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 | | From: | Boris Mohar | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Mon, 20 Dec 2004 12:14:54 -0500 |
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 | On 20 Dec 2004 08:04:26 -0800, shoppa@trailing-edge.com wrote:
>I had some fun this past weekend building an analog computer to
>integrate the Lorenz equations. I started with Paul Horowitz's
>design at
>
>http://frank.harvard.edu/~paulh/misc/lorenz.htm
>
>and added some frills like a rotary switch to select the
>integration capacitor sizes and 10-turn pots and knobs for the
>s, r, and b parameters that allow you to turn them and see the
>attractor change in real time as you twist knobs. Lotsa fun.
>
>Display is on a 10" X-Y scope so the results are richly displayed.
>By moving the patch wires you get to view x, y, z, dx/dt, dy/dt, or
>dz/dt.
>
>Are there any other simplistic chaotic systems to try next? Having
>a small number of parameters is good (to keep the number of knobs
>reasonable) and analog multipliers aren't the cheapest thing in the
>world so it's nice to keep the number of analog multipliers
>necessary small too. (Note that multiplication by a constant is
>usually handled by a fixed resistor divider and multiplication by
>a parameter is usually handled by a potentiometer divider. It's
>only terms like "xy" that need true analog multipliers.)
>
>Even with the Lorenz equations I think that alternative ways of
>"seeing"
>the chaoticity may be useful. For example, right now I'm trying to
>imagine how to present the results through audio, so that a "left
>lobe spiral" might sound different than a "right lobe spiral", and
>maybe even modulate it according to the depth in/out of a spiral.
>(If you haven't seen the equations solved real-time you might not
>know what I mean about the spirals: in the x-z plane there are two
>lobes of semi-periodicity, and on the scope screen at the slower
>integration speeds you see outward spirals from each attractor
>until a switchover point is reached and you end up in the other
>lobe.)
>
>Any other ideas you guys might have?
>
>Tim.
Three very loosely coupled oscillators of similar frequencies. Will they
lock to common frequency or will they be chaotic?
--
Boris Mohar
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| | From: | Stefan Heinzmann | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Mon, 20 Dec 2004 21:34:46 +0100 |
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| Boris Mohar wrote:
> On 20 Dec 2004 08:04:26 -0800, shoppa@trailing-edge.com wrote:
>>I had some fun this past weekend building an analog computer to
>>integrate the Lorenz equations. I started with Paul Horowitz's
>>design at
>>
>>http://frank.harvard.edu/~paulh/misc/lorenz.htm
Here's another implementation:
http://www.electronicsletters.com/papers/0012/paper.html
--
Cheers
Stefan
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