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Loss

Deterministic Context-Free L system implementation to draw fractal curves and axial plants. Made with love, for löve.

Introduction

  • L-Systems, short for Lindenmayer Systems, is a formal contextualization of naturally recurring constructs (ex. fractals and plants) under the light of formal language and automata theory.
  • Wikipedia introduces excellent examples on the topic: https://en.wikipedia.org/wiki/L-system
  • Implemented on version 0.9.1 of the LÖVE engine: https://love2d.org/
  • A Python implementation written in Turtle is also provided.

Example Renders

  • Checkout the Python script attached to this repository
  • Finished products will be coming soon!

Example L Systems by Author

  • Lightning
lightning = {}
lightning.path = "F" -- axiom
lightning.size = 15
lightning.angle = 25
lightning.rules = {}
lightning.rules["F"] = "FL[++F][-FF]"
lightning.rules["L"] = "L+F-F[L]"

ligntning = L:init(lightning.path,lightning.size,lightning.angle,lightning.rules,4)
  • A sample tree
tree = {}
tree.path = "Ff"
tree.maxorder = 4
tree.angle = 18
tree.rules = {}
tree.rules["F"] = "F[+[F]+[Bf]]-B"
tree.rules["B"] = "BFB[--B]+Bf"
-- call L:init() with these values in mind

Usage

  • git clone https://github.com/jryzkns/Loss.git
  • Copy and paste L.lua in the directory containing the target love script.
  • Append local L = require("L") in the love script where drawing will be called.
  • Call L:init() and initialize values inside love.load().
  • Call L:render() to draw the construct.
  • To introduce new symbols into the alphabet, write the following:
  • For straight line drawings, append L.extradrawchars = L.extradrawchars .. "new symbol"
  • For symbols with new functionalities, the code is as follows:
L:drawtable["new symbol"] = function()
    -function details
end

The Alphabet:

  • The built-in alphabet consists of the following symbols:
  • F,B,L,R,f,+,-,[,]
  • F,B,L,R all correspond to drawing a straight line. This semantic distinction is to use the formation rules.
  • f denotes travelling as if drawing a line without producing one.
  • +,- denote rotating the current reference point in the positive or negative direction. The extent of the rotation depends on the Angle variable.
  • [,] denotes the stack operation, push or pop, which operates on the current state of the reference point. This symbol is used to branch the behaviour.

Initialize Axiom, Rules, Iterations, Angle, And Linesize As Variables

  • Axiom is a string denoting the initial state of the system.
  • Rules are tabulated formation rules, initialized as an empty table. The key is the original symbol in the alphabet.
  • Formation rules are tabulated. If the rules states that a -> b, it is written, rules["a"] = "b".
  • Iterations are integers denoting how many iterations the system will evolve.
  • Angle is a value in degrees, which determines how much each call will turn the construct.
  • Linesize is the length of the line. Use a small test value as drawings may enlarge quickly!

Drawing

  • Call L:render() to start drawing. Set love.graphics.translate() to the starting point and call L:render().

A Side Note

  • Rendering L system constructs may exceed 100 calls, which is expensive if it is called on every flip.
  • Instead, draw to a canvas on initialization and draw the canvas on each flip.

jryzkns 2018