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HTML

              
                <div class="wrapper">
  <div class="content">
    <h1>Calculating PI</h1>
    <p>Dividing the number of raindrops that hit the circle and the square and multiplying the result by 4 gives an approximation to PI. This approximation gets better with time.</p>
    <p>This demo is directly inspired by this real-life experiment: <a href="https://www.reddit.com/r/dataisbeautiful/comments/84esm6/pi_as_calculated_by_raindrops_falling_on_square/" target="_blank">See it on Reddit</a></p>
    <p>Number of raindrop impacts so far: <code id="impact-number">0</code></p>
    <p>Current approximation: <code id="approximation-value">N/A</code></p>
    <p>Closest approximation: <code id="closest-approximation">N/A</code> (at impact #: <code id="closest-approximation-at"></code>)</p>
    <p>Actual PI: <code id="actual-pi"></code></p>
  </div>
  <canvas id="zdog-canvas" width="400" height="300"></canvas>
</div>
<canvas id="chart-canvas" width="800" height="300"></canvas>
              
            
!

CSS

              
                html, body {
  min-height: 100vh;
}

body {
  display: flex;
  justify-content: center;
  align-items: center;
  flex-direction: column;
  font: 400 normal 16px/1.4 helvetica, sans-serif;
}

canvas, img {
  vertical-align: center;
  margin: 0;
}

.wrapper {
  display: flex;
}

.content {
  padding: 1em;

  h1 {
    font-size: 2.5em;
    font-weight: bold;
    margin: 0 0 1rem;
  }

  p {
    margin: 0 0 1em;
  }

  code {
    font-family: "Operator Mono", menlo, monaco, monospace;
    background: #fd5;
    padding: .125em .25em;
    border-radius: 3px;
  }
}
              
            
!

JS

              
                const { TAU } = Zdog
const { PI, sqrt, abs, pow, round } = Math

const random = (max = 1, min = 0) => {
  return min + Math.random() * (max - min)
}

const maybeNegative = (number) => {
  if (random() >= .5) {
    return -number
  }
  return number
}

const randomPos = (values) => {
  return {
    x: maybeNegative(random(400)),
    y: maybeNegative(random(400)),
    z: maybeNegative(random(400)),
    ...values
  }
}

const times = (howMany, what) => {
  return [...Array(howMany).keys()].map(what)
}

const rainIntensity = 15
const plateSize = 120
const circlePos = { x: -90, z: 0 }
const squarePos =  { x: 90, z: 0 }

let isSpinning = true
const drawing = new Zdog.Illustration({
  element: '#zdog-canvas',
  rotate: { y: TAU/16, x: TAU/-10 },
  dragRotate: true,
  onDragStart() {
    isSpinning = false
  }
})

const plates = new Zdog.Group({
  addTo: drawing,
  translate: { y: 80 }
})

new Zdog.Ellipse({
  addTo: plates,
  diameter: plateSize,
  stroke: 10,
  color: 'hotpink',
  fill: true,
  translate: circlePos,
  rotate: { x: Zdog.TAU/4 }
})

new Zdog.Rect({
  addTo: plates,
  width: plateSize,
  height: plateSize,
  stroke: 10,
  color: 'mediumspringgreen',
  fill: true,
  cornerRadius: 0,
  translate: squarePos,
  rotate: { x: Zdog.TAU/4 }
})

const createDrop = () => {
  const rgba = [
    round(random(31, 63)),
    round(random(63, 100)),
    round(random(200, 255)),
    random(0.3, 0.6)
  ].join(',')
  return new Zdog.Shape({
    addTo: drawing,
    stroke: 3,
    color: `rgba(${rgba})`,
    translate: randomPos({ y: -400 }),
    path: [
      { y: -10 },
      { y: 10 }
    ]
  })
}

const collides = (plate, { translate: { x, z }}, { isCircle } = {}) => {
  if (isCircle) {
    const xDiff = abs(x - plate.x)
    const zDiff = abs(z - plate.z)
    const distance = sqrt( pow(xDiff, 2) + pow(zDiff, 2) )
    return distance <= plateSize / 2
  }
  const xMin = plate.x - plateSize / 2
  const xMax = plate.x + plateSize / 2
  const xIntersects =  x >= xMin && x <= xMax
  
  const zMin = plate.z - plateSize / 2
  const zMax = plate.z + plateSize / 2
  const zIntersects = z >= zMin && z <= zMax
  
  return xIntersects && zIntersects
}

const getApproximation = () => {
  return Counts.circle/Counts.square * 4
}

const getImpactCount = () => {
  return Counts.circle + Counts.square
}

let drops = []
const Counts = {
  circle: 0,
  square: 0
}
const loop = () => {
  drops.push(...times(rainIntensity, createDrop))
  drops.forEach((drop, index) => {
    if (drop.translate.y <= 300) {
      drop.translate.y += 10
    } else {
      if (collides(circlePos, drop, {isCircle: true})) {
        Counts.circle++
      }
      if (collides(squarePos, drop)) {
        Counts.square++
      }
      drop.remove()
      drops.splice(index, 1)
    }
  })
  if (isSpinning) {
    drawing.rotate.y += .005
  }
  drawing.updateRenderGraph()
  requestAnimationFrame(loop)
}

requestAnimationFrame(loop)

const chartConfig = {
  type: 'line',
  data: {
    labels: [],
    datasets: [{
      label: 'Approximation',
      fill: false,
      backgroundColor: 'blue',
      borderColor: 'blue',
      borderWidth: 1,
      pointRadius: 2,
      pointHoverRadius: 3,
      data: [],
    }]
  },
  options: {
    responsive: true,
    scales: {
      xAxes: [{
        display: true,
        scaleLabel: {
          display: true,
          labelString: 'Number of raindrop impacts'
        }
      }],
      yAxes: [{
        display: true,
        scaleLabel: {
          display: true,
          labelString: 'Values'
        }
      }]
    },
    annotation: {
      annotations: [{
        drawTime: 'beforeDatasetsDraw',
        id: 'hline',
        type: 'line',
        mode: 'horizontal',
        scaleID: 'y-axis-0',
        value: PI,
        borderColor: 'red',
        borderWidth: 1,
        label: {
          backgroundColor: 'transparent',
          fontColor: 'red',
          content: 'Actual PI',
          position: 'left',
          yAdjust: -6,
          xAdjust: -5,
          enabled: true,
        }
      }]
    }
  },
}

const chartCanvas = document.getElementById('chart-canvas')
const chartCtx = chartCanvas.getContext('2d')
const myChart = new Chart(chartCtx, chartConfig)

let chartLoopFrame = 0
let closestApproximation = 0
let closestApproximationAt = 0
let refreshRate = 50

const chartLoop = () => {
  const ratio = getApproximation()
  const impacts = getImpactCount()
  if (abs(PI - ratio) < abs(PI - closestApproximation)) {
    closestApproximation = ratio
    closestApproximationAt = impacts
  }
  if (ratio && !(chartLoopFrame++ % refreshRate)) {
    chartConfig.data.labels.push(impacts)
    chartConfig.data.datasets[0].data.push(ratio)
    if (chartConfig.data.datasets[0].data.length > 50) {
      refreshRate = 60
    }
    if (chartConfig.data.datasets[0].data.length > 100) {
      refreshRate = 70
      chartConfig.options.animation = {
        duration: 0
      }
      chartConfig.options.hover = {
        animationDuration: 0
      }
      chartConfig.options.elements = {
        line: {
          tension: 0
        }
      }
    }
    if (chartConfig.data.datasets[0].data.length > 300) {
      refreshRate = 80
      chartConfig.options.showLines = false 
      chartConfig.data.datasets[0].pointRadius = 1
      chartConfig.data.datasets[0].pointHoverRadius = 2
    }
    myChart.update(chartConfig)
  }
  requestAnimationFrame(chartLoop)
}

requestAnimationFrame(chartLoop)

const approximationView = document.getElementById('approximation-value')
const closestApproximationView = document.getElementById('closest-approximation')
const closestApproximationAtView = document.getElementById('closest-approximation-at')
const impactCountView = document.getElementById('impact-number')

const domLoop = () => {
  const value = getApproximation()
  const impacts = getImpactCount()
  approximationView.innerText = value
  closestApproximationView.innerText = closestApproximation
  closestApproximationAtView.innerText = closestApproximationAt
  impactCountView.innerText = impacts
  requestAnimationFrame(domLoop)
}

requestAnimationFrame(domLoop)

const actualPI = document.getElementById('actual-pi')
actualPI.innerText = Math.PI
              
            
!
999px

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