local IMG_SZ, DEPTH = 512, 3

local fh = assert(io.open("Hilbert_curve.svg", "wb"))
fh:write('<?xml version="1.0" encoding="UTF-8"?>\n',
         '<svg version="1.0" width="', IMG_SZ, '" height="', IMG_SZ,
         '" xmlns="http://www.w3.org/2000/svg">\n')

local L_SYSTEM_RULES = {    -- these are from the Wikipedia article
    L = "+RF-LFL-FR+",
    R = "-LF+RFR+FL-",
}
local ANGLE_COMMANDS = {    -- angle expressed in units of 90 degrees
    [0] = "h",
    [1] = "v",
    [2] = "h-",
    [3] = "v-",
}
local STROKE_STYLE = {      -- each order drawn with different stroke style
    [1] = "stroke:#f00;stroke-width:6;fill:none",
    [2] = "stroke:#00f;stroke-width:4;fill:none",
    [3] = "stroke:#000;stroke-width:2;fill:none",
    [4] = "stroke:#000;stroke-width:1;fill:none",
    [5] = "stroke:#000;stroke-width:0.5;fill:none",
}

function turtle_graphics (input, startpos, line_len)
    local output = "M" .. startpos .. "," .. startpos
    local angle = 0
    for i = 1, input:len() do
        local cmd = input:sub(i, i)
        if cmd == "F" then
            output = output .. ANGLE_COMMANDS[angle] .. line_len
        elseif cmd == "+" then
            angle = (angle + 1) % 4
        elseif cmd == "-" then
            angle = (angle - 1) % 4
        end
    end
    return output
end

local line_len = IMG_SZ / 2
for d = 1, DEPTH do
    local lsys = "L"
    for _ = 1, d do
        -- Apply the production rules.  Note that both 'L' and 'R' rules are
        -- applied simultaneously.
        lsys = lsys:gsub("([LR])", function (orig)
            return L_SYSTEM_RULES[orig]
        end)
    end
    fh:write(' <path style="', STROKE_STYLE[d], '" d="',
             turtle_graphics(lsys, line_len / 2, line_len), '"/>\n')
    line_len = line_len / 2
end

fh:write('</svg>\n')