Perlin Noise - LOVE2D

local random, randomseed = math.random, math.randomseed
local floor = math.floor
local max, min = math.max, math.min

local octaves = 3
local persistence = 0.5
local noised = {}

local function cos_interpolate(a, b, x)
    local ft = x * math.pi
    local f = (1 - math.cos(ft)) * .5

    return  a * (1 - f) + b * f
end

local function noise_2d(x, y, i, seed)
    local nx = noised[x]

    if (nx and nx[y]) then
        return nx[y]
    else
        nx = nx or {}
        randomseed((x * seed + y * i ^ 1.1 + 14) / 789221 + 33 * x + 15731 * y * seed)
    end

    random()

    noised[x] = nx
    nx[y] = random(-1000, 1000) / 1000

    return nx[y]
end

local function smooth_noise_2d(x, y, i, seed)
    local corners = (noise_2d(x - 1, y - 1, i, seed) + noise_2d(x + 1, y - 1, i, seed) + noise_2d(x - 1, y + 1, i, seed) + noise_2d(x + 1, y + 1, i, seed)) / 16
    local sides = (noise_2d(x - 1, y, i, seed) + noise_2d(x + 1, y, i, seed) + noise_2d(x, y - 1, i, seed) + noise_2d(x, y + 1, i, seed)) / 8
    local center = noise_2d(x, y, i, seed) / 4
    return corners + sides + center
end

local function interpolate_noise_2d(x, y, i, seed)
    local int_x = floor(x)
    local frac_x = x - int_x

    local int_y = floor(y)
    local frac_y = y - int_y

    local v1 = smooth_noise_2d(int_x, int_y, i, seed)
    local v2 = smooth_noise_2d(int_x + 1, int_y, i, seed)
    local v3 = smooth_noise_2d(int_x, int_y + 1, i, seed)
    local v4 = smooth_noise_2d(int_x + 1, int_y + 1, i, seed)

    local i1 = cos_interpolate(v1, v2, frac_x)
    local i2 = cos_interpolate(v3, v4, frac_x)

    return cos_interpolate(i1, i2, frac_y)
end

local function perlin_2d(x, y, seed)
    local total = 0
    local p = persistence
    local n = octaves - 1

    for i = 0, n do
        local frequency = 2 ^ i
        local amplitude = p ^ i

        total = total + interpolate_noise_2d(x * frequency, y * frequency, i, seed) * amplitude
    end

    return total
end


local points = {}
local size = 150
local scale = 2
local can
local time_taken = 0

local mx, my = 0, 0

function love.update()
    mx, my = love.mouse.getPosition()
    mx = floor((mx + 100 + (size / 2)) / scale)
    my = floor((my + 100 + (size / 2)) / scale)
end

function love.keydown(key)
    if (key == "escape") then
        love.event.push("quit")
    end
end

function love.load()
    local start = love.timer.getMicroTime()

    for x = -size, size do
        points[x] = {}
        local ax = points[x]
        for y = -size, size do
            ax[y] = min(max(perlin_2d(x / 4, y / 4, 4923), -1), 1)
        end
    end

    time_taken = love.timer.getMicroTime() - start

    can = love.graphics.newCanvas()
    love.graphics.setCanvas(can)

    love.graphics.setPointStyle("rough")
    love.graphics.setPointSize(scale)

    for x = -size, size do
        local ax = points[x]
        for y = -size, size do
            local c = ax[y] * 127.5 + 127.5
            love.graphics.setColor(c, c, c)
            love.graphics.point(x, y)
        end
    end

    love.graphics.setCanvas()
end

function love.draw()
    love.graphics.setColor(255, 255, 255)
    love.graphics.print("Generated in " .. time_taken .. " seconds!", 4, 4)

    if (points[mx] and points[mx][my]) then
        love.graphics.print("(" .. mx .. ", " .. my .. "): " .. points[mx][my], 4, 20)
    end

    love.graphics.draw(can, 100, 100, 0, scale, scale)
end