[FRIAM] Fractal discussion Landscape-bird songs

[glen ☣]

Yes, that makes perfect sense now that you've explained it.  Self-similarity is a tricky thing and would intuitively be sensitive to the delay.  One of the interesting ideas in that paper I posted yesterday was the "Menzerath-Altmann law", which leads to several different "fractal dimension" values, one associated with the size of each word (perhaps analogous to the delay in this context).  I'm not sure I dig the idea of averaging them to aggregate them into a fractal dimension of the text as a whole, though.  I have vague feelings of overhearing conversations about state space reconstruction touching on aggregation over different delay choices ... but it's all lost in the haze at this point.  I suspect there are people on this list who've actually worked on or near the topic.

On 03/01/2017 04:09 PM, Jon Zingale wrote:
> Thank you for the cool image and for
> diving into the code. To answer your
> question, I am using Euler's method to
> compute the trajectories of the Lorenz
> equations. `Eball` denotes the step size
> of the integration. In theory, making the
> Eball param smaller ought give better
> numerical solutions while increasing
> ought give less accurate solutions.
> 
> Takens' method, seems to rely heavily on an
> appropriate choice of delay time. I utilize a
> BBD <https://en.wikipedia.org/wiki/Bucket-brigade_device> style delay line,
> @delay in code.
> 
> In my investigations so far, a step size of 0.003
> seems best paired with a delay of 30 steps. A
> step size of 0.009 seems to benefit from a shorter
> delay of 10 steps. Decreasing the step size to
> 0.0009,  I have been able to increase delay times
> to 100 steps with satisfying result.
> 
> I suspect that by weakening the accuracy of the
> integration, longer delay times force Takens' method
> to rely on less accurate information and the
> reconstruction suffers. I am open to additional
> thoughts and theories.

-- 
☣ glen