Re: [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  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


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Re: [FRIAM] Fractal discussion Landscape-bird songs

[glen ☣]

Yes, zero dimensional things like your string can have fractal dimension > 0.  
I got a bit googly in trying to find an off the shelf library that would do 
this with little work.  Although I had no luck, I did find this:

  The Fractal Patterns of Words in a Text: A Method for Automatic Keyword 
Extraction
  
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0130617#sec005

As to your string, particularly, I don't know.  But here's what a completely 
ignorant call to fd.estimate tells me:

variogram  madogram  rodogram  variation incr1  hallwood  boxcount
 1.488012  1.276855 2   1.276855  1.475277  1.299939  1.169925

arrived at via R:

> require(fractaldim)
> dat <- "ABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcd"
> dat2 <- as.numeric(utf8ToInt(dat))
> out <- 
> fd.estimate(dat2,methods=list("variogram","madogram","rodogram","variation","incr1","hallwood","boxcount"))

I have no idea what, if anything, any of those numbers mean. 8^) Garbage => 
garbage.



On 03/01/2017 09:36 AM, Nick Thompson wrote:
> This is getting embarrassing because I started something here that I am too 
> frigging dumb to understand.  But let me just ask you fractalologists  out 
> there to clarify:  As a matter of definition, can a time series be "fractal". 
>   So is the time series, ...
> 
> ABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcd
> 
> ,..."fractal"?  Or is that just abuse of terminology. 

-- 
☣ glen


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Re: [FRIAM] Fractal discussion Landscape-bird songs

[Jon Zingale]

Glen,

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  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.

Cheers,
Jon

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Re: [FRIAM] Fractal discussion Landscape-bird songs

[glen ☣]

Given that I don't know Processing, much less Ruby Processing, what the heck is 
the EBall?

https://github.com/jonzingale/RubyProcessing/blob/600c83727c77a4d52ac4effe65d7258100bae5b4/lorenz/lorenz.rb#L2

In a misguided attempt to shrink the frame and adjust everything, I increased 
EBall to 9e-3 and get this:

https://goo.gl/photos/JHYfF79NeuxPYWCN9

-- 
☣ glen


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Re: [FRIAM] Fractal discussion Landscape-bird songs

[Nick Thompson]

Dear Glen, and all, 

 

This is getting embarrassing because I started something here that I am too 
frigging dumb to understand.  But let me just ask you fractalologists  out 
there to clarify:  As a matter of definition, can a time series be "fractal".   
So is the time series, ...

 

ABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcdABABABABcdcdcdcd

 

,..."fractal"?  Or is that just abuse of terminology. 

 

Nick 

 

 

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

-Original Message-
From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of gepr
Sent: Wednesday, March 01, 2017 3:34 AM
To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com>
Subject: Re: [FRIAM] Fractal discussion Landscape-bird songs

 

Along those lines but sticking with the fractals, it would be important to 
distinguish the reconstruction of the instrument from that of the melody. I 
assume the self similarity Nick is talking about would still be present even if 
we render the melody in MIDI. It's not clear to me, are the requirements of 
Takens' method met by a discrete time series?

 

 

On February 28, 2017 5:45:00 PM PST, Vladimyr Burachynsky < 
<mailto:vbur...@shaw.ca> vbur...@shaw.ca> wrote:

>Any bird has only so much lung capacity so every utterance is limited 

>to that volume and it must be forcibly discharged to create an audible  

>wave.  To be detectable by the intended target that sound must fall 

>into a range of frequency and volume within the recipient’s 

>capabilities. If the bird is unable to produce syrinx based sounds then 

>it must devise an alternative like ruffed grouse or prairie chickens. 

>They basically seem to beat the crap out of their chests and can sound 

>like English motorcycles for brief moments.

> 

>So let’s break away from some rather extreme avians from the Melodic 

>Songsters of Poetry.

> [...]

>By the way Frisch did this sort of thinking with Honey Bee Waggle 

>Dances and paper and pencil.

> 

>As a student I had to read his work and found that the bees could sense 

>extra dimensions which could include even more information, vibration 

>and scent.

 

--

⛧glen⛧

 



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Re: [FRIAM] Fractal discussion Landscape-bird songs

[gepr]

Along those lines but sticking with the fractals, it would be important to 
distinguish the reconstruction of the instrument from that of the melody. I 
assume the self similarity Nick is talking about would still be present even if 
we render the melody in MIDI. It's not clear to me, are the requirements of 
Takens' method met by a discrete time series?


On February 28, 2017 5:45:00 PM PST, Vladimyr Burachynsky  
wrote:
>Any bird has only so much lung capacity
>so every utterance is limited to that volume and it must be forcibly
>discharged to create an audible  wave.  To be detectable by the
>intended target that sound must fall into a range of frequency and
>volume within the recipient’s capabilities. If the bird is unable to
>produce syrinx based sounds then it must devise an alternative like
>ruffed grouse or prairie chickens. They basically seem to
>beat the crap out of their chests and can sound like English
>motorcycles for brief moments.
>
>So let’s break away from some rather extreme avians from the Melodic
>Songsters of Poetry.
> [...]
>By the way Frisch did this sort of thinking with Honey Bee Waggle
>Dances and paper and pencil.
>
>As a student I had to read his work and found that the bees could sense
>extra dimensions which could include even more information, vibration
>and scent.

-- 
⛧glen⛧


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Re: [FRIAM] Fractal discussion Landscape-bird songs

[Vladimyr Burachynsky]

I am attached to the thread’s name. It strikes me as so outlandish that it 
deserves attention.

 

On the speculated history of song-birds was a recent paper suggesting most if 
not all songbirds

appear to have had a singular ancestry from SE Asia or Australasia.

 

If you seek to embellish the voice of sauropods with something more familiar to 
modern ears try

cranes and herons. Melodic voices do seem to belong to Songbirds and not the 
aquatic residents.

 

You guys are looking for fractals and stepping over more obvious solutions. 
Just prune the branches not the entire forest of mathematics.

Any bird has only so much lung capacity

so every utterance is limited to that volume and it must be forcibly discharged 
to create an audible  wave.  To be detectable by the intended target that sound 
must fall into a range of frequency and

volume within the recipient’s capabilities. If the bird is unable to produce 
syrinx based sounds then it must devise an alternative like ruffed grouse or 
prairie chickens. They basically seem to

beat the crap out of their chests and can sound like English motorcycles for 
brief moments.

So let’s break away from some rather extreme avians from the Melodic Songsters 
of Poetry.

 

Did not the Audubon Society have a library of Bird vocalizations, at one time. 

By the way Frisch did this sort of thinking with Honey Bee Waggle Dances and 
paper and pencil.

As a student I had to read his work and found that the bees could sense extra 
dimensions which could include even more information, vibration and scent.

Glad you  are all back in a constructive mode. 

Suppose graphics of birdsongs could be transformed by functions from one 
species within a family to another to examine the environmental challenges that 
a species contends with

say Mountain species compared to Plains species. 

Nick, I must bow to your wisdom and tip my hat.

vib

oh, Jon I saw you code site and will try and recompile/run it in Maple or 
Processing since I am familiar with those  two.

Some days are harder than others while pulling a barge upstream.

Anyone recall any barge songs.

vib

 

From: Friam [mailto:friam-bounces

@redfish.com] On Behalf Of Jon Zingale
Sent: February-28-17 4:22 PM
To: friam@redfish.com
Subject: Re: [FRIAM] Fractal discussion Landscape-bird songs

 

Nick,

 

Well one way we may be able to understand

birdsong as fractal might be by studying the

underlying mechanism of the syrinx 
<https://en.wikipedia.org/wiki/Syrinx_(bird_anatomy)> . I can 

imagine this section of the birds trachea as a coupled

oscillator, that when driven far from equilibrium

could give way to trajectories along a strange

attractor (which would be fractal). In an attempt

to think about recovering the attractor from the

time-series of the bird song, I ran across Takens'

theorem last night. Then later last night (I couldn't

sleep) I coded up an example of Takens' theorem

in RubyProcessing 
<https://github.com/jonzingale/RubyProcessing/blob/600c83727c77a4d52ac4effe65d7258100bae5b4/lorenz/lorenz_reconstruction.rb>
 . What is amazing about this

theorem is that it suggests how to build a low-

dimensional manifold from a single dimensional

time-series! So freaking cool. As a test case, I

coded up the Lorenz equations and plotted the

manifold. Then I calculated just the time series

for the x dimension. Lastly, I reconstructed the

entire manifold (topologically) from just this one

coordinate! Included below is a screenshot of

the visualizer. It is actually more fun to watch in

motion, but the picture is telling in itself.

 

Jon

 


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Re: [FRIAM] Fractal discussion Landscape-bird songs

[Robert Wall]

This less than 5-minute video seems visually helpful in the context of what
Jon accomplished last night: Takens' theorem in action for the Lorenz
chaotic attractor .  This
video provides some idea of what emerges from the manifold in terms of the
time series with airflow. Yes, very cool! 

On Tue, Feb 28, 2017 at 4:22 PM, Jon Zingale  wrote:

> Nick,
>
> Well one way we may be able to understand
> birdsong as fractal might be by studying the
> underlying mechanism of the syrinx
> . I can
> imagine this section of the birds trachea as a coupled
> oscillator, that when driven far from equilibrium
> could give way to trajectories along a strange
> attractor (which would be fractal). In an attempt
> to think about recovering the attractor from the
> time-series of the bird song, I ran across Takens'
> theorem last night. Then later last night (I couldn't
> sleep) I coded up an example of Takens' theorem
> in RubyProcessing
> .
> What is amazing about this
> theorem is that it suggests how to build a low-
> dimensional manifold from a single dimensional
> time-series! So freaking cool. As a test case, I
> coded up the Lorenz equations and plotted the
> manifold. Then I calculated just the time series
> for the x dimension. Lastly, I reconstructed the
> entire manifold (topologically) from just this one
> coordinate! Included below is a screenshot of
> the visualizer. It is actually more fun to watch in
> motion, but the picture is telling in itself.
>
> Jon
>
>
> 
> 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
>

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