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http://vimeo.com/6797740?hd=1
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> http://vimeo.com/6797740?hd=1
>
Has anyone ever used a Julia fractal for anything other than these
trippy videos?
...Chambers
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Chambers wrote:
> Has anyone ever used a Julia fractal for anything other than these
> trippy videos?
I would guess there's at least one mathematical result of importance about
them, or we'd not be hearing about them so much.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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>> Has anyone ever used a Julia fractal for anything other than these
>> trippy videos?
>
> I would guess there's at least one mathematical result of importance
> about them, or we'd not be hearing about them so much.
Result #1: Simple dynamical systems can give rise to unpredictable
behaviour. (The system has to be non-linear though, even if only
slightly. A perfectly linear system does nothing interesting.)
Result #2: Every basin of attraction contains at least one critical
point of the map. (Only guaranteed for rational maps though.)
Result #3: The Julia set is the boundary of all basins of attraction
simultaneously. (Even if there are three attractors, every point of the
Julia set touches all three basins simultaneously - despite this being
obviously impossible.)
I could go on...
I have no idea whether these results have any particular *practical*
usage. But Julia sets do occasionally pop up when people aren't trying
to do anything related to computer graphics. (Ferromagnatic phase
renormalisation transforms, anyone?)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Darren New schrieb:
> http://vimeo.com/6797740?hd=1
Hey! That's on-topic, and therefore off-topic here...! ;-)
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"clipka" <ano### [at] anonymous org> wrote in message
news:4ac1d34c$1@news.povray.org...
> Darren New schrieb:
>> http://vimeo.com/6797740?hd=1
>
> Hey! That's on-topic, and therefore off-topic here...! ;-)
Careful... Someone reading this might be a computer/life form from the Star
Trek universe. Logic like that makes their heads explode.
With sparks, even.
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Captain Jack schrieb:
>> Hey! That's on-topic, and therefore off-topic here...! ;-)
>
> Careful... Someone reading this might be a computer/life form from the Star
> Trek universe. Logic like that makes their heads explode.
... or, worse yet, makes them raise a single eyebrow? :-)
LLAP
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"clipka" <ano### [at] anonymousorg> wrote in message
news:4ac239d1@news.povray.org...
> Captain Jack schrieb:
> ... or, worse yet, makes them raise a single eyebrow? :-)
>
> LLAP
Fascinating... 8)
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On Tue, 29 Sep 2009 11:28:35 +0200, clipka <ano### [at] anonymousorg> wrote:
>Darren New schrieb:
>> http://vimeo.com/6797740?hd=1
>
>Hey! That's on-topic, and therefore off-topic here...! ;-)
But if it is off topic here then here is the perfect place for it. I would think
;)
--
Regards
Stephen
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Chambers <Ben### [at] gmailcom> wrote:
> Has anyone ever used a Julia fractal for anything other than these
> trippy videos?
I don't know if the Julia fractal in particular has been used, but some
fractals have been used as counter-examples for some mathematical
conjectures, proving them wrong.
--
- Warp
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>> Hey! That's on-topic, and therefore off-topic here...! ;-)
>
> But if it is off topic here then here is the perfect place for it. I would think
> ;)
...did he just invoke the Liar Paradox?
I think he did, you know...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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"Orchid XP v8" <voi### [at] devnull> wrote in message
news:4ac261ea@news.povray.org...
>>> Hey! That's on-topic, and therefore off-topic here...! ;-)
>>
>> But if it is off topic here then here is the perfect place for it. I
>> would think
>> ;)
>
> ...did he just invoke the Liar Paradox?
>
> I think he did, you know...
Paging Dr. Hofstadter! Dr. Douglas Hofstadter, you have a call... Please
come to the front of the Internet.
(humming softly: It rained all night the day I left, the weather it was
dry...)
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On Tue, 29 Sep 2009 20:37:13 +0100, Orchid XP v8 <voi### [at] devnull> wrote:
>>> Hey! That's on-topic, and therefore off-topic here...! ;-)
>>
>> But if it is off topic here then here is the perfect place for it. I would think
>> ;)
>
>...did he just invoke the Liar Paradox?
>
Naw! But what ever I say is not true, Blue.
>I think he did, you know...
Strange, Loop!
--
Regards
Stephen
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On Tue, 29 Sep 2009 16:00:12 -0400, "Captain Jack" <Cap### [at] comcastnet>
wrote:
>"Orchid XP v8" <voi### [at] devnull> wrote in message
>news:4ac261ea@news.povray.org...
>>>> Hey! That's on-topic, and therefore off-topic here...! ;-)
>>>
>>> But if it is off topic here then here is the perfect place for it. I
>>> would think
>>> ;)
>>
>> ...did he just invoke the Liar Paradox?
>>
>> I think he did, you know...
>
>
>Paging Dr. Hofstadter! Dr. Douglas Hofstadter, you have a call... Please
>come to the front of the Internet.
>
>
>(humming softly: It rained all night the day I left, the weather it was
>dry...)
>
One fine day in the middle of the night,
Two dead men got up to fight;
Back-to-back they faced each other,
Drew their swords and shot each other.
;-)
--
Regards
Stephen
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>> ...did he just invoke the Liar Paradox?
>
> Naw! But what ever I say is not true, Blue.
>
>> I think he did, you know...
>
> Strange, Loop!
...and here I am crawling through BWV 590...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
> I don't know if the Julia fractal in particular has been used, but some
> fractals have been used as counter-examples for some mathematical
> conjectures, proving them wrong.
And they are, of course, fractals in general are useful for modeling all
kinds of physical stuff, like landscapes, etc. I just don't know I've seen
the Julian set that way.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> And they are, of course, fractals in general are useful for modeling all
> kinds of physical stuff, like landscapes, etc. I just don't know I've
> seen the Julian set that way.
The quadratic Julia set? There *are* others, you know... ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Darren New <dne### [at] sanrrcom> wrote:
> http://vimeo.com/6797740?hd=1
>
> --
> Darren New, San Diego CA, USA (PST)
> I ordered stamps from Zazzle that read "Place Stamp Here".
With that quality, would have liked to see what they could do with a
cross-section.
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gregjohn wrote:
> With that quality, would have liked to see what they could do with a
> cross-section.
That was a cross section. It's a 4D fractal. ;-)
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> http://vimeo.com/6797740?hd=1
I'm not impressed. So it looks like taffy. Big deal.
-Mike
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> I'm not impressed. So it looks like taffy. Big deal.
Yeah, well, Quaternions aren't a true number field. More like a simple
extension of the set of complex numbers - simple in that it's little
more than a surface of revolution.
What *I* like is 3D slices of the 4D cubic Mandelbrot set - but I don't
know of anything except POV-Ray that can render it. (And POV-Ray doesn't
do it terribly efficiently...)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Tue, 29 Sep 2009 21:54:36 +0100, Orchid XP v8 <voi### [at] devnull> wrote:
>>> ...did he just invoke the Liar Paradox?
>>
>> Naw! But what ever I say is not true, Blue.
>>
>>> I think he did, you know...
>>
>> Strange, Loop!
>
>...and here I am crawling through BWV 590...
Now that is one to play "with feeling" :)
--
Regards
Stephen
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On Wed, 30 Sep 2009 08:05:38 +0100, Orchid XP v8 <voi### [at] devnull> wrote:
>
>What *I* like is 3D slices of the 4D cubic Mandelbrot set - but I don't
>know of anything except POV-Ray that can render it. (And POV-Ray doesn't
>do it terribly efficiently...)
Since you mention it google buddhabrot
Also
http://en.wikipedia.org/wiki/Buddhabrot
--
Regards
Stephen
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>> ...and here I am crawling through BWV 590...
>
> Now that is one to play "with feeling" :)
Ah, I see. I was playing it with a small pipe organ...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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SharkD wrote:
> Darren New wrote:
>> http://vimeo.com/6797740?hd=1
>
> I'm not impressed. So it looks like taffy. Big deal.
Perhaps you missed the title of the post? ;-)
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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On Wed, 30 Sep 2009 15:28:28 +0100, Orchid XP v8 <voi### [at] devnull> wrote:
>>> ...and here I am crawling through BWV 590...
>>
>> Now that is one to play "with feeling" :)
>
>Ah, I see. I was playing it with a small pipe organ...
Too much information :-)
--
Regards
Stephen
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Stephen wrote:
> Since you mention it google buddhabrot
> Also
> http://en.wikipedia.org/wiki/Buddhabrot
This site is pretty awesome.
http://www.enchgallery.com/fractals/fracthumbs.htm
-Mike
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SharkD wrote:
> This site is pretty awesome.
>
> http://www.enchgallery.com/fractals/fracthumbs.htm
Actually yes.
[Which is unusual, I should point out...]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Wed, 30 Sep 2009 16:26:53 -0400, SharkD <mik### [at] gmailcom> wrote:
>Stephen wrote:
>> Since you mention it google buddhabrot
>> Also
>> http://en.wikipedia.org/wiki/Buddhabrot
>
>This site is pretty awesome.
>
>http://www.enchgallery.com/fractals/fracthumbs.htm
>
It is too :D
--
Regards
Stephen
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