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tech / sci.math / Beautiful and Interesting Attractors (3)

SubjectAuthor
* Beautiful and Interesting Attractors (3)casagiannoni
+* Re: Beautiful and Interesting Attractors (3)Mina Arvuti lähedal
|`- Re: Beautiful and Interesting Attractors (3)casagiannoni
`* Re: Beautiful and Interesting Attractors (3)sobriquet
 +* Re: Beautiful and Interesting Attractors (3)sobriquet
 |`- Re: Beautiful and Interesting Attractors (3)Chris M. Thomasson
 `* Re: Beautiful and Interesting Attractors (3)casagiannoni
  `* Re: Beautiful and Interesting Attractors (3)sobriquet
   `* Re: Beautiful and Interesting Attractors (3)casagiannoni
    +- Re: Beautiful and Interesting Attractors (3)casagiannoni
    `* Re: Beautiful and Interesting Attractors (3)sobriquet
     `- Re: Beautiful and Interesting Attractors (3)casagiannoni

1
Beautiful and Interesting Attractors (3)

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Subject: Beautiful and Interesting Attractors (3)
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 by: casagian...@optimum.net - Sun, 30 May 2021 13:34 UTC

A certain type of system has progressive states as represented by
points on the XY coordinate plane. If totally chaotic, then points
would range evenly over the plane, but these systems have strong
attractors that are often beautiful and /or interesting.

Check out a sample of 12 from a library of 512 :
https://postimg.cc/gallery/JB8TtTj

Free Windows software and a detailed descriptive paper are available.

Note capture of program on system 93 :
https://postimg.cc/F7pdpQd1

Post or Email casagiannoni@optonline.net or
631 757 2793 ( calls screened, leave message )

Re: Beautiful and Interesting Attractors (3)

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Subject: Re: Beautiful and Interesting Attractors (3)
From: ya12...@mail.com (Mina Arvuti lähedal)
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 by: Mina Arvuti lähedal - Sun, 30 May 2021 18:46 UTC

casagi...@optimum.net kirjutas pühapäev, 30. mai 2021 kl 16:34:45 UTC+3:
> A certain type of system has progressive states as represented by
> points on the XY coordinate plane. If totally chaotic, then points
> would range evenly over the plane, but these systems have strong
> attractors that are often beautiful and /or interesting.
>
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Re: Beautiful and Interesting Attractors (3)

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Subject: Re: Beautiful and Interesting Attractors (3)
From: dohduh...@yahoo.com (sobriquet)
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 by: sobriquet - Sun, 30 May 2021 19:38 UTC

On Sunday, May 30, 2021 at 3:34:45 PM UTC+2, casagi...@optimum.net wrote:
> A certain type of system has progressive states as represented by
> points on the XY coordinate plane. If totally chaotic, then points
> would range evenly over the plane, but these systems have strong
> attractors that are often beautiful and /or interesting.
>
> Check out a sample of 12 from a library of 512 :
> https://postimg.cc/gallery/JB8TtTj
>
> Free Windows software and a detailed descriptive paper are available.
>
> Note capture of program on system 93 :
> https://postimg.cc/F7pdpQd1
>
> Post or Email casagi...@optonline.net or
> 631 757 2793 ( calls screened, leave message )

Maybe it would be nice to implement more colorful versions of these in a desmos demo.
That way you can rotate them to view them from any direction or zoom in to explore details.

https://www.reddit.com/r/desmos/comments/nmqmtl/the_attractor_simulator_halvorsen_attractor/

Re: Beautiful and Interesting Attractors (3)

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Subject: Re: Beautiful and Interesting Attractors (3)
From: dohduh...@yahoo.com (sobriquet)
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 by: sobriquet - Sun, 30 May 2021 19:50 UTC

On Sunday, May 30, 2021 at 9:38:18 PM UTC+2, sobriquet wrote:
> On Sunday, May 30, 2021 at 3:34:45 PM UTC+2, casagi...@optimum.net wrote:
> > A certain type of system has progressive states as represented by
> > points on the XY coordinate plane. If totally chaotic, then points
> > would range evenly over the plane, but these systems have strong
> > attractors that are often beautiful and /or interesting.
> >
> > Check out a sample of 12 from a library of 512 :
> > https://postimg.cc/gallery/JB8TtTj
> >
> > Free Windows software and a detailed descriptive paper are available.
> >
> > Note capture of program on system 93 :
> > https://postimg.cc/F7pdpQd1
> >
> > Post or Email casagi...@optonline.net or
> > 631 757 2793 ( calls screened, leave message )
> Maybe it would be nice to implement more colorful versions of these in a desmos demo.
> That way you can rotate them to view them from any direction or zoom in to explore details.
>
> https://www.reddit.com/r/desmos/comments/nmqmtl/the_attractor_simulator_halvorsen_attractor/

Shadertoy also has some cool attractor visualizations (some are both interactive and colorful).

https://www.shadertoy.com/view/3tccWs
https://www.shadertoy.com/view/Ws3cz8

This doesn't seem to be an attractor, but still a very nice colorful visualization of dynamic curves.
https://www.shadertoy.com/view/tty3zc

Re: Beautiful and Interesting Attractors (3)

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From: casagian...@optimum.net
Newsgroups: sci.math
Subject: Re: Beautiful and Interesting Attractors (3)
Message-ID: <4418bg90d71dndhll404ifmnnahjst6g3h@4ax.com>
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 by: casagian...@optimum.net - Sun, 30 May 2021 21:40 UTC

>
>Maybe it would be nice to implement more colorful versions of these in a desmos demo.
>That way you can rotate them to view them from any direction or zoom in to explore details.
>

These are very specific entities in 2 dimensions with colors specified
as described in a descriptive paper. It is not possible to either
rotate or translate them. Anyone Email casagiannoni@optonline.net and
I'll send the paper. Very interesting read !

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Subject: Re: Beautiful and Interesting Attractors (3)
From: dohduh...@yahoo.com (sobriquet)
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 by: sobriquet - Sun, 30 May 2021 22:53 UTC

On Sunday, May 30, 2021 at 11:40:47 PM UTC+2, casagi...@optimum.net wrote:
> >
> >Maybe it would be nice to implement more colorful versions of these in a desmos demo.
> >That way you can rotate them to view them from any direction or zoom in to explore details.
> >
> These are very specific entities in 2 dimensions with colors specified
> as described in a descriptive paper. It is not possible to either
> rotate or translate them. Anyone Email casagi...@optonline.net and
> I'll send the paper. Very interesting read !

Can't the paper simply be shared via a link?
Like convert it to pdf and use a free hosting site.

https://pdfhost.io/

Re: Beautiful and Interesting Attractors (3)

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From: casagian...@optimum.net
Newsgroups: sci.math
Subject: Re: Beautiful and Interesting Attractors (3)
Message-ID: <gpo9bgto8abse2ugkjvdb37ftcdjqvdi3m@4ax.com>
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 by: casagian...@optimum.net - Mon, 31 May 2021 13:30 UTC

>
>Can't the paper simply be shared via a link?
>Like convert it to pdf and use a free hosting site.
>
>https://pdfhost.io/

The paper is a Word doc, not a PDF, though I suppose it could be
converted, though offhand I don't know how. I had put it on SCRIBD
( https://www.scribd.com/document/482630123/SA18-Paper ), but there
seems to be some problem there.

Re: Beautiful and Interesting Attractors (3)

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Newsgroups: sci.math
Subject: Re: Beautiful and Interesting Attractors (3)
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 by: casagian...@optimum.net - Mon, 31 May 2021 14:12 UTC

>
>The paper is a Word doc, not a PDF, though I suppose it could be
>converted, though offhand I don't know how. I had put it on SCRIBD
> ( https://www.scribd.com/document/482630123/SA18-Paper ), but there
>seems to be some problem there.

The version on SCRIBD is out of date and corrections have been made.

Re: Beautiful and Interesting Attractors (3)

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Subject: Re: Beautiful and Interesting Attractors (3)
From: dohduh...@yahoo.com (sobriquet)
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 by: sobriquet - Mon, 31 May 2021 14:17 UTC

On Monday, May 31, 2021 at 3:30:47 PM UTC+2, casagi...@optimum.net wrote:
> >
> >Can't the paper simply be shared via a link?
> >Like convert it to pdf and use a free hosting site.
> >
> >https://pdfhost.io/
> The paper is a Word doc, not a PDF, though I suppose it could be
> converted, though offhand I don't know how. I had put it on SCRIBD
> ( https://www.scribd.com/document/482630123/SA18-Paper ), but there
> seems to be some problem there.

Ah, yes, scribd is a bit annoying in that it requires people to sign up to view other people's
uploads.

Don't these attractors generalize in a natural way from 2D to 3D? (Similar how a sphere in 3D is a natural
generalization of a circle in 2D.)

Re: Beautiful and Interesting Attractors (3)

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From: casagian...@optimum.net
Newsgroups: sci.math
Subject: Re: Beautiful and Interesting Attractors (3)
Message-ID: <mqbabgp8d6fmlq0s8v76sh64sjrsgdvq81@4ax.com>
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 by: casagian...@optimum.net - Mon, 31 May 2021 18:52 UTC

>Ah, yes, scribd is a bit annoying in that it requires people to sign up to view other people's
>uploads.
>
>Don't these attractors generalize in a natural way from 2D to 3D? (Similar how a sphere in 3D is a natural
>generalization of a circle in 2D.)

I don't think so. They are not images in the usual sense.

Best if you ( or anyone ) Email to casagiannoni@optonline.net to get a
copy of the paper which tells all.

Re: Beautiful and Interesting Attractors (3)

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From: chris.m....@gmail.com (Chris M. Thomasson)
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Subject: Re: Beautiful and Interesting Attractors (3)
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 by: Chris M. Thomasson - Mon, 31 May 2021 22:00 UTC

On 5/30/2021 12:50 PM, sobriquet wrote:
> On Sunday, May 30, 2021 at 9:38:18 PM UTC+2, sobriquet wrote:
>> On Sunday, May 30, 2021 at 3:34:45 PM UTC+2, casagi...@optimum.net wrote:
>>> A certain type of system has progressive states as represented by
>>> points on the XY coordinate plane. If totally chaotic, then points
>>> would range evenly over the plane, but these systems have strong
>>> attractors that are often beautiful and /or interesting.
>>>
>>> Check out a sample of 12 from a library of 512 :
>>> https://postimg.cc/gallery/JB8TtTj
>>>
>>> Free Windows software and a detailed descriptive paper are available.
>>>
>>> Note capture of program on system 93 :
>>> https://postimg.cc/F7pdpQd1
>>>
>>> Post or Email casagi...@optonline.net or
>>> 631 757 2793 ( calls screened, leave message )
>> Maybe it would be nice to implement more colorful versions of these in a desmos demo.
>> That way you can rotate them to view them from any direction or zoom in to explore details.
>>
>> https://www.reddit.com/r/desmos/comments/nmqmtl/the_attractor_simulator_halvorsen_attractor/
>
> Shadertoy also has some cool attractor visualizations (some are both interactive and colorful).
>
> https://www.shadertoy.com/view/3tccWs
> https://www.shadertoy.com/view/Ws3cz8
>
> This doesn't seem to be an attractor, but still a very nice colorful visualization of dynamic curves.
> https://www.shadertoy.com/view/tty3zc
>

Oh, those are GREAT examples! I have an idea on how to plot my vector
fields in Shadertoy using my line segment variation, and knew I had to
use a buffer. Still have not implemented it, but these will help me, big
time! Thanks.

:^)

1
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