "#fff";
					ctx.lineWidth = 4;
					ctx.strokeText(counters[i], x, y + 20);

					ctx.fillStyle = '#000';
					ctx.textAlign = 'center';
					ctx.textBaseline = 'middle';
					ctx.font = '16px Arial';
					ctx.fillText(counters[i], x, y + 20);
				}
			}

			renderGraph(counters, maxCounter, height) {
				if (!maxCounter) {
					return false;
				}

				const {ctx, gap, graphHeight} = this;

				const scaleFactor = graphHeight / maxCounter;

				for (let i = 0; i < height; i++) {
					const {x} = this.getScreenPos(height - 1, i);
					const y = this.height - (counters[i] * scaleFactor);

					ctx.beginPath();
					ctx.fillStyle = 'rgba(76,164,245, 0.5)';
					ctx.fillRect(x - (gap / 2) + 1, y, gap - 2, this.height);

					ctx.beginPath();
					ctx.fillStyle = 'rgb(255,153,0)';
					ctx.arc(x, y, 3, 0, Math.PI * 2, false);
					ctx.fill();
				}
			}

			renderNormal(counters, maxCounter, height) {
				if (!maxCounter) {
					return false;
				}

				const {ctx, graphHeight} = this;

				const n = counters.reduce((a, b) => a + b);
				const mean = counters.reduce((sum, count, value) => sum + (value * count), 0) / n;
				const stdDev = Math.sqrt(counters.reduce((sum, count, value) => sum + (Math.pow(value - mean, 2) * count), 0) / n);

				const nd = new NormalDistribution(mean, stdDev);

				const scaleFactor = graphHeight / nd.pdf(nd.mean);

				const minPos = this.getScreenPos(height - 1, 0);
				const maxPos = this.getScreenPos(height - 1, height - 1);

				ctx.beginPath();

				ctx.moveTo(minPos.x, this.height - (nd.pdf(0) * scaleFactor));

				for (let i = 1; i < 50; i++) {
					const f = i / (50 - 1);
					const x = lerp(minPos.x, maxPos.x, f);
					const _y = (nd.pdf(lerp(0, height - 1, f)) * scaleFactor);
					const y = this.height - _y;
					ctx.lineTo(x, y);
				}

				ctx.strokeStyle = 'rgba(255,153,0,0.5)';
				ctx.lineWidth = 3;
				ctx.stroke();
			}
		}

		class QuincunxViewer {
			constructor() {
				this.quincunx = new Quincunx();
				this.quincunxRenderer = new QuincunxRenderer(this.quincunx);
				this.dropInterval = false;
				this.ballsPerSecond = 0;
				this.height = 9;
				this.speed = 1;

				this.lastBallDrop = false;

				this.setupControls();

				setInterval(this.tick.bind(this), 1000 / 60);
			}

			tick() {
				const delta = Date.now() - this.lastBallDrop;

				if (this.ballsPerSecond && this.quincunx.speed && delta > 1000 / this.ballsPerSecond / this.quincunx.speed) {
					this.quincunx.drop();
					this.lastBallDrop = Date.now();
				}

			}

			setupControls() {
				const controls = document.createElement('div');

				const frequencyInput = this.createRangeInput(
					'Drop frequency',
					this.onFrequencyInput.bind(this),
					0,
					5,
					0.1,
					this.ballsPerSecond,
					' b/s'
				);

				const heightInput = this.createRangeInput(
					'Levels',
					this.onHeightInput.bind(this),
					3,
					15,
					1,
					this.height
				);

				const speedInput = this.createRangeInput(
					'Speed',
					this.onSpeedInput.bind(this),
					0.1,
					5,
					0.1,
					this.speed,
					'x'
				);

				this.frequencyInput = frequencyInput;
				this.heightInput = heightInput;
				this.speedInput = speedInput;

				controls.appendChild(frequencyInput);
				controls.appendChild(heightInput);
				controls.appendChild(speedInput);

				controls.classList.add('controls');

				document.body.appendChild(controls);
			}

			createRangeInput(label, onInput, min = 0, max = 1, step = 0.1, value = 0, unit = '') {
				const wrapperNode = document.createElement('div');
				wrapperNode.classList.add('input');

				const labelNode = document.createElement('span');
				labelNode.classList.add('input__label');
				labelNode.innerHTML = label;

				const valueNode = document.createElement('span');
				valueNode.classList.add('input__value');
				valueNode.innerHTML = `${value}${unit}`;

				const inputNode = document.createElement('input');
				inputNode.classList.add('input__input', 'input__input--range');
				inputNode.setAttribute('type', 'range');
				inputNode.setAttribute('min', min);
				inputNode.setAttribute('max', max);
				inputNode.setAttribute('step', step);
				inputNode.setAttribute('value', value);
				inputNode.addEventListener('input', e => {
					onInput(e);
					valueNode.innerHTML = `${e.target.value}${unit}`;
				});

				wrapperNode.appendChild(labelNode);
				wrapperNode.appendChild(inputNode);
				wrapperNode.appendChild(valueNode);

				return wrapperNode;
			}

			onFrequencyInput(e) {
				this.ballsPerSecond = parseFloat(e.target.value);
			}

			onSpeedInput(e) {
				this.speed = parseFloat(e.target.value);
				this.quincunx.speed = this.speed;
			}

			onHeightInput(e) {
				this.height = parseInt(e.target.value, 10);
				this.quincunx.setHeight(this.height);
			}
		}

		const q = new QuincunxViewer();
            
          
!
999px
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Console