## Creating Turmites

This exercise allows you to build your own turmites. To pass the exercise, you should simply write a `init()` method which initializes the `rule` to use the following transitions table (from wikipedia), set the buggle initial position at (8;33), and ask for 8342 steps.

| Current color
--- | ---
0 | 1
Write color | Turn | Next state | Write color | Turn | Next state
Current state | 0 | 1 | R | 0 | 1 | R | 1
1 | 0 | N | 0 | 0 | N | 1

where the direction to turn is one of L (90° left), R (90° right), N (no turn) and U (180° U-turn).

## Going further

This exercise is naturally an excuse to let you experiment with your own turmites. Feel free to change the transition table and the amount of steps to experiment by yourself. To that extend, you may find the Ed Pegg Jr's library useful. If you find new interesting patterns, send them per email so that we can integrate them to this list!

In addition, wikipedia is desperately missing some good looking colorful turmites: only black and white ones are depicted. You should consider submitting your creations directly to the free encyclopedia.

Here are some 2-color turmites, extracted from http://demonstrations.wolfram.com/Turmites/ [!python|scala]They are not written using the [!thelang] syntax, but converting them should be easy.[/!]

    {{{1, RIGHT , 0}, {0, LEFT  , 0}}}  # 1: Langton's ant
    {{{1, RIGHT , 0}, {0, NOTURN, 0}}}  # 2: binary counter
    {{{0, LEFT  , 1}, {1, RIGHT , 1}}, {{1, NOTURN, 0}, {1, NOTURN, 1}}} # 3: (filled triangle)
    {{{0, NOTURN, 1}, {0, LEFT  , 1}}, {{1, RIGHT , 0}, {0, NOTURN, 1}}} # 4: spiral in a box
    {{{0, RIGHT , 1}, {0, LEFT  , 0}}, {{1, LEFT  , 1}, {0, RIGHT , 0}}} # 5: stripe-filled spiral
    {{{0, RIGHT , 1}, {0, LEFT  , 0}}, {{1, LEFT  , 1}, {1, NOTURN, 0}}} # 6: stepped pyramid
    {{{0, RIGHT , 1}, {0, NOTURN, 1}}, {{1, RIGHT , 1}, {1, LEFT  , 0}}} # 7: contoured island
    {{{0, RIGHT , 1}, {0, RIGHT , 1}}, {{1, NOTURN, 0}, {0, RIGHT , 1}}} # 8: woven placemat
    {{{0, RIGHT , 1}, {1, RIGHT , 1}}, {{1, LEFT  , 1}, {1, LEFT  , 0}}} # 9: snowflake-ish
    {{{1, LEFT  , 0}, {0, NOTURN, 1}}, {{0, LEFT  , 0}, {0, LEFT  , 1}}} # 10: slow city builder
    {{{1, LEFT  , 0}, {1, RIGHT , 1}}, {{0, RIGHT , 0}, {0, LEFT  , 1}}} # 11: framed computer art
    {{{1, LEFT  , 0}, {1, RIGHT , 1}}, {{0, RIGHT , 1}, {1, LEFT  , 0}}} # 12: balloon bursting (makes a spreading highway)
    {{{1, LEFT  , 1}, {0, LEFT  , 0}}, {{1, NOTURN, 0}, {0, NOTURN, 0}}} # 13: makes a horizontal highway
    {{{1, LEFT  , 1}, {0, LEFT  , 0}}, {{1, RIGHT , 1}, {1, RIGHT , 0}}} # 14: makes a 45 degree highway
    {{{1, LEFT  , 1}, {0, LEFT  , 1}}, {{1, RIGHT , 1}, {0, LEFT  , 0}}} # 15: makes a 45 degree highway
    {{{1, LEFT  , 1}, {0, NOTURN, 0}}, {{1, NOTURN, 0}, {1, RIGHT , 0}}} # 16: spiral in a filled box
    {{{1, LEFT  , 1}, {0, RIGHT , 0}}, {{0, LEFT  , 0}, {0, LEFT  , 0}}} # 17: glaciers
    {{{1, LEFT  , 1}, {1, LEFT  , 1}}, {{1, RIGHT , 1}, {0, NOTURN, 0}}} # 18: golden rectangle!
    {{{1, LEFT  , 1}, {1, RIGHT , 0}}, {{0, LEFT  , 0}, {0, LEFT  , 0}}} # 19: fizzy spill
    {{{1, LEFT  , 1}, {1, RIGHT , 1}}, {{1, NOTURN, 0}, {0, NOTURN, 1}}} # 20: nested cabinets
    {{{1, NOTURN, 1}, {0, LEFT  , 1}}, {{1, RIGHT , 0}, {1, NOTURN, 1}}} # 21: (cross)
    {{{1, NOTURN, 1}, {0, NOTURN, 0}}, {{0, RIGHT , 0}, {1, LEFT  , 0}}} # 22: saw-tipped growth
    {{{1, NOTURN, 1}, {0, NOTURN, 1}}, {{1, RIGHT , 1}, {0, NOTURN, 0}}} # 23: curves in blocks growth
    {{{1, NOTURN, 1}, {0, RIGHT , 0}}, {{0, LEFT  , 0}, {0, LEFT  , 0}}} # 24: textured growth
    {{{1, NOTURN, 1}, {0, RIGHT , 1}}, {{1, LEFT  , 0}, {1, RIGHT , 0}}} # 25: (diamond growth)
    {{{1, NOTURN, 1}, {1, LEFT  , 0}}, {{1, RIGHT , 1}, {0, NOTURN, 0}}} # 26: coiled rope
    {{{1, RIGHT , 0}, {0, LEFT  , 1}}, {{1, LEFT  , 0}, {0, NOTURN, 1}}} # 27: (growth)
    {{{1, RIGHT , 0}, {0, LEFT  , 1}}, {{1, LEFT  , 0}, {0, RIGHT , 1}}} # 28: (square spiral)
    {{{1, RIGHT , 0}, {1, RIGHT , 1}}, {{0, NOTURN, 0}, {0, NOTURN, 1}}} # 29: loopy growth with holes
    {{{1, RIGHT , 1}, {0, LEFT  , 1}}, {{1, NOTURN, 0}, {0, NOTURN, 0}}} # 30: Lanton's Ant drawn with squares
    {{{1, RIGHT , 1}, {0, RIGHT , 0}}, {{0, LEFT  , 1}, {1, LEFT  , 0}}} # 31: growth with curves and blocks
    {{{1, RIGHT , 1}, {0, RIGHT , 0}}, {{0, NOTURN, 0}, {1, RIGHT , 1}}} # 32: distracted spiral builder
    {{{1, RIGHT , 1}, {0, RIGHT , 1}}, {{1, NOTURN, 0}, {1, NOTURN, 1}}} # 33: cauliflower stalk (45 deg highway)
    {{{1, RIGHT , 1}, {1, LEFT  , 1}}, {{1, RIGHT , 1}, {0, RIGHT , 0}}} # 34: worm trails (eventually turns cyclic!)
    {{{1, RIGHT , 1}, {1, NOTURN, 0}}, {{1, NOTURN, 0}, {0, NOTURN, 1}}} # 35: eventually makes a two-way highway!
    {{{1, RIGHT , 1}, {1, RIGHT , 0}}, {{0, NOTURN, 0}, {0, NOTURN, 0}}} # 36: almost symmetric mould bloom
    {{{1, RIGHT , 1}, {1, RIGHT , 0}}, {{0, RIGHT , 0}, {1, NOTURN, 1}}} # 37: makes a 1 in 2 gradient highway
    {{{1, RIGHT , 1}, {1, RIGHT , 1}}, {{1, LEFT  , 1}, {0, RIGHT , 0}}} # 38: immediately makes a 1 in 3 highway
    {{{0, RIGHT , 1}, {1, RIGHT , 1}}, {{0, LEFT  , 2}, {0, LEFT  , 0}}, {{1, RIGHT , 2}, {1, LEFT  , 0}}} # 39: squares and diagonals growth
    {{{1, LEFT  , 1}, {0, NOTURN, 0}}, {{0, RIGHT , 2}, {1, LEFT  , 0}}, {{1, RIGHT , 1}, {1, NOTURN, 0}}} # 40: streak at approx. an 8.1 in 1 gradient
    {{{1, LEFT  , 1}, {0, NOTURN, 2}}, {{0, RIGHT , 2}, {1, NOTURN, 1}}, {{1, RIGHT , 1}, {1, NOTURN, 0}}} # 41: streak at approx. a 1.14 in 1 gradient
    {{{1, LEFT  , 1}, {1, LEFT  , 1}}, {{1, NOTURN, 0}, {0, NOTURN, 2}}, {{0, LEFT  , 1}, {1, NOTURN, 1}}} # 42: maze-like growth
    {{{1, LEFT  , 2}, {0, RIGHT , 0}}, {{1, LEFT  , 0}, {0, RIGHT , 0}}, {{0, LEFT  , 0}, {0, LEFT  , 1}}} # 43: growth by cornices
    {{{1, RIGHT , 0}, {0, RIGHT , 2}}, {{0, LEFT  , 0}, {0, RIGHT , 0}}, {{0, NOTURN, 1}, {1, LEFT  , 0}}} # 44: makes a 1 in 7 highway
    {{{1, RIGHT , 1}, {0, LEFT  , 0}}, {{1, RIGHT , 2}, {0, NOTURN, 0}}, {{1, LEFT  , 0}, {0, LEFT  , 0}}} # 45: makes a 4 in 1 highway

Langton's ants may not share the expressiveness power of the turmites, but they remain fascinating too. You can experiment with them using the initLangton() method, provided in your template, that allows to build a Turmite transition table from a Langton's ant name. Tiny changes in the ant may result huge changes. For example, "RRL" does not seem to lead to any constructed pattern, even after a million steps, but "RLL" starts building a very simple highway pattern after less than 100 steps!

Quite a lot of Langton's ants build highways: RL, of course, but also RLRLRLLRLR (about 2500 steps). The chaotic behavior of ants before the highway can be very short (as with RLL that only need 100 steps to converge) or very long, as with LLLLLLRRLRRR which seems chaotic for more than 500,000 steps before build the highway or even RRLLLRRRLRRR which needs 1170000 to start converging. Some are narrow, and others are very large, such as RRLRLLRLRR (200,000 steps). This ant is also notable since it is somehow squarish even before the highway start where most others do not show anything notable before their highway.

Some ants fill solid sectors, such as RRLLLRLLLRRR (16,000 steps), RRLLLRLLLRRR (30,000 steps), RRLLLRRRRRLR (125,000 steps) or RRLRLLRRRRRR (20,000 steps). Some even fill the whole space (RRLRR after 3000 steps). Some of my personal favorite ones are the ones where the ant seem to be bouncing within a box that gets bigger on each bump, such as LRRRRRLLR (30,000 steps). LRRRRLLLRRR is even more impressing since the bounces within the box are regular and since it converges more rapidly to its stable behavior (15,000 steps are enough).

Finally, some ants are just build artistic patterns. You should check this video for some beautiful ones: http://www.youtube.com/watch?v=1X-gtr4pEBU. If you want to convert them into your code, you have to shift them by one: For example, the one depicted at 3:42 is not RRLRLRLLRL, but RLRLRLLRLR (the first visible move should be read as last one).

As you can see by exploring the above set of turmites, they are usually not as colorful as the ants, but this may be because very few colors suffice to exhibit complex behaviors. For example, there is a specific class of turmites called busy beavers which are turmites that write a lot of things before stopping (busy beavers are usually classical turing machines, but the idea fits perfectly to turmites too). There is a sort of international competition where people strive to find the turmite that covers the biggest area before stopping. The web page is here: http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines