User blog:GamesFan2000/Powerful Array Notation (Part 2)

Rules: Nested Arrays
Rule 8: (1[#], …) = 1

Rule 9: (a[1], …) = (a, a, a, …a a’s…a, …)

Rule 10: (a[1], b[1], c[1], …) = (a, a, …a a’s…a, b, b, …b b’s…b, c, c, …c c’s…c, …)

Rule 11: (a[2], …) = (a[1], a[1], …a[1] a[1]’s…a[1], …)

Rule 12: (a[#], …) = (a[#-1], a[#-1], …a[#-1] a[#-1]’s…a[#-1], …) (Ex: (2[2]) = (2[1], 2[1], 2[1], 2[1])

Rule 13: (a[#], b[#], …) = (a[#-1], a[#-1], …a[#-1] a[#-1]’s…a[#-1], b[#-1], b[#-1], …b[#-1] b[#-1]’s…b[#-1])

Examples
(2[1]) = (2, 2)

(5[1], 4[1]) = (5, 5, 5, 5, 5, 4, 4, 4, 4)

(4[2]) = (4[1], 4[1], …4[1] 4[1]’s…4[1])

(4[3]) = (4[2], 4[2], …4[2] 4[2]’s…4[2])

(3[5], 6[7], 4[4]) = (3[4], 3[4], …3[4] 3[4]’s…3[4], 6[6], 6[6], …6[6] 6[6]’s…6[6], 4[3], 4[3], …4[3] 4[3]’s…4[3])

F(n) = (n[n], n[n], …n n[n]’s…n[n])

Rules: Super-Nested Arrays
Rule 14: (a[b, c], …) = (a[b→b→b …c b’s…b], …)

Rule 15: (a[b, c, d, …], e[f, g, h, …], …) = (a[(b, c, d, …), (b, c, d, …), (b, c, d, …), …], e[(f, g, h, …), (f, g, h, …), (f, g, h, …), …], …)

Rule 16: (a[b[#]], …) = (a[b[#-1], b[#-1], …b[#-1] b[#-1]’s…b[#-1]], …)

Rule 17: (a[b[c…[d[#]]…]], …) = (a[b[c…[d[#-1], d[#-1], …d[#-1] d[#-1]’s…d[#-1]]…]], …)

Rule 18: (a1, …) = a[a[a…a []’s…[a[a, a, …a a’s…a]]…]], …a[a[a…[a[a, a, …a a’s…a]]…]] a[a[a…a[a[a, a, …a a’s…a]]…]]’s…a[a[a…[a[a, a, …a]]…]], …)

Rule 19: (a, …) = (a, a, …a a’s…a, …)

Rule 20: (a[…n brackets…[[[1]…]]], …) = (a[…n-1 brackets…[[[a[[[…[[[a…a [[[…[[[‘s…[[[a, a, …a a’s…a]…]]]…]]]…]]]…]]], …a[…n-1 brackets…[[[a[[[…[[[a…a [[[…[[[‘s…[[[a, a, …a a’s…a]…]]]…]]]…]]]…]]] a[…n-1 brackets…[[[a[[[…[[[a…a [[[…[[[‘s…[[[a, a, …a a’s…a]…]]]…]]]…]]]…]]]’s… a[…n-1 brackets…[[[a[[[…[[[a…a [[[…[[[‘s…[[[a, a, …a a’s…a]…]]]…]]]…]]]…]]], …)

Rule 21: (a[…n brackets…[[[]…]]], …) = (a[…n brackets…[[[]…]]], …a[…n brackets…[[[]…]]] a[…n brackets…[[[]…]]]’s…a[…n brackets…[[[]…]]], …)

Examples
(3[3, 3]) = (3[3^^^3])

(3[4, 4, 4, 4], 3[3, 3, 3]) = (3[(4, 4, 4, 3), (4, 4, 4, 3), (4, 4, 4, 3), 3], 3[(3, 3, 2), (3, 3, 2), 2])

(3[1]) = (33[[3[[3, 3, 3]]]], …33[[3[[3, 3, 3]]]] 33[[3[[3, 3, 3]]]]’s…33[[3[[3, 3, 3]]]])

(5[[[[6]]]], 72) = (5[[[[5]]]], …5[[[[5]]]] 5[[[[5]]]]’s…5[[[[5]]]], 71, …71 71’s…71)