require "bitmap"

local bmp = bitmap.of(500, 500, color.black, "Superellipse")

local function superellipse(n, a)
    local hw = bmp:width() // 2
    local hh = bmp:height() // 2

    -- Calculate y for each x.
    local y = {}
    for x = 1, a + 1 do
        local aa = a ^ n
        local xx = (x - 1) ^ n
        y[x] = math.round((aa - xx) ^ (1 / n))
    end

    -- Draw quadrants.
    local prev = {hw + a, hh - y[a + 1]}
    for x = a - 1, 0, -1 do
        local curr = {hw + x, hh - y[x + 1]}
        bmp:line(prev[1], prev[2], curr[1], curr[2], color.white)
        prev = {curr[1], curr[2]}
    end

    prev = {hw, hh + y[1]}
    for x = 1, a do
        local curr = {hw + x, hh + y[x + 1]}
        bmp:line(prev[1], prev[2], curr[1], curr[2], color.white)
        prev = {curr[1], curr[2]}
    end
    prev = {hw - a, hh + y[a + 1]}
    for x = a - 1, 0, -1 do
        local curr = {hw - x, hh + y[x + 1]}
        bmp:line(prev[1], prev[2], curr[1], curr[2], color.white)
        prev = {curr[1], curr[2]}
    end

    prev = {hw, hh - y[1]}
    for x = 1, a do
        local curr = {hw - x, hh - y[x + 1]}
        bmp:line(prev[1], prev[2], curr[1], curr[2], color.white)
        prev = {curr[1], curr[2]}
    end
end

-- Draw 200 concentric superellipses with gradually decreasing 'n'.
for a = 200, 1, -1 do
    superellipse(a / 80, a)
end
bmp:view()