​

//This is a quick program to test out an idea about

//Newton polynomials and the Fibonacci sequence.

//Need to replace hard-coded values with vars, probably

//do more refactoring, etc.

​

//See Sketch Files for classes.

​

//VARIABLES

let cnv; //canvas

let win; //graph window (includes origin and scale for axes)

let points; //array of [x, y] pairs

let fibCurves = []; //array of interpolants (as curves)

let maxDegree = 1; //max degree of polynomial interpolants

​

//CUSTOM FUNCTIONS

function falling(x, k) {//kth falling power of x for integer k >=0

  let power = 1;

  for (let i = 0; i < k; i++) {

    power *= x - i;

  }

  return power;

}

​

function fib(n) {//nth term in Fibonacci sequence, n = 0, 1, 2...

  let f0 = 0;

  let f1 = 1;

  let fn = 0;

  if (n === 0) {

    fn = f0;

  }

  else if (n === 1) {

    fn = f1;

  }

  else {

    for (let k = 0; k < n - 1; k++) {

      fn = f0 + f1;

      f0 = f1;

      f1 = fn;

    }

  }  

  return fn;

}

​

function c(n) {//coefficient for interpolant

  return (-1) ** (n+1) * fib(n) / falling(n,n);

}

​

function p(x, n) {//interpolant for fib(0), ... ,fib(n), evaluated at x

  let poly = 0;

  for (let k = 0; k < n + 1; k++) {

    poly += c(k) * falling(x, k);

  }

  return poly;

}

​

function pFunc(n) {

  return x => p(x, n);

}

​

//return graph of f, starting from x = a, with given step size and count

function graph(f, a, stepCount, stepSize = 0.01) {

  let xi, yi;

  let pairs = [];

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

    xi = a + i * stepSize;

    yi = f(xi);

    pairs.push([xi, yi]);

  }

  return pairs;

}

​

//SETUP AND DRAW

function setup() {

  createCanvas(400, 400);

  plot = createGraphics(400, 400);

  win = createGraphWindow(20, 380, 50, 50);

}

​

function draw() {

  //make window

  plot.background(229, 255, 234);

  plot.stroke(0);

  plot.strokeWeight(1);

  win.axis('horizontal', plot);

  win.axis('vertical', plot);

  //make curves

  for (let n = 1; n <= maxDegree; n++) {

    points = graph(pFunc(n), 0, 800);

    fibCurves.push(createCurve(points, win));

  }

​

  plot.stroke(232, 51, 232);

  plot.strokeWeight(2);

  for (let i = 0; i < fibCurves.length; i++) {

    fibCurves[i].draw(plot);

  }

  //show plot

  image(plot, 0, 0);

  noLoop();

}

​

//INTERACTIVITY

function mousePressed() {

  maxDegree++;

  loop();

}