Model.swift

import Foundation

public class Model {

    func makeMandelbrotSet(
        max: (Double, Double),
        min: (Double, Double),
        size: Int,
        limit: Double = 100.0,
        maxCycle: Int = 500
    ) -> [[Int]] {
        
        let scale = (
            (max.0 - min.0) / Double(size - 1),
            (max.1 - min.1) / Double(size - 1)
        )
        var table = [(Double, Double)]()
        table.append(min)
        for i in 1 ..< size {
            table.append((
                table[i - 1].0 + scale.0,
                table[i - 1].1 + scale.1
            ))
        }
        var history = [(Double, Double)](repeating: (0, 0), count: maxCycle)

        var result = [[Int]](repeating: [Int](repeating: 0, count: size), count: size)
        for row in 0 ..< size {
            for col in 0 ..< size {
                for cycle in 1 ..< maxCycle {
                    let previous = history[cycle - 1]
                    history[cycle] = (
                        previous.0 * previous.0 - previous.1 * previous.1 + table[row].0,
                        2 * previous.0 * previous.1 + table[col].1
                    )

                    if (limit <= sqrt(history[cycle].0 * history[cycle].0 + history[cycle].1 * history[cycle].1)) {
                        result[row][col] = (cycle % 255) + 1
                        break
                    }
                }
            }
        }

        return result
    }
}