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:
“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a sequence of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”
—Philip Roth (b. 1933)
“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)