Pi + 5 Day (Monte Carlo method)

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Hello folks!

It is never to late for Pi!

// Monte Carlo Pi
// glv
// 2026-03-19

// Reference:
// https://en.wikipedia.org/wiki/Monte_Carlo_method

// The exact math:
// Area of circle: PI*r*r
// Area of square: 2*r * 2*r = 4*r*r
// Area of circle/Area of square = (PI*r*r)/(4*r*r) = PI/4
// PI = 4*(PI*r*r)/(4*r*r)

// The code does not use geometric area directly.
// It uses the ratio of random points in those regions
// to statistically estimate pi.

int numPoints = 5000;

float r = 200;
float r2, rr;
float w2, h2;

int inCircle = 0;
int counter = 0;

void setup()
  {
  size(500, 550, P2D);
  background(0);
  
  rr = r*r;
  r2 = r*2;
  
  w2 = width/2;
  h2 = height/2;

  resetRun();
  }

void resetRun()
  {
 push();
  translate(w2, h2);
  
  background(0);
  strokeWeight(2);
  stroke(128);
  fill(0);
  
  rectMode(CENTER);
  rect(0, 0, r2, r2);

  ellipseMode(CENTER);
  circle(0, 0, r2);
 pop();

  inCircle = 0;
  counter = 0;
  }

void draw()
  {    
  if (counter >= numPoints)
    {
    resetRun();
    return;
  }

// Plot

  float x = random(-r, r);
  float y = random(-r, r);

  float rCol = 128 + random(128);
  if (x*x + y*y < rr)
    {
    stroke(0, rCol, rCol);  
    inCircle++;
    } 
  else
    stroke(255, 0, 0);
    
  strokeWeight(3);
  point(x+w2, y+h2);
  counter++;
  
// HUD Overlay (Heads Up Display)

  textAlign(LEFT, CENTER);
  textSize(36);  
  
  fill(0);  // Change to 128 to see where it is
  noStroke();
  rectMode(CORNER);
  rect(0, 0, width, 60);
  rect(0, height - 60, width, 60);
 
  float mcPi = 4.0*inCircle/counter;
  
  fill(255, 255, 0);
  String s1 =  "Monte Carlo π : " + "  " + nfs(mcPi, 1, 5);
  float xt = textWidth(s1);

  text(s1, (width-xt)/2, 30);    
  String s2 =  "Total Points: " + "  " + str(counter);
  float xt2 = textWidth(s2);
  text(s2, (width-xt2)/2, height-35);  
  
  //println(counter, inCircle, mcPi);
  }
  
void mousePressed()
  {
  resetRun();
  }

image
image502×582 28.3 KB

References:

:)

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