A Swift implementation of the Collatz Conjecture, with full playground markup.

Collatz.playground

import UIKit

//: # The Collatz Conjecture
//: *This process will eventually reach the number 1, regardless of which positive integer is chosen initially. (See [Wikipedia](https://en.wikipedia.org/wiki/Collatz_conjecture).)* 
//: \
//: Create an array to capture the sequence of numbers returned by the `collatz` function.
var sequence = [Int]()

//: The `collatz(start:Int, initial:Bool) -> [Int]` function takes an integer and will perform the following:
//:- if the integer (`n`) is 1, it will return an `[Int]` array.
//:- if the integer (`n`) is even, it will divide `n` by 2, append `n` to `[Int]`, and run the function again with `n`.
//:- if the integer (`n`) is odd, it will perform multiply `n` by 3 and add 1, add `n` to `[Int]`, and run the function again with `n`.
//: - note: If `initial` == `true`, the `start` variable is added to `[Int]`.
func collatz(start:Int, initial:Bool = true) -> [Int] {
    var n = start
    if initial == true {
        sequence.append(start)
    }
    
    if n == 1 {
        return sequence
    }
    
    else if n % 2 == 0 {
        n /= 2
        sequence.append(n)
    }
    
    else {
        n = (3 * n) + 1
        sequence.append(n)
    }
    
    return collatz(start: n, initial: false)
}

/*: 
 - example: The basic use case for the `collatz` function.\
 \
The array in this example contains all values for the sequence starting at n = 27. var x = n is used to show the graph.
 */
for n in collatz(start: 27, initial: true) {
    var x = n
}