Re: The Landscape Within and Without: Similarities between landscape photography and fractals
On Apr 30, 2:16 am, "Wayne J. Cosshall" <w...@dimagemaker.com> wrote:
> My latest column is up with some thoughts about the links between
> landscape photography and fractal images:http://www.dimagemaker.com/specials/dimw.php
>
It is indeed intriguing. I think it also goes deeper. We have a
"landscape" of possible fractals once we fix the algorithm, and we
move around by changing some parameters. if we have n parameters, it
is an n-dimensional landscape. So our aim is to find the set of
parameters which produces the fractal we wish (eg which looks like a
tree, or which expresses "pain" in some sense, or whatever). We do
this either by aimlessly wandering about the landscape until we find
what we want, or by "walking around" by looking near to where we are,
or other techniques.
But generalise this a bit: any problem we try to solve (in a general
sense; it could be an attempt to write a poem) will be solved in the
same way, ie by wandering around some space of possibilities
(analogous to changing the parameters of the fractal algorithm) until
we get what we want. Doing science (eg trying to explain something) is
done this way: I know some facts, and have various ways of putting
them together; so I try various things (the "wandering around the
landscape") until I get what I want (an explanation). So is writing
poetry, in some sense: I try to express something (say); I have words,
phrases etc which carry meaning, emotions, and which rhyme, don't
rhyme, and so on, and I want to put them together in some way to
achieve my goal. It's all the same, for sufficiently general
definitions of "landscape" and "walk".
The main difference between different people, it seems to me, is how
they search around this space. Sometimes, looking just near you isn't
enough (because you have to go in a nonobvious direction to get to the
"solution"), and people who have the ability to find these nonobvious
directions do things others can't (think of Einstein, Bach etc).
Of course it is possible to generalise these definitions ("space",
"search") so much that what one says is true but useless; this is a
constant danger to all philosophers, I guess
Re: The Landscape Within and Without: Similarities between landscape photography and fractals
"Wayne J. Cosshall" <wayne@dimagemaker.com> wrote in message
news:46351945$0$21475$afc38c87@news.optusnet.com.a u...
> My latest column is up with some thoughts about the links between
> landscape photography and fractal images:
> http://www.dimagemaker.com/specials/dimw.php
>
> Cheers,
>
> Wayne
Interesting Wayne--I've been doing fractal exploration for a number of years
and my feelings are quite similar. I've written a number of formulae and
coloring algorithms for Ultra Fractal and a few other proggies, and as I go
exploring Mandelbrot or Julia sets I feel much like I do when I am out with
my camera looking for juicy frames.
Of course with the classic Mandelbrot there are repeating self-similarities
which are not present in nature, but as soon as that is modified by applying
various functions things change quite a bit. Finding pleasing symmetries
amidst the chaos is quite pleasing, isn't it? And, of course, there is
something weirdly satisfying about realizing that there is no end to the
detail, no matter what magnification one uses. This certainly mimics the
natural world.
I'm not trolling for views, but if you are interested in my fractals (and
some photos) have a look at:
Re: The Landscape Within and Without: Similarities between landscape photography and fractals
Toby wrote:
> Of course with the classic Mandelbrot there are repeating
> self-similarities which are not present in nature,
Actually, I disagree. There are many self-similarities in nature.
Look at e.g. streams that become rivers that become creeks that become a
brook that becomes a streamlet.
Same with valleys which have offsprings which in turn have even smaller side
valleys which in turn ....
Or coast lines. A statement like "country x has y miles of cost line" is
meaningless. Did they really measure around each headland and cape into each
tiny bay? Did they measure around each rocky outcrop? Did they measure
around each rock laying on the beach? Did they measure around each grain of
sand? I think this is typical fractal nature.
And of course the prime example snow flakes, although that probably doesn't
qualify as landscape photography ;-)
Re: The Landscape Within and Without: Similarities between landscape photography and fractals
On Apr 30, 4:49 am, "Jürgen Exner" <jurge...@hotmail.com> wrote:
> Toby wrote:
> > Of course with the classic Mandelbrot there are repeating
> > self-similarities which are not present in nature,
>
> Actually, I disagree. There are many self-similarities in nature.
> Look at e.g. streams that become rivers that become creeks that become a
> brook that becomes a streamlet.
In fact, turbulent flows (ie most flows in nature, streams etc) are
self-similar (eddies of various sizes coexist), frustrating our
attempts to understand it in a deep way (for some definition of
"deep"). Other examples of this type of self-similarity abound.
Someone even got a Nobel prize in 1982 for exploiting this self-
similarity in a particular field of physics.
>
> Same with valleys which have offsprings which in turn have even smaller side
> valleys which in turn ....
>
> Or coast lines. A statement like "country x has y miles of cost line" is
> meaningless. Did they really measure around each headland and cape into each
> tiny bay? Did they measure around each rocky outcrop? Did they measure
> around each rock laying on the beach? Did they measure around each grain of
> sand? I think this is typical fractal nature.
Well coastlines are a prototypical example. Mandelbrot goes on about
this in his book.
>
> And of course the prime example snow flakes, although that probably doesn't
> qualify as landscape photography ;-)
However those are usually symmetrical, not self-similar on different
scales. Still very nice, of course
achilleaslazarides@yahoo.co.uk wrote:
> On Apr 30, 2:16 am, "Wayne J. Cosshall" <w...@dimagemaker.com> wrote:
>> My latest column is up with some thoughts about the links between
>> landscape photography and fractal images:http://www.dimagemaker.com/specials/dimw.php
>>
>
> It is indeed intriguing. I think it also goes deeper. We have a
> "landscape" of possible fractals once we fix the algorithm, and we
> move around by changing some parameters. if we have n parameters, it
> is an n-dimensional landscape. So our aim is to find the set of
> parameters which produces the fractal we wish (eg which looks like a
> tree, or which expresses "pain" in some sense, or whatever). We do
> this either by aimlessly wandering about the landscape until we find
> what we want, or by "walking around" by looking near to where we are,
> or other techniques.
>
> But generalise this a bit: any problem we try to solve (in a general
> sense; it could be an attempt to write a poem) will be solved in the
> same way, ie by wandering around some space of possibilities
> (analogous to changing the parameters of the fractal algorithm) until
> we get what we want. Doing science (eg trying to explain something) is
> done this way: I know some facts, and have various ways of putting
> them together; so I try various things (the "wandering around the
> landscape") until I get what I want (an explanation). So is writing
> poetry, in some sense: I try to express something (say); I have words,
> phrases etc which carry meaning, emotions, and which rhyme, don't
> rhyme, and so on, and I want to put them together in some way to
> achieve my goal. It's all the same, for sufficiently general
> definitions of "landscape" and "walk".
>
> The main difference between different people, it seems to me, is how
> they search around this space. Sometimes, looking just near you isn't
> enough (because you have to go in a nonobvious direction to get to the
> "solution"), and people who have the ability to find these nonobvious
> directions do things others can't (think of Einstein, Bach etc).
>
> Of course it is possible to generalise these definitions ("space",
> "search") so much that what one says is true but useless; this is a
> constant danger to all philosophers, I guess
>
Re: The Landscape Within and Without: Similarities between landscapephotography and fractals
Toby, you have some wonderful fractal work there. Most impressive.
As I see others have pointed out, I also disagree with you only on the
lack of self-similarity in the landscape. I see much that is
self-similar, from mountain ranges to the edge of rocks to the mentioned
by others water flows, etc.
Toby wrote:
> "Wayne J. Cosshall" <wayne@dimagemaker.com> wrote in message
> news:46351945$0$21475$afc38c87@news.optusnet.com.a u...
>> My latest column is up with some thoughts about the links between
>> landscape photography and fractal images:
>> http://www.dimagemaker.com/specials/dimw.php
>>
>> Cheers,
>>
>> Wayne
>
> Interesting Wayne--I've been doing fractal exploration for a number of years
> and my feelings are quite similar. I've written a number of formulae and
> coloring algorithms for Ultra Fractal and a few other proggies, and as I go
> exploring Mandelbrot or Julia sets I feel much like I do when I am out with
> my camera looking for juicy frames.
>
> Of course with the classic Mandelbrot there are repeating self-similarities
> which are not present in nature, but as soon as that is modified by applying
> various functions things change quite a bit. Finding pleasing symmetries
> amidst the chaos is quite pleasing, isn't it? And, of course, there is
> something weirdly satisfying about realizing that there is no end to the
> detail, no matter what magnification one uses. This certainly mimics the
> natural world.
>
> I'm not trolling for views, but if you are interested in my fractals (and
> some photos) have a look at:
>
> http://www.renderosity.com/mod/galle...user_id=113004
>
> More to the point, browse the fractal galleries there in general...
>
> Toby
>
>
Re: The Landscape Within and Without: Similarities between landscapephotography and fractals
Wayne J. Cosshall wrote:
> I like this line of thinking.
>
So do I, because it allows Photoshop clone tool retouching of parts of
landscapes with related parts, and the eye can never spot it (image
analysis can!). The fractal nature of trees, grass, rocks etc means you
can even change scales of image parts, copy, and retouch.
We have just ordered Bryce, for my wife to mess around with creating
some imaginary landscapes. We had it years ago but it was painfully slow
on a Mac IIcx. I found the software recently, and tried it on a modern
Mac with Classic running - it was still slow, but also, the image size
was limited to something like XVGA! We are hoping that modern Bryce is
capable of big, big output files.
Re: The Landscape Within and Without: Similarities between landscape photography and fractals
On 2007-04-29 15:16:33 -0700, "Wayne J. Cosshall" <wayne@dimagemaker.com> said:
> My latest column is up with some thoughts about the links between
> landscape photography and fractal images:
> http://www.dimagemaker.com/specials/dimw.php
>
> Cheers,
>
> Wayne
The interesting thing is unpredictability. One might generate a
fractal, for example, that models the exact behavior of the stock
market for all of its history, but the model will still be unable to
predict the future. The same goes for the weather. It is possible to
create a fractal algorithm that predicts the past, but not one that
predicts the future. A fractal may describe the current appearance of a
range of mountains but it will be incapable of predicting what the
mountains will look like in 10,000 years.
The problem is resolution, of course. Very tiny differences accumulate
and amount to huge variations, often in a very short time. You reach a
point where the very act of observing can change the future.
Thus, a fractal can mimic reality, but it can never duplicate it. There
are fractal generators that allow a photographer to upsize an image and
maintain an appearance of reality, but it is not the same image that
would be obtained by a higher resolution photograph. The effect of
higher resolution is unpredictable.
A brush stroke on a painting can be seen as a part of a fractal image.
The single brush stroke does not seem to resemble any part of the
subject of the painting, but the combined brush strokes may create a
realist masterwork.
A photograph can never look exactly like reality because of its fractal
limitations. It can never capture enough information to exactly
duplicate the subject. If it did, it would be the subject, one in
identity with it.
--
Waddling Eagle
World Famous Flight Instructor
The Landscape Within and Without: Similarities between landscapephotography and fractals 
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