Friam

Re: Fractal discussion Landscape-bird songs

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jon zingale

Re: 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. 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

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bird_song?.png (623K) Download Attachment

Robert Wall

Re: Fractal discussion Landscape-bird songs

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 <[hidden email]> 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

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Meets Fridays 9a-11:30 at cafe at St. John's College
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Vladimyr Burachynsky

Re: Fractal discussion Landscape-bird songs

In reply to this post by jon zingale

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: [hidden email]
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. 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

gepr

Re: 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 <[hidden email]> 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⛧

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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uǝʃƃ ⊥ glen

Nick Thompson

Re: Fractal discussion Landscape-bird songs

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:[hidden email]] On Behalf Of gepr
Sent: Wednesday, March 01, 2017 3:34 AM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Fractal discussion Landscape-bird songs

On February 28, 2017 5:45:00 PM PST, Vladimyr Burachynsky <[hidden email]> 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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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

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gepr

Re: Fractal discussion Landscape-bird songs

In reply to this post by jon zingale

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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Meets Fridays 9a-11:30 at cafe at St. John's College
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uǝʃƃ ⊥ glen

jon zingale

Re: Fractal discussion Landscape-bird songs

In reply to this post by 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

gepr

Re: Fractal discussion Landscape-bird songs

In reply to this post by Nick Thompson

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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Meets Fridays 9a-11:30 at cafe at St. John's College
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FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

uǝʃƃ ⊥ glen

gepr

Re: Fractal discussion Landscape-bird songs

In reply to this post by jon zingale

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

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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uǝʃƃ ⊥ glen