Thue-Morse.bf

Read input until newline and translate into a number
 , ----- ----- [ +++++ +++++
  > [ - > +++++ +++++ < ]
  +++++ +++ [ - < ----- - > ]
  < [ - >> + << ]
  >> [ - < + > ]
  << , ----- ----- ]

Start loop and run the algorithm on each number between zero and the input number
>> - < [ > +
  [ - > + >> + <<< ] > [ - < + > ] >> 

Decide the parity of the number
Divide the number by two until it is zero and sum the remainders
[
  [ >> + << - < + >> + < [ < - >> - < [ - << + >> ] ] << [ - >> + << ] > [ - > + >> - <<< ] > - ]
  >> [ - << + >> ] <<
] >

Run Modulo 2 on the remainder sum and print the result

[ - < + >> + < [ < - >> - < [ - << + >> ] ] << [ - >> + << ] > [ - > + < ] > - ] >
< +++++ +++ [ - > +++++ + < ] > . [-]

End the loop if the input number has reached zero
<<<<<< -]

Print newline
+++++ +++++ .