Thue-Morse Sequence and Turtle Graphics
A Turtle Graphic is the curve that is generated if an automaton is programmed with a sequence. If the Thue–Morse sequence members are used in order to select program states:
- If t(n) = 0, move ahead by one unit,
- If t(n) = 1, rotate counterclockwise by an angle of π/3,
the resulting curve converges to the Koch snowflake.
Read more about this topic: Koch Snowflake
Famous quotes containing the words sequence and/or turtle:
“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”
—Walter Benjamin (1892–1940)
“My beloved spake, and said unto me, Rise up, my love, my fair one,
and come away.
For lo, the winter is past, the rain is over and gone;
The flowers appear on the earth; the time of the singing of birds is come, and the voice of the turtle is heard in our land;”
—Bible: Hebrew The Song of Solomon (l. II, 10–12)