Title: Estimating PI value from possibility of two random number being coprime and plotting them on graph.

  Author: PhoenixCreation(https://github.com/PhoenixCreation)

  Original sketch: https://editor.p5js.org/codingtrain/sketches/FiOG6uajS

  Referenace Video: https://youtu.be/EvS_a921dBo

  Issues: 

    1. This uses avearge as a final reusult which may not be the most efficient way.

    2. It runs for too long if your screen width is very big.(line 58)

    3. It uses JavaScript's inbuilt Math.random() method for random number generation.(line 42) Because of that the final results and progress varies each time you run the sketch.

*/

​

let coprimeCount = 0;

let total = 0;

let pies = []; // Array to store all calculated PI values from each iteration

​

function setup() {

  createCanvas(windowWidth, windowHeight);

  // creating a common graph layout

  background(0);

  strokeWeight(2);

  stroke(255)

  line(40, 0, 40, height); // Vertical graph line - Y axis

  line(40, height / 2, width, height / 2); // Horizontal graph line - X axis

  strokeWeight(1);

  fill(255);

  stroke(0)

  text("3.14", 0, height / 2) // Middle value

  stroke(255, 0, 0);

  strokeWeight(10)

  point(width - 125, 50) // Indiacators on top right corner

  stroke(255, 255, 0)

  point(width - 125, 75)

  noStroke()

  fill(255)

  text(" - Current PI", width - 115, 52.5)

  text(" - Average PI", width - 115, 77.5)

}

​

function draw() {

  // Calculate probability 500 random pairs for each iteration

  for (let n = 0; n < 500; n++) {

    var a = Math.floor(Math.random() * 1000000) + 1;

    var b = Math.floor(Math.random() * 1000000) + 1;

    total++;

    if (gcd(a, b) === 1) {

      coprimeCount++;

    }

  }

​

  var pie = sqrt(6 * total / coprimeCount); // Main equation

  pies.push(pie); // Add to the array to keep track of all

​

  var currentPI = pies.reduce((acc, current) => acc + current, 0) / pies.length; // Calculate the average of PI values in `pies` array

  stroke(0)

  text("current PI:" + nf(pie, 1, 6), 100, 10); // show the current PI value on top

  strokeWeight(3)

​

  // Continue calculating till you reach the right side of the canvas

  if (40 + pies.length / 2 < width - 40) {

    stroke(255, 255, 0);

    point(40 + pies.length / 2, height / 2 - ((currentPI - Math.PI) * 10000)); // draw a yellow point for average value

    stroke(255, 0, 0);

    point(40 + pies.length / 2, height / 2 - ((pie - Math.PI) * 10000)); // draw a red point for current PI value

  } else {

    // Now stop calculating and display results

    noStroke();

    textSize(24);

    text(`Original Value of PI: ${Math.PI}`, 100, 50)

    text(`Derived Value of PI: ${currentPI}`, 100, 100)

    text(`Difference between values: ${currentPI - Math.PI}`, 100, 150)

    noLoop(); // No more iterations of draw loop

  }

}

​

/* Function to calculate GCD from Euclid's Algorithm */

function gcd(a, b) {

  let r = a % b;

  if (r == 0) {

    return b;

  } else {

    return gcd(b, r);

  }

}