Dragon curves. Wikipedia reference: https://en.wikipedia.org/wiki/Dragon_curve

main.lua

local curves = {}
local timer = 0
local iterations = 0

function newCurve(startX, startY, startDir, lineLen, color)
    return {
        startX = startX,
        startY = startY,
        startDir = startDir,
        lineLen = lineLen,
        color = color,
        vals = {"F", "X"}
    }
end

function updateCurve(curve)
    local newCurve = {}
    for i, r in pairs(curve.vals) do
        if r == "X" then
            table.insert(newCurve, "X")
            table.insert(newCurve, "+")
            table.insert(newCurve, "Y")
            table.insert(newCurve, "F")
            table.insert(newCurve, "+")
        elseif r == "Y" then
            table.insert(newCurve, "-")
            table.insert(newCurve, "F")
            table.insert(newCurve, "X")
            table.insert(newCurve, "-")
            table.insert(newCurve, "Y")
        else
            table.insert(newCurve, r)
        end
    end
    curve.vals = newCurve
end

function drawCurve(curve)
    love.graphics.setColor(curve.color)
    local x1 = curve.startX
    local y1 = curve.startY
    local x2, y2
    local dir = curve.startDir
    local lineLen = curve.lineLen
    for i, r in pairs(curve.vals) do
        if r == "F" then
            x2 = x1 + lineLen * math.sin(dir)
            y2 = y1 + lineLen * math.cos(dir) 
            love.graphics.line(x1, y1, x2, y2)
            x1 = x2
            y1 = y2
        elseif r == "+" then
            dir = dir + math.pi / 2
        elseif r == "-" then
            dir = dir - math.pi / 2
        end
    end
end


function love.load()
    curves = {
        newCurve(400, 300,           0, 4, {178, 139, 101}),
        newCurve(400, 300,   math.pi/2, 4, { 25, 255,  49}),
        newCurve(400, 300,     math.pi, 4, {255, 125,   0}),
        newCurve(400, 300, 3*math.pi/2, 4, { 72,  20, 204}),
    }
end

function love.update(dt)
    timer = timer + dt
    if timer >= 2 then
        iterations = iterations + 1
        for i, curve in pairs(curves) do
            updateCurve(curve)
        end
        timer = 0
    end
end

function love.draw()
    for i, curve in pairs(curves) do
        drawCurve(curve)
    end
    if iterations >= 16 then
        love.event.quit()
    end
end