fractal.swift

import Foundation

typealias Matrix = [[Bool]]
typealias Vector = [Bool]

func fractal(n: Int) {
    let width = 63
    let height = width / 2 + 1
    
    var matrix = createMatrix(w: width, h: height)
    
    if n == 0 {
        printing(matrix)
        return
    }
    
    matrix = drawPartition(matrix: matrix, slide: Node(x: 0, y: 0, w: width, h: height))
    
    if n == 1 {
        printing(matrix)
        return
    }
    
    let slides = split(matrix: matrix, level: n - 1)
    
    for i in slides {
        for slide in i {
            matrix = drawPartition(matrix: matrix, slide: slide)
        }
    }
    
    printing(matrix)
}

// ready
func createMatrix(w: Int, h: Int) -> Matrix {
    var mat: Matrix = []
    var i = 1
    for _ in 0..<h {
        var row = Vector.init(repeating: false, count: w)
        row = switching(list: row, value: i)
        i += 2
        mat.append(row)
    }
    
    return mat
}

//
func drawPartition(matrix: Matrix, slide: Node) -> Matrix {
    var m = matrix
    let w = slide.w
    let h = slide.h
    
    let x = slide.x + (w / 2 / 2) + 1
    let y = slide.y + h / 2
    
    var n = 1
    
    for i in y..<y+h/2 {
        m[i] = switchingInSlice(row: m[i], a: x, b: x + w / 2 - 1, value: w / 2 + 1 - n)
        n += 2
    }
    
    return m
}

// ready
func switchingInSlice(row: Vector, a: Int, b: Int, value: Int) -> Vector {
    let slice = Array(row[a...b])
    let new = switching(list: slice, value: value)
    
    var result = row
    
    var j = 0
    (a...b).forEach { i in
        result[i] = new[j]
        j += 1
    }
    
    return result
}

// ready
func switching(list: Vector, value: Int) -> Vector {
    var l = list
    let center = list.count / 2
    
    l[center] = !l[center]
    
    let times = (value - 1) / 2
    
    if times == 0 {
        return l
    }
    
    (1...times).forEach { i in
        l[center + i] = !l[center + i]
        l[center - i] = !l[center - i]
    }
    
    return l
}

// ready
func split(matrix: Matrix, level: Int) -> [[Node]] {
    return split(matrix: matrix, acc: [], level: level)
}

// ready
struct Node {
    var x: Int
    var y: Int
    var w: Int
    var h: Int
}

// ready
func split(matrix: Matrix, acc: [[Node]], level: Int) -> [[Node]] {
    if level == acc.count {
        return acc
    }
    
    if acc.isEmpty {
        let w = matrix[0].count / 2
        let h = matrix.count / 2
        let top = Node(x: matrix[0].count / 2 / 2 + 1, y: 0, w: w, h: h)
        let left = Node(x: 0, y: matrix.count / 2, w: w, h: h)
        let right = Node(x: matrix[0].count / 2 + 1, y: matrix.count / 2, w: w, h: h)
        
        return split(matrix: matrix, acc: [[top, left, right]], level: level)
    }
    
    let lastLevel = acc[acc.count - 1]
    var levelNodes: [Node] = []
    
    for i in lastLevel {
        let w = i.w / 2
        let h = i.h / 2
        let top = Node(x: i.x + i.w / 2 / 2 + 1, y: i.y, w: w, h: h)
        let left = Node(x: i.x, y: i.y + i.h / 2, w: w, h: h)
        let right = Node(x: i.x + i.w / 2 + 1, y: i.y + i.h / 2, w: w, h: h)
        levelNodes.append(top)
        levelNodes.append(left)
        levelNodes.append(right)
    }
    
    var totalAcc = acc
    totalAcc.append(levelNodes)
    return split(matrix: matrix, acc: totalAcc, level: level)
}

// ready
func printing(_ mat: Matrix) {
    for i in mat {
        let j = i.map({ $0 ? "1" : "_" }).joined()
        print(j)
    }
}

fractal(n: 5)

"""
_______________________________1_______________________________
______________________________1_1______________________________
_____________________________1___1_____________________________
____________________________1_1_1_1____________________________
___________________________1_______1___________________________
__________________________1_1_____1_1__________________________
_________________________1___1___1___1_________________________
________________________1_1_1_1_1_1_1_1________________________
_______________________1_______________1_______________________
______________________1_1_____________1_1______________________
_____________________1___1___________1___1_____________________
____________________1_1_1_1_________1_1_1_1____________________
___________________1_______1_______1_______1___________________
__________________1_1_____1_1_____1_1_____1_1__________________
_________________1___1___1___1___1___1___1___1_________________
________________1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1________________
_______________1_______________________________1_______________
______________1_1_____________________________1_1______________
_____________1___1___________________________1___1_____________
____________1_1_1_1_________________________1_1_1_1____________
___________1_______1_______________________1_______1___________
__________1_1_____1_1_____________________1_1_____1_1__________
_________1___1___1___1___________________1___1___1___1_________
________1_1_1_1_1_1_1_1_________________1_1_1_1_1_1_1_1________
_______1_______________1_______________1_______________1_______
______1_1_____________1_1_____________1_1_____________1_1______
_____1___1___________1___1___________1___1___________1___1_____
____1_1_1_1_________1_1_1_1_________1_1_1_1_________1_1_1_1____
___1_______1_______1_______1_______1_______1_______1_______1___
__1_1_____1_1_____1_1_____1_1_____1_1_____1_1_____1_1_____1_1__
_1___1___1___1___1___1___1___1___1___1___1___1___1___1___1___1_
1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1
"""