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 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
