Fern 3

This Fern is an L-System Fractal. It is generated by the L-System Algorithm with the following settings:

const fern3: Ruleset = {
    color: "#91fc8e",
    minIterations: 1,
    maxIterations: 5,
    axiom: "F",
    replace: {
      F: "F[+FF][-FF]F[-F][+F]F",
    },
    angle: 22.5,
    initLength: (ctx) => ctx.height * 0.9,
    initTranslation: (ctx) => [ctx.width / 2, ctx.height],
    divideFactor: 3,
};

Ferns are cool, and they are one of the original applications of L-Systems. There is a great book out there called ABOP - The Algorithmic Beauty of Plants. It covers how to model plants with algorithms in-depth and incidentally, and also has a long section on how to use L-Systems to generate grasses, bushes, trees and ferns.

This fractal, by its nature as an L-System, is also related to all the other L-System Fractals. A few you can check out: Hilbert Curve, Sierpinski Triangle, and the Lévy Curve.

You can also check out the other plant-like structures from the Fractal Garden – the Barnsley Fern and the Fractal Canopy.

The alphabet to instructions set used to draw this fractal are the same as for the other L-Systems:

const drawRules: Record<string, () => void> = {
    V: () => {},
    W: () => {},
    X: () => {},
    Y: () => {},
    Z: () => {},
    G: drawForward,
    F: drawForward,
    f: () => ctx.translate(0, -len),
    "+": () => ctx.rotate(angle * rotationDirection),
    "-": () => ctx.rotate(angle * -rotationDirection),
    "|": () => ctx.rotate(180),
    "[": () => ctx.push(),
    "]": () => ctx.pop(),
    "#": () => (ctx.lineWidth = weight += weightIncrement) ,
    "!": () => (ctx.lineWidth = weight -= weightIncrement) ,
    ">": () => (len *= scale),
    "<": () => (len /= scale),
    "&": () => (rotationDirection = -rotationDirection),
    "(": () => (angle += angleIncrement),
    ")": () => (angle -= angleIncrement),
};