SierpinskiTriangle.kt

package io.uuddlrlrba.ktalgs.geometry

import io.uuddlrlrba.ktalgs.math.log2

class SierpinskiTriangle {
    /**
     * @param d base of the triangle (i.e. the smallest dimension)
     * @param n fractalization depth (must be less than log2(d))
     * @throws IllegalArgumentException if n > log2(d)
     */
    fun makeTriangles(base: Int, n: Int): Array<BooleanArray> {
        if (n > log2(base)) throw IllegalArgumentException("fractalization depth must be less than log2(base): " +
                "$n > ${log2(base).toInt()}")
        val arr = Array(base, { BooleanArray(base * 2 - 1) })
        drawTriangles(n, arr, 0, 0, base - 1, base * 2 - 2)
        return arr
    }

    fun drawTriangles(n: Int, arr: Array<BooleanArray>, top: Int, left: Int, bottom: Int, right: Int) {
        if (n > 0) {
            val width = right - left
            val height = bottom - top
            drawTriangles(n - 1, arr,
                    top,
                    left + width / 4 + 1,
                    top + height / 2,
                    right - width / 4 - 1
            )
            drawTriangles(n - 1, arr,
                    top + 1 + height / 2,
                    left,
                    bottom,
                    left + width / 2 - 1
            )
            drawTriangles(n - 1, arr,
                    top + 1 + height / 2,
                    left + width / 2 + 1,
                    bottom,
                    right
            )
        } else {
            drawTriangles(arr, top, left, bottom, right)
        }
    }

    fun drawTriangles(arr: Array<BooleanArray>, top: Int, left: Int, bottom: Int, right: Int) {
        val height = bottom - top
        val width = right - left
        for (i in 0..height) {
            for (j in (height - i)..width / 2) {
                arr[top + i][left + j] = true
            }
            for (j in (width / 2..width / 2 + i)) {
                arr[top + i][left + j] = true
            }
        }
    }
}

fun main(args : Array<String>) {
    SierpinskiTriangle()
            .makeTriangles(128, 7)
            .map { array ->
                array.map { if (it) 'x' else ' ' }.joinToString(separator = "")
            }
            .forEach { println(it) }
}