lsystem-ts

A simple TypeScript implementation of an Lindenmayer System.

This is not feature complete. If you want a more feature rich library, you might want to look at lindenmayer.

Install

For browser, use lsystem.browser.js from the build directory.

Usage

The LSystem class accepts an object as argument that needs the following:

• axiom: the starting string
• productions: the production rules for the system
• functions: a set of javascript production functions associated with each character in the system's alphabet

The library is agnostic to the drawing system. In the examples listed here I am using canvas. For example, here's how you might generate a Hilbert Curve:

var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");

// translate to center of canvas
ctx.translate(canvas.width / 1.5, canvas.height / 1.5);
ctx.rotate(Math.PI / 2);
ctx.lineWidth = 1;

var hilbert = new LSystem({
  axiom: "A",
  productions: {
    A: "lBfrAfArfBl",
    B: "rAflBfBlfAr"
  },
  functions: {
    f: () => {
      ctx.beginPath();
      ctx.moveTo(0, 0);
      ctx.lineTo(0, canvas.width / Math.pow(2, hilbert.generations + 1));
      ctx.stroke();
      ctx.translate(0, canvas.width / Math.pow(2, hilbert.generations + 1));
    },
    l: () => ctx.rotate((Math.PI / 180) * 90),
    r: () => ctx.rotate((Math.PI / 180) * -90)
  }
});

hilbert.produce(6);

Examples

Hilbert Curve

code

var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");

// translate to center of canvas
ctx.translate(canvas.width / 1.5, canvas.height / 1.5);
ctx.rotate(Math.PI / 2);
ctx.lineWidth = 1;

var hilbert = new LSystem({
  axiom: "A",
  productions: {
    A: "lBfrAfArfBl",
    B: "rAflBfBlfAr"
  },
  functions: {
    f: () => {
      ctx.beginPath();
      ctx.moveTo(0, 0);
      ctx.lineTo(0, canvas.width / Math.pow(2, hilbert.generations + 1));
      ctx.stroke();
      ctx.translate(0, canvas.width / Math.pow(2, hilbert.generations + 1));
    },
    l: () => ctx.rotate((Math.PI / 180) * 90),
    r: () => ctx.rotate((Math.PI / 180) * -90)
  }
});

hilbert.produce(6);

Sierpinski Arrowhead Curve

code

let canvas = document.getElementById('canvas');
let ctx = canvas.getContext('2d');

// translate to center of canvas
ctx.translate(canvas.width / 4, canvas.height / 2);
ctx.rotate((Math.PI / 180) * 270);
ctx.lineWidth = 0;

var sierpinskiArrowHead = new LSystem({
    axiom: 'A',
    productions: {
        A: 'B-A-B',
        B: 'A+B+A',
    },
    functions: {
        A: () => {
            ctx.beginPath();
            ctx.moveTo(0, 0);
            ctx.lineTo(
                0,
                canvas.height / Math.pow(2, sierpinskiArrowHead.generations + 1),
            );
            ctx.stroke();
            ctx.translate(
                0,
                canvas.height / Math.pow(2, sierpinskiArrowHead.generations + 1),
            );
            ctx.closePath();
        },
        B: () => {
            ctx.beginPath();
            ctx.moveTo(0, 0);
            ctx.lineTo(
                0,
                canvas.height / Math.pow(2, sierpinskiArrowHead.generations + 1),
            );
            ctx.stroke();
            ctx.translate(
                0,
                canvas.height / Math.pow(2, sierpinskiArrowHead.generations + 1),
            );
            ctx.closePath();
        },
        '+': () => {
            ctx.rotate((Math.PI / 180) * -60);
        },
        '-': () => {
            ctx.rotate((Math.PI / 180) * 60);
        },
    },
});

sierpinskiArrowHead.produce(10);

Dragon Curve

code

var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");

// translate to center of canvas
ctx.translate(canvas.width / 3, canvas.height / 2);
ctx.rotate(Math.PI);

var dragon = new LSystem({
  axiom: "FX",
  productions: {
    X: "X+YF+",
    Y: "-FX-Y"
  },
  functions: {
    F: () => {
      ctx.beginPath();
      ctx.moveTo(0, 0);
      ctx.lineTo(0, canvas.height / (dragon.generations + 100));
      ctx.stroke();
      ctx.translate(0, canvas.height / (dragon.generations + 100));
      ctx.closePath();
    },
    "+": () => {
      ctx.rotate((Math.PI / 180) * +90);
    },
    "-": () => {
      ctx.rotate((Math.PI / 180) * -90);
    }
  }
});

dragon.produce(10);

Fractal Plant

code

var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");

// translate to center of canvas
ctx.translate(canvas.width / 3, canvas.height);
ctx.scale(-1, 1);
ctx.rotate((Math.PI / 180) * 150);
ctx.lineWidth = 0.3;

var plant = new LSystem({
  axiom: "X",
  productions: {
    X: "F+[[X]-X]-F[-FX]+X",
    F: "FF"
  },
  functions: {
    F: () => {
      ctx.beginPath();
      ctx.moveTo(0, 0);
      ctx.lineTo(0, canvas.width / Math.pow(2, plant.generations + 2));
      ctx.stroke();
      ctx.translate(0, canvas.width / Math.pow(2, plant.generations + 2));
    },
    "+": () => {
      ctx.rotate((Math.PI / 180) * 25);
    },
    "-": () => {
      ctx.rotate((Math.PI / 180) * -25);
    },
    "[": () => {
      ctx.save();
    },
    "]": () => {
      ctx.restore();
    }
  }
});

plant.produce(10);