an over-elaborate way of generating the mandelbrot fractal

mandel.lua

#!/usr/bin/lua
-- complex number class
do
    local _meta = {
        __tostring = function(self)
            return "(" .. self.re .. ", " .. self.im .. ")"
        end,
        __add = function(self, rhs)
            return Complex(self.re + rhs.re, self.im + rhs.im)
        end,
        __sub = function(self, rhs)
            return Complex(self.re - rhs.re, self.im - rhs.im)
        end,
        __mul = function(self, rhs)
            return Complex(self.re*rhs.re - self.im*rhs.im, self.im*rhs.re + self.re*rhs.im)
        end,
        __div = function(self, rhs)
            local d = rhs:size_sq()
            return Complex((self.re*rhs.re + self.im*rhs.im)/d, (self.im*rhs.re - self.re*rhs.im)/d)
        end,
        __unm = function(self)
            return Complex(-self.re, -self.im)
        end
    }

    local function _size_sq(self)
        return self.re*self.re + self.im*self.im
    end

    function Complex(_re, _im)
        local self = {
            re = _re or 0,
            im = _im or 0,
            size_sq = _size_sq
        }
        setmetatable(self, _meta)
        return self
    end
end

-- generates the mandelbrot iteration
function mandel_gen(c, max_iter)
    local z = Complex()
    return function()
        if max_iter <= 0 then return nil end
        max_iter = max_iter - 1
        z = z*z + c
        return z:size_sq() < 4 and z or nil
    end
end

-- iterates over the [a, b] range in 'ns' steps
function range_gen(a, b, ns)
    incr = ns and (b - a) / (ns - 1) or 1
    return coroutine.wrap(function()
        for i = a, b, incr do
            coroutine.yield(i)
        end
    end)
end

-- converts a value into an ascii-art gradient
do
    local ascii = " `.,:;*o0@#"
    function ascii_gradient(val, max)
        local i = (#ascii - 1) * val / (max + 1)
        return ascii:sub(i+1, i+1)
    end
end

-- draws the mandelbrot set
local max_it = 32
for y in range_gen(-1.25, 1.25, 21) do
    local line = ""
    for x in range_gen(-2, 1, 40) do
        local i = 0
        for z in mandel_gen(Complex(x, y), max_it) do
            i = i + 1
        end
        line = line .. ascii_gradient(i, max_it)
    end
    print(line)
end