Hexagon-hard-way.swift

// without turtle drawing a hexagon is math heavy and not trivial to modify

let numberOfSides: CGFloat = 6
let radiusOuterCircle: CGFloat = 30
let sideLength = radiusOuterCircle / 2
let theta = (CGFloat.pi * 2) / numberOfSides
let centerX = sideLength / 2
let centerY = sideLength / 2

let initialPoint = CGPoint(x: radiusOuterCircle * cos(2 * CGFloat.pi * 0/numberOfSides + theta) + centerX, y: radiusOuterCircle * sin(2 * CGFloat.pi * 0/numberOfSides + theta) + centerX)

let shapePath = UIBezierPath()
shapePath.move(to: initialPoint)
for i in 1...Int(numberOfSides) {
    shapePath.addLine(to: CGPoint(x: radiusOuterCircle * cos(2 * CGFloat.pi * CGFloat(i) / numberOfSides + theta) + centerX, y: radiusOuterCircle * sin(2 * CGFloat.pi * CGFloat(i) / numberOfSides + theta) + centerY))
}
shapePath.close()

Hexagon-turtle-way.swift

// with turtle the code is clear, composable and easy to modify
// but it’s less efficient for sure

let sideLength = square.width / 2

let turtle = UITurtlePath()
for _ in 0..<6 {
    turtle.scuttle(sideLength)
    turtle.turn(.pi / 3)
}

UITurtle.swift

/// “draw” shapes like moving a turtle around

class UITurtlePath {
    let path = UIBezierPath()

    init() {
        path.move(to: .zero)
    }

    func scuttle(_ amount: CGFloat) {
        path.addLine(to: .init(x: amount, y: 0))
        path.apply(CGAffineTransform(translationX: -amount, y: 0))
    }

    func hop(_ amount: CGFloat) {
        path.move(to: .init(x: amount, y: 0))
        path.apply(CGAffineTransform(translationX: -amount, y: 0))
    }

    func turn(_ radians: CGFloat) {
        path.apply(CGAffineTransform(rotationAngle: radians))
    }

    func close() {
        let pt = path.currentPoint
        path.addLine(to: .init(x: 0, y: 0))
        path.apply(CGAffineTransform(translationX: -pt.x, y: -pt.y))
        path.close()
    }
}