Period detection of chaotic sequences

represented with finite precision

The Period class implements in C++ the sliding window algorithm in order to find periods in a chaotic sequence represented with finite precision. The class is templated so that the precision can be externally specified. The following finite representations are known to be supported:
  1. floating point (see IEEE754 class) single precision (32 bits)
  2. floating point double precision (64 bits)
  3. fixed point (see TFixed class)
The chaotic sequences are generated using generators of the form x_n = f(x_{n-1}), where f:[0,1]->[0,1] is the chaotic map. The following chaotic maps are implemented:
  1. logistic map
  2. tent map
  3. Chebyshev polynomials
  4. skew tent map
  5. Bernoulli map (a.k.a. r-adic map)
  6. piece-wise linear chaotic map
Other chaotic maps could be implemented by modifying Period<T,U>::chaotic_map function.
For usage examples see period.cpp, scan_interval.cpp, show_seq.cpp or bin_stream.cpp.
Cristea Bogdan,
Oct 31, 2009, 4:19 AM