On 29.06.2013 20:55, Rupert Swarbrick wrote:
> Adam <adammaj1 at o2.pl> writes:
>> At the end it should be :
>>
>> I can do it using linear function , but then curve is not smooth. I
>> would like to use nonlinear function.
>
> I don't know whether Maxima has functions for smooth curve
> fitting. Maybe other respondents can help you there. Hopefully the
> following general pointers will be of some use to you:
>
> This is a non-trivial problem: after all, there are lots of curves that
> go exactly through your points: how do you choose which one to use?
> Presumably, you want the "least wiggly" one, but defining that isn't all
> that simple. You probably want to search for ideas using terms like
> "spline approximation" or "spline interpolation".
OK, Thx
>
> Something you also need to know is whether the points you have are exact
> or have some sort of experimental uncertainty. If they are "exactly
> right", then you want a curve that goes through them and then bends
> around to ensure that it's smooth (think Bezier curves and the like).
I think that the curve should go thru all points.
>
> Sorry that I can't say anything more specific. Can you give us an
> example of what you're trying to do?
Yes.
This numbers are argument of complex point of ray ( curve that run from
infinity to some point) that land on the point of Julia set.
The index of array describes distance to this point so I have all info
to draw the curve. Because of slow dynamics ( parabolic case) it is hard
( for me) to compute it directly near it's landing point .
On this image there are no this curves ( or in another words one can see
only some parts of it near it's landing point ( black dots with 15 arms ) .
Compare with this video where one can see only curves :
http://commons.wikimedia.org/wiki/File:Parabolic_rays_landing_on_fixed_point.ogv
Near landing point curves are interpolated with linear function
so a small distortion can be seen.
Some theory with Maxima images is here :
http://math.stackexchange.com/questions/361205/what-is-the-shape-of-parabolic-critical-orbit
Thank you for your answer.
Adam