🚀 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
>
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If your time series is chaotic, then your spline will be always in some way
"wrong". What is the point of getting a spline, then?
Do you have any other example?
How do you know that your time series is chaotic?

Gabriel