Extension To Multiple Colors
Greg Turk and Jim Propp considered a simple extension to Langton's ant where instead of just two colors, more colors are used. The colors are modified in a cyclic fashion. A simple naming scheme is used: for each of the successive colors, a letter 'L' or 'R' is used to indicate whether a left or right turn should be taken. Langton's ant has the name 'RL' in this naming scheme.
Some of these extended Langton's ants produce patterns that become symmetric over and over again. One of the simplest examples is the ant 'RLLR'. One sufficient condition for this to happen is that the ant's name, seen as a cyclic list, consists of consecutive pairs of identical letters 'LL' or 'RR' (the term "cyclic list" indicates that the last letter may pair with the first one.) The proof involves Truchet tiles.
- Some example patterns in the multiple-color extension of Langton's Ants:
-
RLR: grows chaotically. It is not known if this ant ever produces a highway.
-
LLRR: grows symmetrically.
-
LRRRRRLLR: fills space in a square around itself.
-
LLRRRLRLRLLR: creates a convoluted highway.
-
RRLLLRLLLRRR: creates a filled triangle shape that grows and moves.
Read more about this topic: Langton's Ant
Famous quotes containing the words extension, multiple and/or colors:
“We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.”
—James P. Comer (20th century)
“... the generation of the 20’s was truly secular in that it still knew its theology and its varieties of religious experience. We are post-secular, inventing new faiths, without any sense of organizing truths. The truths we accept are so multiple that honesty becomes little more than a strategy by which you manage your tendencies toward duplicity.”
—Ann Douglas (b. 1942)
“He hath ribbons of all the colors i’the rainbow.”
—William Shakespeare (1564–1616)