// implementation of Lorenz's attractor
// more: https://en.wikipedia.org/wiki/Lorenz_attractor
// x axis: x position
// y axis: z position

// starting positions
let x = 0.01;
let y = 0;
let z = 0;

// dynamical variables for lorenz attractors
let a = 10;
let b = 28;
let c = 8.0 / 3.0;

// store previous positions so to draw fluid lines
let px = 0;
let py = 0;
let pz = 0;

function setup() {
  createCanvas(400, 400);
  background(255);
}

function draw() {
  translate(200, 100);

  let dt = 0.01;
  let dx = a * (y - x) * dt;
  let dy = (x * (b - z) - y) * dt;
  let dz = (x * y - c * z) * dt;
  x = x + dx;
  y = y + dy;
  z = z + dz;
  scale(5);
  strokeCap(SQUARE);
  stroke(z * 2, 40);

  if (frameCount > 0) {
    line(x, z, px, pz);
  }

  px = x;
  py = y;
  pz = z;
}

// implementation of Lorenz Attractor
// more: https://en.wikipedia.org/wiki/Lorenz_attractor
// each plot corresponds to the x, y, and z positions

// starting positions
let x = 0.01;
let y = 0;
let z = 0;

// dynamical variables for lorenz attractors
let a = 10;
let b = 28;
let c = 8.0 / 3.0;

let points = []; // store points

function setup() {
  createCanvas(400, 250);
}

function draw() {
  background(255);
  // iterate Lorenz equation
  let dt = 0.01;
  let dx = a * (y - x) * dt;
  let dy = (x * (b - z) - y) * dt;
  let dz = (x * y - c * z) * dt;
  x = x + dx;
  y = y + dy;
  z = z + dz;

  // add new point to array of points, forget oldest one to scroll
  points.push(createVector(x, y, z));
  if (points.length > width) {
    points.shift(); // remove oldest value
  }

  // move down, draw x value
  translate(0, 50);
  for (let i = 1; i < points.length; i++) {
    line(i - 1, points[i - 1].x, i, points[i].x);
  }

  // move down, draw y value
  translate(0, 50);
  for (let i = 1; i < points.length; i++) {
    line(i - 1, points[i - 1].y, i, points[i].y);
  }

  // move down, draw z value
  translate(0, 50);
  for (let i = 1; i < points.length; i++) {
    line(i - 1, points[i - 1].z, i, points[i].z);
  }
}

// implementation of period doubling bifurcation.
// X axis designates increasing rate of growth (r)
// Y axis designates population (x)
// more: https://en.wikipedia.org/wiki/Period-doubling_bifurcation

let x = 0.5; // current population, between 0 and 1
let r = 2; // growth rate, between 0 and 4 usually

function setup() {
  createCanvas(400, 400);
  background(255);
  stroke(0, 50);
}

function draw() {
  // run simulation as long as r is less than 4
  if (r < 4.0) {
    x = 0.5; // reset pop

    // Iterate to let the system settle (transient behavior)
    for (let i = 0; i < 100; i++) {
      x = r * x * (1 - x);
    }

    // Plot the final 100 points to show the stable orbit
    for (let i = 0; i < 100; i++) {
      x = r * x * (1 - x);
      let px = map(r, 2, 4, 0, width);
      let py = map(x, 0, 1, height, 0); // display population with lower values at the bottom of canvas
      point(px, py);
    }
    r += 0.002; // add to r
  } else {
    noLoop(); // stop sketch at r = 4;
  }
}

// implementation of Sierzpinki's triangle
// more: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle

let a, b, c; // triangle vertices
let vertices = [];
let pos; // current position
function setup() {
  createCanvas(400, 400);
  a = createVector(20, 20);
  b = createVector(380, 20);
  c = createVector(180, 380);
  vertices = [a, b, c];

  let inside = false;
  while (!inside) {
    pos = createVector(random(width), random(height));
    inside = checkInside();
  }

  strokeWeight(0.5);
  background(255);
  stroke(0);
}

function draw() {
  let v = random(vertices); // get a random vertex of the three
  //console.log(v);
  pos = p5.Vector.lerp(pos, v, 0.5);

  point(pos);
}

function checkInside() {
  //calculate edge vectors
  let ab = p5.Vector.sub(a, b);
  let bc = p5.Vector.sub(b, c);
  let ca = p5.Vector.sub(c, a);
  // calculate point to vertex vectors
  let ap = p5.Vector.sub(pos, a);
  let bp = p5.Vector.sub(pos, b);
  let cp = p5.Vector.sub(pos, c);
  // calc cross products
  let cp1 = p5.Vector.cross(ab, ap);
  let cp2 = p5.Vector.cross(bc, bp);
  let cp3 = p5.Vector.cross(ca, cp);

  return (
    (cp1.z <= 0 && cp2.z <= 0 && cp3.z <= 0) ||
    (cp1.z >= 0 && cp2.z >= 0 && cp3.z >= 0)
  );
}