const a0 = 100000; // Bohr radius in pixels

let points = []; // to store points and their densities

let angle = 0; // rotation angle

​

function setup() {

  createCanvas(windowWidth, windowHeight);

  background(0);

  // Generate points and calculate probability densities

  for (let i = 0; i < numPoints; i++) {

    // Generate random spherical coordinates (r, theta, phi)

    let r = random(0, 200); // Random radius

    let theta = random(PI); // Polar angle (0 to PI)

    let phi = random(TWO_PI); // Azimuthal angle (0 to 2PI)

    // Convert spherical coordinates to Cartesian (x, y, z)

    let x = r * sin(theta) * cos(phi);

    let y = r * sin(theta) * sin(phi);

    let z = r * cos(theta);

    // Calculate probability density with spherical harmonics for l=1, m=0

    let probDensity = calculateProbabilityDensity(r, theta);

    // Store the point and its properties

    points.push({ x: x, y: y, z: z, probDensity: probDensity });

  }

}

​

function draw() {

  background(0); // reset the background each time

  // Apply a small rotation over time

  angle += 0.01;

  // Rotate the points in 3D space

  let rotatedPoints = points.map(p => {

    // Simple 3D rotation (around Y-axis)

    let newX = p.x * cos(angle) - p.z * sin(angle);

    let newZ = p.x * sin(angle) + p.z * cos(angle);

    return { x: newX, y: p.y, z: newZ, probDensity: p.probDensity };

  });

  // Sort the points based on the Z-coordinate (depth) to create the 3D effect

  rotatedPoints.sort((a, b) => a.z - b.z); // Draw farther points first

  // Find the min and max probability densities for brightness scaling

  let minDensity = min(rotatedPoints.map(p => p.probDensity));

  let maxDensity = max(rotatedPoints.map(p => p.probDensity));

  // Translate the origin to the center of the canvas

  translate(width / 2, height / 2);

  // Draw the points

  for (let p of rotatedPoints) {

    // Map the probability density to brightness

    let brightness = map(p.probDensity, minDensity, maxDensity, 0, 255);

    // Simulate perspective by scaling points based on depth (Z-coordinate)

    let perspective = map(p.z, -200, 200, 0.5, 1.5); // Change point size based on depth

    // Draw the point with shades of gray based on brightness (no transparency)

    noStroke();

    fill(brightness); // Set color based on brightness

    ellipse(p.x * perspective, p.y * perspective, 2 * perspective, 2 * perspective); // scale size based on depth

  }

}

​

// Probability density with spherical harmonics for l=1, m=0

function calculateProbabilityDensity(r, theta) {

  let radialPart = (1 / (PI * pow(a0, 3))) * exp(-r / a0); // Radial part

  let angularPart = cos(theta); // Spherical harmonic Y_1^0

  return pow(radialPart * angularPart, 2); // Probability density

}

​