File:Hilbert curve 3.svg

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[edit] Summary

Description	Hilbert curve 3.svg English: First, second, and third order Hilbert Curves overlayed, with the lines getting thinner and darker as the order increases.
Date	13 July 2008(2008-07-13)
Source	Own work by uploader, generated by an original program described below
Author	Geoff Richards (Qef)
Permission (Reusing this image)	See below.
Other versions	Same with only first order shown Same with only first and second orders shown

[edit] Source code

This SVG image, as well as the other two versions draw to lower orders, were generated by running the following Lua program. It uses the L-system described in the Wikipedia article on Hilbert curves, using simple string replacement to generate a complete turtle-graphics program, which is then run to generate SVG path instructions.

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')

[edit] Licensing

This image has been released into the public domain by its author, Qef. This applies worldwide. In some countries this may not be legally possible; if so: Qef grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Alemannisch | العربية | Беларуская (тарашкевіца) | Български | Català | Česky | Deutsch | Ελληνικά | English | Español | Eesti | فارسی | Suomi | Français | עברית | Italiano | 日本語 | 한국어 | Lietuvių | Македонски | Malti | Plattdüütsch | Nederlands | Polski | Русский | Српски / Srpski | Svenska | தமிழ் | ไทย | Türkçe | Українська | Vèneto | Tiếng Việt | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | +/−

File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	15:18, 13 July 2008		512×512 (619 B)	Qef (Talk | contribs)	({{Information |Description={{en|1=First, second, and third order Hilbert Curves overlayed, with the lines getting thinner and darker as the order increases.}} |Source=Own work by uploader, generated by an original program described below |Author=Geoff Ric)

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Global file usage

The following other wikis use this file:

• Usage of Hilbert curve 3.svg on enwiki
  • List of fractals by Hausdorff dimension
  • Hilbert curve