Lindenmayer2DSwift

Lindenmayer2DSwift is a swift framework that generates trees and other fractal structures using L-Systems.

Examples

Installation

The Lindenmayer2DSwift framework can be installed using the Swift Package Manager. In Xcode: File > Swift Packages > Add Package Dependency.. with URL: https://github.com/TateLiang/Lindenmayer2DSwift.git

Or alternatively:

• Add .package(url: "https://github.com/TateLiang/FortuneSwift.git", from: "1.0.3") to your Package.swift file's dependencies.
• Update your packages using $ swift package update.

Setup

1. Add package dependancy
2. Import import Lindenmayer2DSwift
3. Create a Turtle object

var turtle = Turtle()

4. Create a LSystem object

var lsystem = LSystem("X", [
    "F": "FF",
    "X": "F-[[X]+X]+F[+FX]-X"
])

Alternatively, use one of the preset trees of type Tree:

var tree = Library.tree3

5. Setup the turtle with custom values:

private func setupTurtle() {
    turtle.initialLength = 100
    turtle.initialPos = Turtle.Coordinate(canvas.bounds.midX, canvas.bounds.minY)
    turtle.initialAngle = .pi/2
    turtle.angle = .pi/6
    turtle.lengthFactor = 1.3
}

Alternatively, use the preset tree's values:

private func setupTurtle() {
    turtle.initialLength = 100
    turtle.initialPos = Turtle.Coordinate(canvas.bounds.midX, canvas.bounds.minY)
    turtle.angle = tree.angle
    turtle.lengthFactor = tree.lengthFactor
}

Processing Graph

Example of using Lindenmayer2DSwift:

var tree = Library.tree3
var turtle = Turtle(initialLength: 100)

private func setupTurtle() {
    turtle.initialPos = Turtle.Coordinate(canvas.bounds.midX, canvas.bounds.minY)
    turtle.angle = tree.angle
    turtle.lengthFactor = tree.lengthFactor
}
    
private func nextGeneration() {
    let string = tree.lsystem.advanceGeneration()
        
    turtle.run(string)
    turtle.initialLength *= 0.66
        
    let edges = turtle.edgeList.map { ($0.cgPoint, $1.cgPoint) }
    canvas.clear()
    canvas.drawEdges(at: edges, type: .thick)
}

Details

Lindenmayer2DSwift uses two main objects, LSystem and Turtle.

1. An LSystem object is defined by the axiom and rules:

LSystem("X", [
    "F": "FF",
    "X": "F-[[X]+X]+F[+FX]-X"
])

The generation can be advanced using either:

@discardableResult public mutating func advanceGeneration() -> String
public mutating func advanceGeneration(by generations: Int)

The following properties are provided for accessing the string:

public var strings: [String]
public var currentString: String { strings.last ?? "" }
public var generations: Int { strings.count }

2. The Turtle object can be run by using:

public mutating func run(_ string: String)

The following properties are provided for accessing the resulting graph:

public var root: Coordinate?
public var graph: [Coordinate: [Coordinate]] = [:]
public var edgeList: [(Coordinate, Coordinate)]

Sample Features

Coloring the edges differently depending on depth:

private func getEdgesByDepth(cutoff: Int) -> (near: [(CGPoint, CGPoint)], far: [(CGPoint, CGPoint)])? {
    guard let root = turtle.root else { return nil }
    let graph = turtle.graph
    var nearEdges: [(CGPoint, CGPoint)] = []
    var farEdges: [(CGPoint, CGPoint)] = []
        
    func dfs(node: Turtle.Coordinate, depth: Int) {
        if let nextNodes = graph[node] {
            if depth < cutoff {
                nextNodes.forEach {
                    nearEdges.append((node.cgPoint, $0.cgPoint))
                    dfs(node: $0, depth: depth+1)
                }
            }else {
                nextNodes.forEach {
                    farEdges.append((node.cgPoint, $0.cgPoint))
                    dfs(node: $0, depth: depth+1)
                }
            }
        }
    }
    dfs(node: root, depth: 0)
        
    return (near: nearEdges, far: farEdges)
}