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:
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)
“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)