wrote

> Are there any other simplistic chaotic systems to try next?

The temperature, Down Jones average, height of blades of grass ...

All constrained, cyclic and unpredictable.

It's not chaos that's the odd duck in the universe, the
odd duck is deterministic mathematics. There is _nothing_
in this universe that repeats itself, let me repeat that...

"God created real numbers, Man made the integers",

- Somebody famous, if you move
in the right circles, but I
forgot his name.

"And the Devil made 0 and infinity"

- Me, but I am sure Somebody
Else wrote it down first

--
Post brought to you by Me, Somebody and Somebody Else

From:	Lou Pecora
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 09:08:40 -0500

In article <5yGxd.5232$Z47.4945@newsread2.news.atl.earthlink.net>,
"Nicholas O. Lindan" wrote:

> The temperature, Down Jones average, height of blades of grass ...

The temperature? Maybe since it's connected to the weather system which
can display chaotic behaviors, but it's VERY high dimensional. That
would be a BIG circuit.

Dow Jones? Nah. Best modeled as a stochastic system. If you think the
weather is high dimensional...

Blades of Grass? Huh? I don't get that one. Fractal, maybe? Maybe,
not. Connection to chaos or dynamics?

Being Cyclic is not a necessary trait of chaos.

Look (google) for simpler systems. Check out papers by Tom Carroll (in
the 1990's), Sprott (1990's and later), Rulkov (late 1990's paper on
just your topic), and the double-scroll circuit (often mislabeled as
Chua's circuit, but that latter label has stuck).

-- Lou Pecora (my views are my own)

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 15:09:36 GMT

"Lou Pecora" wrote
> "Nicholas O. Lindan" wrote:
>
> > The temperature, Down Jones average, height of blades of grass ...
>
> The temperature? Maybe since it's connected to the weather system which
> can display chaotic behaviors, but it's VERY high dimensional. That
> would be a BIG circuit.

Not to simulate, temperature as the system itself.

> Being Cyclic is not a necessary trait of chaos.

I think it is: if the values aren't cyclic then they have to
march of to infinity (or the universe ends). They cycle around
the 'attractor': a mean value.

> -- Lou Pecora (my views are my own)

-- Nicholas O. Lindan (my views are a product of all the people I met,
I don't have a single unique view in me.)

From:	prep at prep.synonet.com
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Sat, 25 Dec 2004 00:17:37 +0800

John Popelish writes:

> That is a conclusion. Lets see your argument. Lorentz discovered the
> effect he named the butterfly effect after modeling a weather system
> in the simplest way he could imagine.

That is the `Butterfly' or Lorenz *attractor*.

> He modeled a 2 dimensional convection cell, with heat applied at the
> bottom and lost at the top. This model convinced him that even
> apparently simple systems like this exhibit chaotic operation under
> some conditions, and so, the essence of the butterfly effect, and
> that larger, more complicated (actual) weather systems mush have
> this property, also.

Are you sure you are not confusing it with the `Helium in a Small Box'
experiment by Libchaber?

--
Paul Repacholi 1 Crescent Rd.,
+61 (08) 9257-1001 Kalamunda.
West Australia 6076
comp.os.vms,- The Older, Grumpier Slashdot
Raw, Cooked or Well-done, it's all half baked.
EPIC, The Architecture of the future, always has been, always will be.

From:	John Popelish
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Sat, 25 Dec 2004 12:59:50 -0500

prep@prep.synonet.com wrote:
>
> John Popelish writes:
>
> > That is a conclusion. Lets see your argument. Lorentz discovered the
> > effect he named the butterfly effect after modeling a weather system
> > in the simplest way he could imagine.
>
> That is the `Butterfly' or Lorenz *attractor*.

I may be wrong about this, but I think there is a common confusion
between the butter fly effect (extreme sensitivity to initial
conditions), named by Lorentz, and the sort of butterfly shape of some
3 dimensional displays of the trajectory of the Lorentz attractor.
The butterfly effect does not refer to the shape of the attractor.

> > He modeled a 2 dimensional convection cell, with heat applied at the
> > bottom and lost at the top. This model convinced him that even
> > apparently simple systems like this exhibit chaotic operation under
> > some conditions, and so, the essence of the butterfly effect, and
> > that larger, more complicated (actual) weather systems mush have
> > this property, also.
>
> Are you sure you are not confusing it with the `Helium in a Small Box'
> experiment by Libchaber?

I read (in James Gleick's Chaos, I think) that the 3 equations that
demonstrate the Lorentz attractor are a simplified model of a 2
dimensional convection cell.
I also saw a television program on public TV in which Lorentz
explained how he came to discover the Lorentz attractor.

--
John Popelish

From:	Lou Pecora
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 12:37:43 -0500

In article ,
"Nicholas O. Lindan" wrote:

> Not to simulate, temperature as the system itself.

That doesn't make sense. It's the temperature of 'something.' What's
the something?

> > Being Cyclic is not a necessary trait of chaos.
>
> I think it is: if the values aren't cyclic then they have to
> march of to infinity (or the universe ends). They cycle around
> the 'attractor': a mean value.

What you mean here is bounded. The motion is bounded. And you are
correct that without that all trajectories might diverge to infinity.

The word 'cyclic' in most science and engineering usually means periodic
or nearly so or repeating. Chaotic motion does have periodic motions,
but these are unstable and the motion on the attractor is not cyclic
itself.

-- Lou Pecora (my views are my own)

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 02:26:13 GMT

"Lou Pecora" wrote

> > Not to simulate, temperature as the system itself.
>
> That doesn't make sense. It's the temperature of 'something.' What's
> the something?

Anything. A bad way of saying the universe is chaotic, and one can
pick any old measurement of it as an example: The temperature goes
up and down, staying within bounds and is only predictable in the
general sense.

Chaos is safe; order is dangerous. Although I imagine with a .mil
address you won't quite agree with that sentiment.

The universe also has a random factor so maybe chaotic isn't
the right category of things fuzzy.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	Lou Pecora
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 10:49:35 -0500

In article <9X4yd.7751$Z47.3483@newsread2.news.atl.earthlink.net>,
"Nicholas O. Lindan" wrote:

> Anything. A bad way of saying the universe is chaotic, and one can
> pick any old measurement of it as an example: The temperature goes
> up and down, staying within bounds and is only predictable in the
> general sense.

I don't understand that last sentence. Back to the original request:
How do you design a circuit to model the temperature of "Anything."

> Chaos is safe; order is dangerous.

Huh?

> Although I imagine with a .mil
> address you won't quite agree with that sentiment.

Best not to assume what anybody thinks based on their email address.

-- Lou Pecora (my views are my own)

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 17:06:36 GMT

"Lou Pecora" wrote
> "Nicholas O. Lindan" wrote:
>
> > ... the universe is chaotic, and one can pick any old measurement
> > of it as an example

> I don't understand that last sentence. Back to the original request:
> How do you design a circuit to model the temperature of "Anything."

I'm lost here. I think we are talking about two different things. Best
drop it.

> > Chaos is safe; order is dangerous.
> Huh?

Chaos is bounded. Order isn't.
"Muddle on Through" Vs "Alles in Ordnung".

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	Pig Bladder
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Thu, 23 Dec 2004 02:47:47 GMT

On Wed, 22 Dec 2004 17:06:36 +0000, Nicholas O. Lindan wrote:

> "Lou Pecora" wrote
>> "Nicholas O. Lindan" wrote:
>>
>> > ... the universe is chaotic, and one can pick any old measurement
>> > of it as an example
>
>> I don't understand that last sentence. Back to the original request:
>> How do you design a circuit to model the temperature of "Anything."
>
> I'm lost here. I think we are talking about two different things. Best
> drop it.
>
>> > Chaos is safe; order is dangerous.
>> Huh?
>
> Chaos is bounded. Order isn't.
> "Muddle on Through" Vs "Alles in Ordnung".

Chaos is Life. Order is Death.
Take your pick! ;-)
--
The Pig Bladder From Uranus, still waiting for
some hot babe to ask what my favorite planet is.

From:	Rich Grise
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 02:55:01 GMT

On Mon, 20 Dec 2004 20:24:33 +0000, Nicholas O. Lindan wrote:

> wrote
>
>> Are there any other simplistic chaotic systems to try next?
>
> The temperature, Down Jones average, height of blades of grass ...
>
> All constrained, cyclic and unpredictable.
>
> It's not chaos that's the odd duck in the universe, the
> odd duck is deterministic mathematics. There is _nothing_
> in this universe that repeats itself, let me repeat that...
>
> "God created real numbers, Man made the integers",
>
> - Somebody famous, if you move
> in the right circles, but I
> forgot his name.
>
> "And the Devil made 0 and infinity"
>
> - Me, but I am sure Somebody
> Else wrote it down first

I heard that the Big Bang was what happened when God tried to divide by
zero. ;-)

Cheers!
Rich

From:	Jürgen_Kahrs
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 00:19:24 +0100

Nicholas O. Lindan wrote:

> It's not chaos that's the odd duck in the universe, the
> odd duck is deterministic mathematics. There is _nothing_
> in this universe that repeats itself, let me repeat that...

Determinism is a necessary ingredient of chaos.
There is no contradiction between them.
Remember that chaos and determinism are idealistic
notions, while observations of physical objects
are always approximations. You should not mix up
ideals with material stuff.

> "God created real numbers, Man made the integers",
>
> - Somebody famous, if you move
> in the right circles, but I
> forgot his name.

Kronecker

> "And the Devil made 0 and infinity"
>
> - Me, but I am sure Somebody
> Else wrote it down first

It is the Inuitionist/Constructivist (Brouwer)
school of thought in mathematics which avoids
the use of infinity.

From:	Lou Pecora
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 09:09:37 -0500

In article <32p501F3qf8taU1@individual.net>,
Jurgen Kahrs wrote:

> It is the Inuitionist/Constructivist (Brouwer)
> school of thought in mathematics which avoids
> the use of infinity.

I don't recall that they avoid the use of zero. Or maybe I am
mis-remembering.

-- Lou Pecora (my views are my own)

From:	Jürgen_Kahrs
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Tue, 21 Dec 2004 17:38:56 +0100

Lou Pecora wrote:

>>It is the Inuitionist/Constructivist (Brouwer)
>>school of thought in mathematics which avoids
>>the use of infinity.
>
>
> I don't recall that they avoid the use of zero. Or maybe I am
> mis-remembering.

Zero is quite acceptable to them.