// Asssignemnt 1; Levy Flight X 3D space and color modification 

let positions = [];

let stepSize;

let yRotation = 0; // Y-axis rotation angle

​

function setup() {

  // Create a canvas

  createCanvas(400, 400, WEBGL); // Use the WEBGL renderer for 3D

​

  // Initialize the starting position within the canvas boundaries

  positions.push(createVector(random(-width / 2, width / 2), random(-height / 2, height / 2), random(-100, 100)));

​

  // Initialize the initial step size within a range to control speed

  stepSize = random(5, 20); // Adjust this range for different speeds

}

​

function draw() {

  background(220);

​

  // Apply 3D transformations

  translate(0, 0, mouseY); // Move the scene along the z-axis based on mouseY

  rotateY(yRotation); // Rotate around the y-axis

  yRotation += 0.01; // Increment the rotation angle for animation

​

  // Levy Flight: Generate random angles and magnitudes for the step in 3D

  let theta = random(TWO_PI); // Random angle around the x-y plane

  let phi = random(TWO_PI);   // Random angle around the x-z plane

  let r = random(1, 100);     // Random magnitude for the step

​

  // Calculate the new position in 3D space based on the angles and magnitude

  let newX = positions[positions.length - 1].x + cos(theta) * sin(phi) * stepSize;

  let newY = positions[positions.length - 1].y + sin(theta) * sin(phi) * stepSize;

  let newZ = positions[positions.length - 1].z + cos(phi) * stepSize;

​

  // Constrain the new position to stay within the canvas boundaries

  newX = constrain(newX, -width / 2, width / 2);

  newY = constrain(newY, -height / 2, height / 2);

  newZ = constrain(newZ, -100, 100); // Adjust the constraints for the z-axis

​

  // Update the position to the new position

  positions.push(createVector(newX, newY, newZ));

​

  // Draw lines connecting previous positions with varying RGB color

  stroke(map(newX, -width / 2, width / 2, 0, 255), map(newY, -height / 2, height / 2, 0, 255), map(newZ, -100, 100, 0, 255), 50); // Color based on position

  strokeWeight(1);

  for (let i = 1; i < positions.length; i++) {

    let prevPos = positions[i - 1];

    let currentPos = positions[i];

    line(prevPos.x, prevPos.y, prevPos.z, currentPos.x, currentPos.y, currentPos.z);

  }

​

  // Draw a point at the current position with RGB color

  stroke(map(newX, -width / 2, width / 2, 0, 255), map(newY, -height / 2, height / 2, 0, 255), map(newZ, -100, 100, 0, 255));

  strokeWeight(2);

  point(positions[positions.length - 1].x, positions[positions.length - 1].y, positions[positions.length - 1].z);

​

  // Occasionally change the step size with a probability of 10%

  if (random(1) < 0.1) {

    stepSize = random(5, 20); // Change step size to a new random value for variation

  }

}

​