The Thue-Morse Sequence: A Turtle Graphics

The ThueMorse sequence 01101001100101101001011001... is a well-known binary sequence. It can be defined as recurrence relation by M(0) = 0 and M(2n) = M(n), M(2n+1) = 1 - M(n).
From the ThueMorse sequence we can obtain the von Koch snowflake if we interpret the bits of the sequence as drawing instructions: for 0 move one unit length forward, for 1 we turn 60 degrees to the left. When scaling the drawing back appropriately, the von Koch snowflake is obtained in the limit.
This connection of Thue--Morse with the snowflake of von Kochhas been discovered by Coquet and Dekking in the beginning of the 80's, and was recently rediscovered by Holdener: "When Thue-Morse meets Koch", Fractals 13 (2005).

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• Thue-Morse sequence
• turtle graphics
• fractals

[Jekichan21]

100101100110100110010110011010­­01...

1nn1nn1nn1nn1nn1nn0nn1nn0nn0nn­­0n... period equals to three

11111101000... - very haotic sequence

period may be not only the three

example:

011111111010111010011001101011­­01100001111001001010...

period equals to seven

[IAINMAN96]

Very nice. What program do you use? Kturtle? Py? Perl?