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I've always referred to this type of space-filling curve as a Dragon Curve.
I'm not sure if that's its true mathematical name or not. Can anyone out
there identify this class of curves?
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Attachments:
Download 'Dragons5.JPG' (48 KB)
Preview of image 'Dragons5.JPG'
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I've seen these curves (they are very good to animate (change randomly the
orientation of each 1/4 tori), I made a 2D program to do that years ago)
under the name of "Truchet's Curves" from the name of Mr Truchet (don't ask
me who he is)
Philippe
>I've always referred to this type of space-filling curve as a Dragon Curve.
>I'm not sure if that's its true mathematical name or not. Can anyone out
>there identify this class of curves?
>
>
>
>
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Well, whoever he is, no matter, because the "fractal" of this particular
type thing is pretty darned interesting. You can see singular torii and
continuous curves stretching a great distance in eventual loops. And the
double lobed, triple lobed and all the rest. Very nice indeed.
Ph Gibone wrote:
>
> I've seen these curves (they are very good to animate (change randomly the
> orientation of each 1/4 tori), I made a 2D program to do that years ago)
> under the name of "Truchet's Curves" from the name of Mr Truchet (don't ask
> me who he is)
>
> Philippe
> >I've always referred to this type of space-filling curve as a Dragon Curve.
> >I'm not sure if that's its true mathematical name or not. Can anyone out
> >there identify this class of curves?
> >
> >
> >
> >
--
omniVERSE: beyond the universe
http://members.aol.com/inversez/homepage.htm
mailto://inversez@aol.com?Subject=PoV-News
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By the way I'm not sure they are fractal :-)
Philippe
>Well, whoever he is, no matter, because the "fractal" of this particular
>type thing is pretty darned interesting. You can see singular torii and
>continuous curves stretching a great distance in eventual loops. And the
>double lobed, triple lobed and all the rest. Very nice indeed.
>
>
>Ph Gibone wrote:
>>
>> I've seen these curves (they are very good to animate (change randomly
the
>> orientation of each 1/4 tori), I made a 2D program to do that years ago)
>> under the name of "Truchet's Curves" from the name of Mr Truchet (don't
ask
>> me who he is)
>>
>> Philippe
>> >I've always referred to this type of space-filling curve as a Dragon
Curve.
>> >I'm not sure if that's its true mathematical name or not. Can anyone out
>> >there identify this class of curves?
>> >
>> >
>> >
>> >
>
>--
> omniVERSE: beyond the universe
> http://members.aol.com/inversez/homepage.htm
> mailto://inversez@aol.com?Subject=PoV-News
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If who is Mr Truchet interests anyone :
Father Sebastien Truchet : He was born at Lyon in 1657, and is known for his
work in the definition of the metrics of fonts (that we still use !).
The drawing saw in the same thread is known as the Truchet-tiling.
I suppose they are the same people but not sure
Philippe
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For those of you who were interested, the results of this posting:
Thanks to Philippe for the information on the origins of this curve. I took
a look at the Truchet tiling, and it seems to be a bit simpler than the
space-filling-curve (SFC) that I submitted. I also looked into Dragon Curves
and confirmed that this is not of that classification. I was fooling around
with SFC's back in the early 80's and after so many years, my neurons are
all cross-linked between Hilbert, Sierpinsky, Peano, Dragon, etc.
This SFC is actually a simple contouring algorithm. I'd been tinkering with
this at the same time I was messing with the SFC's and subsequently merged
it in with the the other regular patterns.
In response to Bob Hughes suggestion that this has a "fractal" quality, I
have to agree. This is a fractal in the same sense that a plasma is a
fractal, i.e., the details are random, but the structure is coherent.
"Regular" SFC's such as Hilbert, Peano, etc., are recursive and predictable.
Philippe had suggested animating this, but I have to humbly admit that I
don't know how this might work. Philippe, please elaborate, se vous plez...
Last, but not least, thanks for everyone's comments and suggestions!
David Cook <nos### [at] home com> wrote in message
news:372b2123.0@news.povray.org...
> I've always referred to this type of space-filling curve as a Dragon
Curve.
> I'm not sure if that's its true mathematical name or not. Can anyone out
> there identify this class of curves?
Post a reply to this message
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Now theese look really cute... Hmm, lead water through them, an excellent heat
exchanger... (is that the name in english?) If they all were connected. that is.
David Cook wrote:
>
> I've always referred to this type of space-filling curve as a Dragon Curve.
> I'm not sure if that's its true mathematical name or not. Can anyone out
> there identify this class of curves?
>
> [Image]
--
//Spider -- [ spi### [at] bahnhofse ]-[ http://www.bahnhof.se/~spider/ ]
And the meek'll inherit what they damn well please
Get ahead, go figure, go ahead and pull the trigger
Everything under the gun
--"Sisters Of Mercy" -- "Under The Gun"
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Heat pump is what is commonly said around here. Heat exchanger sounds more
New England to me. I wondered about the animation aspect myself. Seems
impossible, how would the torii stay linked and yet move, aside from the
usual way? :)
Spider wrote:
>
> Now theese look really cute... Hmm, lead water through them, an excellent heat
> exchanger... (is that the name in english?) If they all were connected. that is.
>
> David Cook wrote:
> >
> > I've always referred to this type of space-filling curve as a Dragon Curve.
> > I'm not sure if that's its true mathematical name or not. Can anyone out
> > there identify this class of curves?
> >
> > [Image]
>
> --
> //Spider -- [ spi### [at] bahnhofse ]-[ http://www.bahnhof.se/~spider/ ]
> And the meek'll inherit what they damn well please
> Get ahead, go figure, go ahead and pull the trigger
> Everything under the gun
> --"Sisters Of Mercy" -- "Under The Gun"
--
omniVERSE: beyond the universe
http://members.aol.com/inversez/homepage.htm
mailto://inversez@aol.com?Subject=PoV-News
Post a reply to this message
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Philippe sent me an example of what he had in mind for animation. It was
simply re-randomizing the pattern, which isn't what I would consider
animation - the pattern just jumps around. I'm still thinking about it, but
I'm not sure a smooth animation can be done.
Bob Hughes <inv### [at] aolcom> wrote in message
news:372CDF29.6B21FE12@aol.com...
> Heat pump is what is commonly said around here. Heat exchanger sounds more
> New England to me. I wondered about the animation aspect myself. Seems
> impossible, how would the torii stay linked and yet move, aside from the
> usual way? :)
>
>
> Spider wrote:
> >
> > Now theese look really cute... Hmm, lead water through them, an
excellent heat
> > exchanger... (is that the name in english?) If they all were connected.
that is.
> >
> > David Cook wrote:
> > >
> > > I've always referred to this type of space-filling curve as a Dragon
Curve.
> > > I'm not sure if that's its true mathematical name or not. Can anyone
out
> > > there identify this class of curves?
> > >
> > > [Image]
> >
> > --
> > file://Spider --
[ spi### [at] bahnhofse ]-[ http://www.bahnhof.se/~spider/ ]
> > And the meek'll inherit what they damn well please
> > Get ahead, go figure, go ahead and pull the trigger
> > Everything under the gun
> > --"Sisters Of Mercy" -- "Under The Gun"
>
> --
> omniVERSE: beyond the universe
> http://members.aol.com/inversez/homepage.htm
> mailto://inversez@aol.com?Subject=PoV-News
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Spider wrote:
>
> Now theese look really cute... Hmm, lead water through them, an excellent heat
> exchanger... (is that the name in english?) If they all were connected. that is.
Radiator.
--
Ken Tyler
mailto://tylereng@pacbell.net
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