involute.jl

using Base.Iterators

RIGHT = (0, 1)
DOWN = (1, 0)
LEFT = (0, -1)
UP = (-1, 0)

function involute(n::Int)::Matrix{Int}
    directions = cycle((RIGHT, DOWN, LEFT, UP))
    repeats = pushfirst!(collect(flatten(zip(n-1:-1:1, n-1:-1:1))), n-1)
    moves = flatten(repeated(d, r) for (d, r) in zip(directions, repeats))
    indices = pushfirst!(accumulate(.+, moves), (0, 0))
    sorted_nums = sort(1:n^2, by=(i)->indices[i])
    return transpose(reshape(sorted_nums, (n, n)))
end

display(involute(5))
# 5×5 transpose(::Matrix{Int64}) with eltype Int64:
#   1   2   3   4  5
#  16  17  18  19  6
#  15  24  25  20  7
#  14  23  22  21  8
#  13  12  11  10  9