🚀 go-pugleaf

    Given a chaotic time series with a fractal dimension, does anyone know of
    any theory or whatever which relates splines to the interpolation of the
    chaotic time series corresponding to the given fractal dimension?  For
    example, if I have a signal that can be best interpolated by cubic splines,
    then that is what I would use (using a linear or quadratic spline would not
    do so well).  Now, given a chaotic time series (perhaps one similar to that
    of Brownian motion), it would seem that you cannot interpolate it with any
    spline of some order, or you need a very high order spline in order to 
    interpolate it accurately.  This may sound crazy, but would it be that you
    would need a spline of some fractional order (in relation to the fractal
    dimension of the time series) in order to do an accurate interpolation?  Or,
    would the spline needed have to have fractal properties itself (a fractal
    interpolating a fractal, so to speak.  I got this idea from Barnsley's IFS
    where a base fractal is used to interpolate a fractal image).

     If anyone can give me any guidance at all on this problem, I would greatly
     appreciate it.  Also, any reference to literature that may help me would
     be nice.

                          John