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)
“I think of the nestling fallen into the deep grass,
The turtle gasping in the dusty rubble of the highway,
The paralytic stunned in the tub, and the water rising,—
All things innocent, hapless, forsaken.”
—Theodore Roethke (1908–1963)