Editing Thue–Morse sequence (section)

=== Fractals and turtle graphics ===
Using [[turtle graphics]], a curve can be generated if an automaton is programmed with a sequence.
When 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 by an angle of π/3 [[radian]]s (60°)

The resulting curve converges to the [[Koch snowflake|Koch curve]], a [[fractal curve]] of
infinite length containing a finite area. This illustrates the fractal nature of the Thue–Morse Sequence.{{sfnp|Ma|Holdener|2005}}

It is also possible to draw the curve precisely using the following instructions:<ref>{{Cite web|url=http://blog.zacharyabel.com/2012/01/thue-morse-navigating-turtles/|title=Thue-Morse Navigating Turtles|last=Abel|first=Zachary|date=January 23, 2012|website=Three-Cornered Things}}</ref>

*If ''t''(''n'') = 0, rotate by an angle of π radians (180°),
* If ''t''(''n'') = 1, move ahead by one unit, then rotate by an angle of π/3 radians.