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)
“The second day of Christmas,
My true love sent to me
Two turtle doves,”
—Unknown. The Twelve Days of Christmas (l. 4–6)