In article <AANLkTik2TWMhLxCmQAR7t8yWZsK3S8UEGU_cyRy13pvT@mail.gmail.com>,

   "Tony (Anthony) Hanmer" <a.hanmer@gmail.com> writes:

> I'm looking for the order number translation for the string bbbbbbaaaaaa to
> use in Fractint, which produces this Lyapunov fractal:
> http://commons.wikimedia.org/wiki/File:Lyapunov-fractal.png
> (It's a famous one, called Zircon City.)
> Any help?

I found this in a comment in the code.  It should probably migrate to
the help file for this fractal type:

       The sequence is coded in the bit pattern in an integer.
       Briefly, the sequence starts with an A the leading zero bits
       are ignored and the remaining bit sequence is decoded.  The
       sequence ends with a B.  Not all possible sequences can be
       represented in this manner, but every possible sequence is
       either represented as itself, as a rotation of one of the
       representable sequences, or as the inverse of a representable
       sequence (swapping 0s and 1s in the array.)  Sequences that
       are the rotation and/or inverses of another sequence will generate
       the same lyapunov exponents.

       A few examples follow:
           number    sequence
               0       ab
               1       aab
               2       aabb
               3       aaab
               4       aabbb
               5       aabab
               6       aaabb (this is a duplicate of 4, a rotated inverse)
               7       aaaab
               8       aabbbb  etc.

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