All that amazing mandelbulb stuff has inspired me to dig out a strange 
attractor search/plot app I wrote a few years ago, and try to get some 
decent plots into POV-Ray. Here's a few of the nicer ones I've found 
over the last couple of weeks.

Bill

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Attachments:
Download 'dancer.jpg' (90 KB) Download 'shuriken.jpg' (96 KB) Download 'scribble.jpg' (88 KB) Download 'topshell.jpg' (84 KB) Download 'loop.jpg' (81 KB) Download 'barbwire.jpg' (70 KB) Download 'ribbons.jpg' (81 KB) Download 'hook.jpg' (62 KB) Download 'spidery.jpg' (74 KB) Download 'crownothorns.jpg' (72 KB)

Preview of image 'dancer.jpg'

Preview of image 'shuriken.jpg'

Preview of image 'scribble.jpg'

Preview of image 'topshell.jpg'

Preview of image 'loop.jpg'

Preview of image 'barbwire.jpg'

Preview of image 'ribbons.jpg'

Preview of image 'hook.jpg'

Preview of image 'spidery.jpg'

Preview of image 'crownothorns.jpg'

"Bill Pragnell" <bil### [at] hotmailcom> wrote in message 
news:4b1c3281@news.povray.org...
> All that amazing mandelbulb stuff has inspired me to dig out a strange
> attractor search/plot app I wrote a few years ago, and try to get some
> decent plots into POV-Ray. Here's a few of the nicer ones I've found
> over the last couple of weeks.
>
> Bill
>

AWESOME!!!!

Really, they are WOW images to me :)

I'd love to know some more about how you did this!

Cheers Dre

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Lovely...Just lovely!

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Now model a modern art gallery and put these on pedestals therein.

--
Tim Cook
http://empyrean.freesitespace.net

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Bill Pragnell wrote:

> Here's a few of the nicer ones I've found 
> over the last couple of weeks.

Neat! I take it these images are essentially an exorbitant
number of spheres around externally generated data points?

I wondered if it's a blob but I thought some transitions
didn't quite look like it, although it's hard to tell
with the small object size. If it's spheres it might
be worth to try a blob for faster rendering.

Post a reply to this message

"Bill Pragnell" <bil### [at] hotmailcom> schreef in bericht 
news:4b1c3281@news.povray.org...
> All that amazing mandelbulb stuff has inspired me to dig out a strange
> attractor search/plot app I wrote a few years ago, and try to get some
> decent plots into POV-Ray. Here's a few of the nicer ones I've found
> over the last couple of weeks.
>

Strange and attractive, Bill :)

Good work!

Thomas

Post a reply to this message

"Dre" <and### [at] gmailcom> wrote:
> Really, they are WOW images to me :)

Thanks! It's just a shame they don't look as good at higher resolutions.

> I'd love to know some more about how you did this!

Most of the work is done externally, I'm really only using POV-Ray to plot a
dataset and do pretty lighting. I used some of the equations given on the
Chaoscope website (http://www.chaoscope.org/doc/attractors.htm), originally in a
Java app (the quickest way I knew to implement some sort of gui at the time).
Basically, if the orbit doesn't collapse or escape within a few hundred
iterations I plot it properly for inspection. Most of these turn out to be
mundane, but every now and again an 'interesting' one crops up. At this point I
save the equation coefficients in a data file.

Java is entirely unsuitable for iterating 1e8 points over a 30+ coefficient
dynamical system, so eventually I wrote a simple tool in C++ to do some proper
plotting from the saved coefficients, and (optionally) to write a text file full
of vectors suitable for reading from POV-Ray SDL.

Add some random lights using the data file as a seed, and away we go...

:)

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Tim Cook <z99### [at] gmailcom> wrote:
> Now model a modern art gallery and put these on pedestals therein.

Good idea! I could make some of them really big, put 2D plots in picture
frames... *gazes into middle distance*

Post a reply to this message

Christian Froeschlin <chr### [at] chrfrde> wrote:
> Neat! I take it these images are essentially an exorbitant
> number of spheres around externally generated data points?

Exactly right. :) (See my other post for my somewhat hacky workflow)

The data files vary in size from a few 100k for the thin spindly ones, up to
20MB+ for the more voluminous ones. Luckily even the vast ones are pretty quick
to produce from just the equation coefficient data. The slowest part appears to
be writing the data file!

> I wondered if it's a blob but I thought some transitions
> didn't quite look like it, although it's hard to tell
> with the small object size. If it's spheres it might
> be worth to try a blob for faster rendering.

I tried blobs, but they turn out to be many times slower for this case. These do
use radiosity and multiple area_lights, after all. With antialiasing off, they
render in a couple of minutes (parsing can be longer!). With AA on, an hour or
so.

Actually I quite like the expanded-polystyrene/gritty look that bare spheres
produce!

Post a reply to this message

I Really love "barbwire"... How did you code these ?

  Bill Pragnell a écrit :
> All that amazing mandelbulb stuff has inspired me to dig out a strange 
> attractor search/plot app I wrote a few years ago, and try to get some 
> decent plots into POV-Ray. Here's a few of the nicer ones I've found 
> over the last couple of weeks.
> 
> Bill
> 
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Post a reply to this message

Bill Pragnell <bil### [at] hotmailcom> wrote:
> All that amazing mandelbulb stuff has inspired me to dig out a strange
> attractor search/plot app I wrote a few years ago, and try to get some
> decent plots into POV-Ray. Here's a few of the nicer ones I've found
> over the last couple of weeks.
>
> Bill

Excellent really interesting shapes, I don't think I will even try to understand
how they were made and just accept I should have paid more attention at school.
It's a shame they don't look as good at high resolutions you could make some
fairly good abstract poster art.

Sean

Post a reply to this message

Bill Pragnell a écrit :
> Tim Cook <z99### [at] gmailcom> wrote:
>> Now model a modern art gallery and put these on pedestals therein.
> 
> Good idea! I could make some of them really big, put 2D plots in picture
> frames... *gazes into middle distance*
> 
> 
Beter yet:

Make them *for real!*


Alain

Post a reply to this message

Bill Pragnell a écrit :
> Christian Froeschlin <chr### [at] chrfrde> wrote:
>> Neat! I take it these images are essentially an exorbitant
>> number of spheres around externally generated data points?
> 
> Exactly right. :) (See my other post for my somewhat hacky workflow)
> 
> The data files vary in size from a few 100k for the thin spindly ones, up to
> 20MB+ for the more voluminous ones. Luckily even the vast ones are pretty quick
> to produce from just the equation coefficient data. The slowest part appears to
> be writing the data file!
> 
>> I wondered if it's a blob but I thought some transitions
>> didn't quite look like it, although it's hard to tell
>> with the small object size. If it's spheres it might
>> be worth to try a blob for faster rendering.
> 
> I tried blobs, but they turn out to be many times slower for this case. These do
> use radiosity and multiple area_lights, after all. With antialiasing off, they
> render in a couple of minutes (parsing can be longer!). With AA on, an hour or
> so.
> 
> Actually I quite like the expanded-polystyrene/gritty look that bare spheres
> produce!
> 
> 

You could output as DF3 file and render as an isosurface. You also could 
render those as media. It can be worth a try.



Alain

Post a reply to this message

Alain <aze### [at] qwertyorg> wrote:
> You could output as DF3 file and render as an isosurface. You also could
> render those as media. It can be worth a try.

That was the first method I tried. However, the df3 is very wasteful since most
of the volume is empty. Furthermore, the df3s for these examples would be at
least 512MB each! During testing at ~100x100x100, I found that generating,
reading in and rendering a df3 was much slower than the method I'm currently
using for a volume 64x larger.

I'm using a 3d vector<bool> to store the volume during iteration, then only
write out the voxel coordinates that were hit. That way, memory usage and file
size is at a minimum and I throw away all the empty locations. Unfortunately, I
also throw away the cumulative information, but it's very quick to iterate so
I'll probably come back and do something with it in future.

Bill

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LightBeam <seb### [at] gmailcom> wrote:
> I Really love "barbwire"...

Yes, I like that one too - looks like the Sorting Hat from Harry Potter!

>How did you code these ?

The equations can be found here:

http://www.chaoscope.org/doc/attractors.htm

Using different coefficients in these equations produces different attractors
(although most combinations don't produce an attractor - you need to 'search'
random combinations of coefficients to find interesting shapes). Each new point
is calculated from the previous point, and the attractor is built up point by
point. It's just a matter of storing those points and plotting them, either as a
2D projection, or in 3D.

I wrote a java app some time ago to search for and plot attractors, but I had to
rewrite the plotting in C++ (for speed) to get data files that I could then read
into POV-Ray.

Bill

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Looks like a job for a 3D printer!   :-)

Here's one for only $5000:  http://www.desktopfactory.com/our_product/



On 2009-12-07 21:14, Alain wrote:
> Bill Pragnell a écrit :
>> Tim Cook <z99### [at] gmailcom> wrote:
>>> Now model a modern art gallery and put these on pedestals therein.
>>
>> Good idea! I could make some of them really big, put 2D plots in picture
>> frames... *gazes into middle distance*
>>
>>
> Beter yet:
>
> Make them *for real!*
>
>
> Alain

Post a reply to this message

Rick Gutleber a écrit :
> Looks like a job for a 3D printer!   :-)
> 
> Here's one for only $5000:  http://www.desktopfactory.com/our_product/
> 
> 
> 
> On 2009-12-07 21:14, Alain wrote:
>> Bill Pragnell a écrit :
>>> Tim Cook <z99### [at] gmailcom> wrote:
>>>> Now model a modern art gallery and put these on pedestals therein.
>>>
>>> Good idea! I could make some of them really big, put 2D plots in picture
>>> frames... *gazes into middle distance*
>>>
>>>
>> Beter yet:
>>
>> Make them *for real!*
>>
>>
>> Alain
> 

I've seen one made out from an old ploter converted with the laser from 
an old fax machine. You can also reuse one from any old laser printer. 
It could create stuning models out of ordinary sugar with a granyness of 
about 0.5mm.
It can be home made for under $100 or about, and the functioning cost is 
prety low.



Alain

Post a reply to this message

I've seen demos of that as well.  In one instance, they "printed" a 
chain made out of sugar, with the links already connected.

The raw materials are very cheap.  It's a fast-moving field of research 
and development.  Very exciting stuff.  In another 10 years, we might 
have machine to fabricate 3D objects out of all kinds of materials, 
including food!

Imagine the possibilities:

Strange Attractor Crackers
Chocolate Mandelbulbs
Menger Sponge Cake
Cantor Cheese Logs
Moebius Strip Steaks
Solenoid Licorice
(see http://www.dgp.toronto.edu/~mjmcguff/codeGallery/*)

Rick

* Many years ago, I wrote code to generate Pickover's solenoids in POV-Ray.


On 2009-12-08 13:36, Alain wrote:
> Rick Gutleber a écrit :
>> Looks like a job for a 3D printer! :-)
>>
>> Here's one for only $5000: http://www.desktopfactory.com/our_product/
>>
>>
>>
>> On 2009-12-07 21:14, Alain wrote:
>>> Bill Pragnell a écrit :
>>>> Tim Cook <z99### [at] gmailcom> wrote:
>>>>> Now model a modern art gallery and put these on pedestals therein.
>>>>
>>>> Good idea! I could make some of them really big, put 2D plots in
>>>> picture
>>>> frames... *gazes into middle distance*
>>>>
>>>>
>>> Beter yet:
>>>
>>> Make them *for real!*
>>>
>>>
>>> Alain
>>
>
> I've seen one made out from an old ploter converted with the laser from
> an old fax machine. You can also reuse one from any old laser printer.
> It could create stuning models out of ordinary sugar with a granyness of
> about 0.5mm.
> It can be home made for under $100 or about, and the functioning cost is
> prety low.
>
>
>
> Alain

Post a reply to this message

They didn't teach anything like that when I was in school, although I 
still didn't pay enough attention.

My mind managed to completely block out all memories of differential 
equations completely.  To this day I couldn't tell you the first thing 
about them.  :-)

But thanks to POV-Ray, I'm very comfortable with trigonometry!

On 2009-12-07 16:31, s.day wrote:
> Bill Pragnell<bil### [at] hotmailcom>  wrote:
>> All that amazing mandelbulb stuff has inspired me to dig out a strange
>> attractor search/plot app I wrote a few years ago, and try to get some
>> decent plots into POV-Ray. Here's a few of the nicer ones I've found
>> over the last couple of weeks.
>>
>> Bill
>
> Excellent really interesting shapes, I don't think I will even try to understand
> how they were made and just accept I should have paid more attention at school.
> It's a shame they don't look as good at high resolutions you could make some
> fairly good abstract poster art.
>
> Sean
>

Post a reply to this message

Rick Gutleber <ric### [at] hiscom> wrote:
> They didn't teach anything like that when I was in school, although I
> still didn't pay enough attention.
>
> My mind managed to completely block out all memories of differential
> equations completely.  To this day I couldn't tell you the first thing
> about them.  :-)
>
> But thanks to POV-Ray, I'm very comfortable with trigonometry!

I'm sure I would have paid a lot more attention if they had used POV to try to
teach me (although I don't think it was around back then...). Still, my daughter
was the only pupil in her class that knew what a radius was as she had asked me
how I created pictures on the computer and I had shown her how to make a very
basic scene. I'm sure using something like POV would make the lessons much more
memorable.

Sean

Post a reply to this message

Bill Pragnell <bil### [at] hotmailcom> wrote:
> All that amazing mandelbulb stuff has inspired me to dig out a strange
> attractor search/plot app I wrote a few years ago, and try to get some
> decent plots into POV-Ray. Here's a few of the nicer ones I've found
> over the last couple of weeks.
>
> Bill

Wow, those are awesome Bill! I wrote a little app a couple of years back to plot
2d attractors but never came up with anything as cool as your 3d versions. The
renders are very artistically done - I love the lighting.

Seeing these made me go searching through my own stuff - here's one I did that's
a "morph" between two attractors. I loaded the data sets into SDL arrays and
used elements from each array as cylinder endpoints (with gradient pigments
along their arbitrary axes). Good times.

Rob

http://www.McGregorFineArt.com

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Attachments:
Download 'attractormorph1.png' (2179 KB)

Preview of image 'attractormorph1.png'

And here's another one where I used the attractor data to generate a height
field and associated pigment.

:)

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Attachments:
Download 'attractor_hftest2.png' (1430 KB)

Preview of image 'attractor_hftest2.png'

"Robert McGregor" <rob### [at] mcgregorfineartcom> wrote:
> Wow, those are awesome Bill!

Thanks!

> 2d attractors but never came up with anything as cool as your 3d versions. The
> renders are very artistically done - I love the lighting.

Random colours and positions, seeded by the data file. Usually needs a bit of a
tweak to get a nice combo, but quite handy!

> Seeing these made me go searching through my own stuff - here's one I did that's
> a "morph" between two attractors.

Looks interesting - it's a pity you can't quite make out the attractors'
shapes... good idea though. I might try an animation using my sphere technique,
if I turn off AA they only take a minute or so.

Bill

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Gobsmackingly goodlooking!

But I think you got the spidery one wrong:  looks more like a butterfly and a
very good looking one at that!

Povray abstracts at its best, ladies and gentleman! :D

Post a reply to this message

"nemesis" <nam### [at] gmailcom> wrote:
> But I think you got the spidery one wrong:  looks more like a butterfly and a
> very good looking one at that!

Hehe, naming was an issue, until I decided to call them the first noun that came
to mind when looking at the 2D plot. Some of them look utterly different in
3D... :)

> Povray abstracts at its best, ladies and gentleman! :D

There's plenty more. I'll put them all up on a web page at some point :)

Post a reply to this message

Robert McGregor wrote:

> Seeing these made me go searching through my own stuff - here's one I did that's
> a "morph" between two attractors. I loaded the data sets into SDL arrays and
> used elements from each array as cylinder endpoints (with gradient pigments
> along their arbitrary axes). Good times.
> 

What a good idea to use that background. :D


-- 

Best Regards,
	Stephen

Post a reply to this message

"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> Looks interesting - it's a pity you can't quite make out the attractors'
> shapes... good idea though.

Ah, excellent point - here are the source attractors for the morph.

-Rob
-------------------------------------------------------------------------------
http://www.McGregorFineArt.com

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Attachments:
Download 'sourceattractors.png' (325 KB)

Preview of image 'sourceattractors.png'

"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> I might try an animation using my sphere technique,
> if I turn off AA they only take a minute or so.

This morning I found this morph animation in a subfolder of my attractors
folder; I had completely forgotten about it! Originally rendered as an 1920x1080
(HD) AVI, I just squashed it down into this little MPEG-4 to post here.

-Rob
-------------------------------------------------------------------------------
http://www.McGregorFineArt.com

Post a reply to this message

Attachments:
Download 'morph1.mp4.mpg' (92 KB)

"Robert McGregor" <rob### [at] mcgregorfineartcom> wrote:
> "Bill Pragnell" <bil### [at] hotmailcom> wrote:
> > I might try an animation using my sphere technique,
> > if I turn off AA they only take a minute or so.
>
> This morning I found this morph animation in a subfolder of my attractors
> folder; I had completely forgotten about it! Originally rendered as an 1920x1080
> (HD) AVI, I just squashed it down into this little MPEG-4 to post here.

That's fascinating! I take it these two attractors use the same set of
equations? It looks like it - there appears to be a certain congruence between
some of the features (if that's the right phrase!).

I've got to try this!

:)

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I like them all.
A worthy tribute to chaos theory.
;-)
Paolo

 >Bill Pragnell  on date 06/12/2009 23:31 wrote:
> All that amazing mandelbulb stuff has inspired me to dig out a strange 
> attractor search/plot app I wrote a few years ago, and try to get some 
> decent plots into POV-Ray. Here's a few of the nicer ones I've found 
> over the last couple of weeks.
> 
> Bill
>

Post a reply to this message

Bill Pragnell wrote:
> All that amazing mandelbulb stuff has inspired me to dig out a strange 
> attractor search/plot app I wrote a few years ago, 

My primary suggestion is to try making stereoscopic pairs. I found that to 
be great fun when I was playing with such stuff. It really brings out the 
complexity better.

-- 
Darren New, San Diego CA, USA (PST)
   Human nature dictates that toothpaste tubes spend
   much longer being almost empty than almost full.

Post a reply to this message

"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> "Robert McGregor" <rob### [at] mcgregorfineartcom> wrote:
> > "Bill Pragnell" <bil### [at] hotmailcom> wrote:
> > > I might try an animation using my sphere technique,
> > > if I turn off AA they only take a minute or so.
> >
> > This morning I found this morph animation in a subfolder of my attractors
> > folder; I had completely forgotten about it! Originally rendered as an 1920x1080
> > (HD) AVI, I just squashed it down into this little MPEG-4 to post here.
>
> That's fascinating! I take it these two attractors use the same set of
> equations? It looks like it - there appears to be a certain congruence between
> some of the features (if that's the right phrase!).
>
> I've got to try this!
>
> :)

Well, my little app calculates Lyapunov exponents based on some random numbers,
looping over the function until I get lucky and the series doesn't tend toward
zero or infinity. Then it creates 100,000 or so particles and draws a preview in
the viewport. If I like what I see I can click a button that saves the data as a
POV include file (an array of vectors) along with the preview bitmap, or click a
"Try Another" button to start over. I saved off more than a hundred interesting
varieties over the couple of weeks that I was exploring these types of
attractors.

Something I found really exciting and fascinating was seeing a real-life
attractor a couple of months later, one I thought I recognized from my
experiments! It was early June, 2007, nearing sunset here on the east coast of
Florida and the space shuttle had launched about 15 miles from my home. Some
weird chaotic upper air currents were doing an attractor dance up there and the
smoke trail left by the shuttle showed the pattern. I grabbed my camera and took
a few shots for posterity. Here's the attractor saved by my app preview and the
similar real-life version:

Post a reply to this message

Attachments:
Download 'shuttleattractorcloud.jpg' (92 KB)

Preview of image 'shuttleattractorcloud.jpg'

Life imitates art. :)

glad you're quick on the camera!

Post a reply to this message

"Robert McGregor" <rob### [at] mcgregorfineartcom> schreef in bericht 
news:web.4b1ff4dde6b3a3e086ff1d480@news.povray.org...
> Something I found really exciting and fascinating was seeing a real-life
> attractor a couple of months later, one I thought I recognized from my
> experiments! It was early June, 2007, nearing sunset here on the east 
> coast of
> Florida and the space shuttle had launched about 15 miles from my home. 
> Some
> weird chaotic upper air currents were doing an attractor dance up there 
> and the
> smoke trail left by the shuttle showed the pattern. I grabbed my camera 
> and took
> a few shots for posterity. Here's the attractor saved by my app preview 
> and the
> similar real-life version:
>

Incredible! This is a fantastic experience.

Thomas

Post a reply to this message

>> I've seen one made out from an old ploter converted with the laser from
>> an old fax machine. You can also reuse one from any old laser printer.
>> It could create stuning models out of ordinary sugar with a granyness of
>> about 0.5mm.
>> It can be home made for under $100 or about, and the functioning cost is
>> prety low.

The CupCake 3D printer kit is $750.
http://store.makerbot.com/cupcake-cnc.html

The RepRap Darwin runs about $400 in parts,
they're close to finalizing the Mendel model as well.
There's a nice photo of some printed objects on display
at Massey University on the front page.
http://reprap.org/bin/view/Main/WebHome

Post a reply to this message

Robert McGregor wrote:
> Something I found really exciting and fascinating was seeing a real-life
> attractor a couple of months later, one I thought I recognized from my
> experiments! It was early June, 2007, nearing sunset here on the east coast of
> Florida and the space shuttle had launched about 15 miles from my home. Some
> weird chaotic upper air currents were doing an attractor dance up there and the
> smoke trail left by the shuttle showed the pattern. I grabbed my camera and took
> a few shots for posterity. Here's the attractor saved by my app preview and the
> similar real-life version:
> 
> 
> ------------------------------------------------------------------------
> 
That looks great! I wonder if it's possible to render something similar 
to the clouds/smoke, instead of just a lot of spheres...

Post a reply to this message