L Systems

L System

L-systems (Lindenmayer-systems, named after Aristid Lindenmayer, 1925-1989), allow definition of complex shapes through the use of iteration. They use a mathematical language in which an initial string of characters is matched against rules which are evaluated repeatedly, and the results are used to generate geometry. The result of each evaluation becomes the basis for the next iteration of geometry, giving the illusion of growth.

 Output Screenshots:

Code:

let x, y;
let currentangle = 0;
let step = 20;
let angle = 90;

let thestring = 'A';
let numloops = 5;
let therules = [];
therules[0] = ['A', '-BF+AFA+FB-'];
therules[1] = ['B', '+AF-BFB-FA+'];

let whereinstring = 0;

function setup() {
  createCanvas(710, 400);
  background(255);
  stroke(0, 0, 0, 255);

  x = 0;
  y = height-1;

  // COMPUTE THE L-SYSTEM
  for (let i = 0; i < numloops; i++) {
    thestring = lindenmayer(thestring);
  }
}

function draw() {

 
  drawIt(thestring[whereinstring]);


  whereinstring++;
  if (whereinstring > thestring.length-1) whereinstring = 0;

}


function lindenmayer(s) {
  let outputstring = '';

 
  for (let i = 0; i < s.length; i++) {
    let ismatch = 0;
    for (let j = 0; j < therules.length; j++) {
      if (s[i] == therules[j][0])  {
        outputstring += therules[j][1];
        ismatch = 1;
        break;
      }
    }
   
    if (ismatch == 0) outputstring+= s[i];
  }

  return outputstring;
}

function drawIt(k) {

  if (k=='F') {
   
    let x1 = x + step*cos(radians(currentangle));
    let y1 = y + step*sin(radians(currentangle));
    line(x, y, x1, y1);

   
    x = x1;
    y = y1;
  } else if (k == '+') {
    currentangle += angle;
  } else if (k == '-') {
    currentangle -= angle;
  }


  let r = random(128, 255);
  let g = random(0, 192);
  let b = random(0, 50);
  let a = random(50, 100);

  let radius = 0;
  radius += random(0, 15);
  radius += random(0, 15);
  radius += random(0, 15);
  radius = radius / 3;

  fill(r, g, b, a);
  ellipse(x, y, radius, radius);
}