Logo by reallybigname - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. March 29, 2024, 06:24:26 AM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1] 2 3   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: GNOMON  (Read 4550 times)
0 Members and 1 Guest are viewing this topic.
stereoman
Fractal Lover
**
Posts: 221


« on: January 31, 2014, 12:09:11 PM »

I start this thread to create a point of reference on the subject, because I think is interesting enough, time will tell.
     As I have been trying to show in different threads, recursive processes, by themselves, produce   accidental results at best, or mathematically sterile.
     There is something in nature that directs the processes to a particular order, as we can see in the picture, that something is the gnomon.
     In my view, we need a programmable gnomon that can be applied to fractal generating programs.
     If anyone wants to try, or just discuss it, this is the place.
   


* img185.gif (200.1 KB, 487x498 - viewed 586 times.)
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #1 on: February 01, 2014, 01:46:56 PM »

At first glance, it seems odd that people generally do not value or appreciate many beautiful images generated fractally .
For those who do not understand this issue, it is a matter of nerds and actually is something that computers do , and for those who understand , it is clear that it is mathematically very simple, and artistically worthless .
    For a work of art is valuable must be unique , something done by thousands, is not art .
    Because for something to be art, an artist must do it.
    And you must have a content , an idea, a meaning, without it , there can be no art .
    And we all agree that penetrate to infinity in an M -set does not bring any meaning , because , as above so below , if at first it does not mean anything. the same at the end.
    The competition this year, we have seen several ways to create an axolot by fractal media, all valid, of course, I want to note is that each creator had to do their part , what programs do not reach to do , namely to introduce a specific purpose in the process .
    What is at issue, then, is to increase the control of the artist on the generation, allowing you to introduce your ideas to direct fractalisation .
    I have no idea how to implement this, but I can not believe that there is not an interesting challenge for matemathics  .
 This is the tool true artists will need if fractals  have to be artworks.
« Last Edit: February 01, 2014, 01:54:35 PM by stereoman » Logged
Chillheimer
Global Moderator
Fractal Schemer
******
Posts: 972


Just another fractal being floating by..


chilli.chillheimer chillheimer
WWW
« Reply #2 on: February 01, 2014, 06:54:59 PM »

First of all: I find it a great idea to elaborate on the topic of gnomons that you brought up in other posts.
Very intersting and a crucial element of fractals, i think. It's the first time I heard a proper desciption of the phenomenon of recurring shapes in fractals like the seahorse or the 2-3-4-.. folded spirals.., the minibrots themselves
this seems very important.
and (as so often with such things) I'm surprised it hasn't been seen/discussed for such a long time.

but I need to make a little detour because of some of your statements:
At first glance, it seems odd that people generally do not value or appreciate many beautiful images generated fractally .
For those who do not understand this issue, it is a matter of nerds and actually is something that computers do , and for those who understand , it is clear that it is mathematically very simple...
until here, well said!

..and artistically worthless
From here I disagree.
Not because I'm 'insulted' as an 'artist'. I see myself as a novice explorer. I find stuff that is already there.
The actual artist probably is the formula. Nature. Everything around us.
Some might call it god (I don't)

I think to bring out art, to show it, craftmanship is needed.
Take a stone block.
Every thinkable form is already in there. The artist 'just' has to set it free. Is Michelangelos David not art? The form (human body) existed long before.
Yet we clearly classifie this 'simple, accurate depiction of a man' as art.

ok, for fractals, the entry point is much easier, as all the beauty is obviously already there, calculated by some 'mindless' programm, a simple formula...
but still, it takes time and craftmanship to really show all the beauty that it contains in places that need to be discovered.

the images of paudelbrot are a perfect example. they are not simple snapshots anyone can do.
i tried.
i can't..

   Because for something to be art, an artist must do it.
    And you must have a content , an idea, a meaning, without it , there can be no art .
I'm a professional musician.
When I make music it often just happens. It's a flow. It starts with a small idea, the flow takes over and a few hours later I 'wake up' and the layout is done.
Sometimes when a song is finished and I hear it some months later I wonder if it was really me who did this.
It's like my concious mind wasn't involved, except for working out the details. Besides playing a minor and G major on a guitar. wink
Maybe this is similar to zooming into the m-set.
I might have had a short musical idea "that sounds good" in the beginning (like "I'll zoom here in the m-set that looks interesting") but when the result is about to become really good, 'subconciousness' takes over. whatever that is..
the melody has already been there, in theory.

the picture also is already there. but hidden.


All this reminds me on the quote "We're all standing on the shoulders of giants" (by whom I forgot).



So now that I've got this off my mind I can proceed to your core idea:
   What is at issue, then, is to increase the control of the artist on the generation, allowing you to introduce your ideas to direct fractalisation .
    I have no idea how to implement this, but I can not believe that there is not an interesting challenge for matemathics  .
 This is the tool true artists will need if fractals  have to be artworks.
To this I can strongly say YES! I agree!
I approached this from a different side, biomimicry-style.
I was wondering, do we know the exact formula for romanesco brocolli, or for mushroom gills ...natural fractals.
and could we invent new ones?!
this is where it becomes incredible interesting!
I think jesse did this on a large scale. and others did it(and keep doing it) with contributing new formulas.
combining these formulas into new stufff

I can only say, I wish I could do that(besides random strikes of luck).
I'd love to see an inspiring shape in nature, find the formula, vary it, explore it, do "my own" little evolution and then finalize it with a little personal touch.

or even come up with totally new formulas...


after all.. if new stuff comes up, I'm pretty shure we're at the best place to find out first.. wink


------
sorry& back to gnomons!  wink


edit: to avoid anymore offtopic, regarding great krams video in the following post:
vsauce, a great science channel also has a video about this:
youtube.com/watch?v=DAcjV60RnRw
"will we ever run out of new music"

thanks kram for your video! i never got into 12tone music, it's too far out for me.. but her little example at 12:30.. interesting, and more important, one can listen to it, without aching ears wink
I should give that music a second chance.. thanks! smiley

edit 2: wow! i love that sentence 14:50
"creative people are just skilled at navigating an exponential tree of possibilities..."
« Last Edit: February 01, 2014, 10:10:57 PM by Chillheimer » Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
kram1032
Fractal Senior
******
Posts: 1863


« Reply #3 on: February 01, 2014, 08:38:14 PM »

I don't intend to keep up the diversion for longer than this but I want to add to Chillheimer's analysis of art this video, or at least a part of it:
<a href="http://www.youtube.com/v/4niz8TfY794&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/4niz8TfY794&rel=1&fs=1&hd=1</a>
From 10:08 onward but then especially from 13:39 to 15:30.
There are more sections relevant to this in that video. If you have time, watch the whole thing: It's amazing!
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #4 on: February 01, 2014, 11:27:31 PM »



To start somewhere, I will try to define the type of interface.
   Basically, what is needed is something like the image.
   Above, we see the appearance of the gnomon in two configurations.
   Below, some of the changes that you need to do, namely, to transform a single line and let it spread its influence, or transform a number independently.
   Naturally, the ultimate goal is a gnomon in 3D, but we must start in 2D, I think.


* gnomon-01.jpg (104.29 KB, 510x459 - viewed 295 times.)
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #5 on: February 01, 2014, 11:38:33 PM »



but I need to make a little detour because of some of your statements:until here, well said!
From here I disagree.
Not because I'm 'insulted' as an 'artist'. I see myself as a novice explorer. I find stuff that is already there.
The actual artist probably is the formula. Nature. Everything around us.
Some might call it god (I don't)

I think to bring out art, to show it, craftmanship is needed.
Take a stone block.
Every thinkable form is already in there. The artist 'just' has to set it free. Is Michelangelos David not art? The form (human body) existed long before.
Yet we clearly classifie this 'simple, accurate depiction of a man' as art.

ok, for fractals, the entry point is much easier, as all the beauty is obviously already there, calculated by some 'mindless' programm, a simple formula...
but still, it takes time and craftmanship to really show all the beauty that it contains in places that need to be discovered.

the images of paudelbrot are a perfect example. they are not simple snapshots anyone can do.
i tried.
i can't..
I'm a professional musician.
When I make music it often just happens. It's a flow. It starts with a small idea, the flow takes over and a few hours later I 'wake up' and the layout is done.
Sometimes when a song is finished and I hear it some months later I wonder if it was really me who did this.
It's like my concious mind wasn't involved, except for working out the details. Besides playing a minor and G major on a guitar. wink
Maybe this is similar to zooming into the m-set.
I might have had a short musical idea "that sounds good" in the beginning (like "I'll zoom here in the m-set that looks interesting") but when the result is about to become really good, 'subconciousness' takes over. whatever that is..
the melody has already been there, in theory.

the picture also is already there. but hidden.


All this reminds me on the quote "We're all standing on the shoulders of giants" (by whom I forgot).




 First of all, I agree with your latest sentence, gnomons are found in egyptian tombs.
  I must admit I´ve been a bit rude  with the old good M-set, but I wanted to make a clear cut.
  While I agree that the creative process overcome us and flows trough us , the fact remains that only true artists can reach this level, and only trough long effort and endurance.
   The beautiful images found in fractal programs can only be attributed to nature, I agree, the autor is nature and they are beautiful artforms, but you can say the same about everything around us, you still need an artist to create art.
   I agree that some skills are needed to bring the best of a scene, but these are artistic skills. wink
« Last Edit: February 01, 2014, 11:50:49 PM by stereoman » Logged
kram1032
Fractal Senior
******
Posts: 1863


« Reply #6 on: February 02, 2014, 12:03:10 AM »

What exactly is a gnomon anyway? I'm assuming you are using Hero's definition as found here http://en.wikipedia.org/wiki/Gnomon ?
And how does that relate to the images you showed so far?

Edit: Oh, you're using the definition given by Midhat J. Gazalé in which case it's just a word for being self-similar.
« Last Edit: February 02, 2014, 12:05:08 AM by kram1032 » Logged
Chillheimer
Global Moderator
Fractal Schemer
******
Posts: 972


Just another fractal being floating by..


chilli.chillheimer chillheimer
WWW
« Reply #7 on: February 02, 2014, 01:29:48 AM »

If I understand stereoman correctly, I wouldn't say Gnomon is just another word for self-similar, but the gnomon is more like a word for 'the group of self-similar shapes of a specific kind'
The spiral is a gnomon I'd say.
or the branching pattern of rivers..

Do I understand you right stereoman?


Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
stereoman
Fractal Lover
**
Posts: 221


« Reply #8 on: February 02, 2014, 11:17:11 AM »

What exactly is a gnomon anyway? I'm assuming you are using Hero's definition as found here http://en.wikipedia.org/wiki/Gnomon ?
And how does that relate to the images you showed so far?

Edit: Oh, you're using the definition given by Midhat J. Gazalé in which case it's just a word for being self-similar.

     As you can see, there are many definitions of gnomon.
The Hero is the definition I used but just to have something to talk about.
I think the human head drawing   makes it clear what it is, you name it.
The fact is that recursion is a very simple process, such as a spinning wheel, no matter how long you continue to turn, never produce a thought.
The way we use fractals, is much like the proverbial bunch of monkeys typing away, hoping that by the sheer number of words Hamlet will be written at the end. .
   Nature uses the gnomons continually understand what they are is easier if they are observed, take an onion, cut it in half.
    No matter how you name it,it´s the mathematic and geometric tool each of us needs to work with fractals.
   
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #9 on: February 02, 2014, 11:26:08 AM »

If I understand stereoman correctly, I wouldn't say Gnomon is just another word for self-similar, but the gnomon is more like a word for 'the group of self-similar shapes of a specific kind'
The spiral is a gnomon I'd say.
or the branching pattern of rivers..

Do I understand you right stereoman?




     Probably the Word gnomon can be used  in such many ways because  the idea behind is greater than what we can reach, after all, it´s one of the life´s most hidden secrets, ancient people think  gnomon was sacred.
     Maybe I should talk a bit about the horizon to make this a bit clear.
     Geometrically, horizon is just a line, very useful in perspective drawing, but for ancient egyptian people, it was a God,,Horus, the horizon line, separates the earth from the heavens, life, from death, light from shadows, and thus was sacred and was a concept far beyond it´s strictu sensu as we understand it.
      This was usual, Art, Science and Religion were one single thing, and all of our problems come from having separate these.
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #10 on: February 02, 2014, 11:31:48 AM »

Another useful transform


* gnomon-02.jpg (83.39 KB, 640x480 - viewed 302 times.)
Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #11 on: February 02, 2014, 11:54:15 AM »

This one is really complex, and probably must be the core for a 3D gnomon
  Note that the logarithmic spirals allow for an unlimited growing, while closed circles implies a limit.
  Edit to note that this design can be found at ancient petroglyphs


* gnomon-03.jpg (65.73 KB, 596x306 - viewed 314 times.)
« Last Edit: February 02, 2014, 12:16:01 PM by stereoman » Logged
Chillheimer
Global Moderator
Fractal Schemer
******
Posts: 972


Just another fractal being floating by..


chilli.chillheimer chillheimer
WWW
« Reply #12 on: February 02, 2014, 12:15:39 PM »

hm.. if my "the group of self-similar shapes of a specific kind" isn't the core of the concept of gnomons, then I don't get it at all and wish you could try to clarify it. to be honest, the pictures don't yet help, it hasn't made click wink
I'd like to stay with this interesting topic. i can feel that there is lots of importance in it.


it sounds like that for you the gnomon is "larger" than the fractal. in my understanding fractals contain, include gnomons.
having different gnomons is a telltale sign for a fractal, but not the only one.

Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
stereoman
Fractal Lover
**
Posts: 221


« Reply #13 on: February 02, 2014, 12:33:11 PM »

hm.. if my "the group of self-similar shapes of a specific kind" isn't the core of the concept of gnomons, then I don't get it at all and wish you could try to clarify it. to be honest, the pictures don't yet help, it hasn't made click wink
I'd like to stay with this interesting topic. i can feel that there is lots of importance in it.


it sounds like that for you the gnomon is "larger" than the fractal. in my understanding fractals contain, include gnomons.
having different gnomons is a telltale sign for a fractal, but not the only one.



First I´ll try to define what I mean by fractal
   I think this is a very simple process, since nature always uses simple methods.
   In this case, recursion, but to start a process, you must have something to process.
   And here comes the gnomon, gnomon provides the information necessary for the recursion reaches a particular purpose, therefore the gnomon, is the heart, the engine and the reason for the recursion.
   Understand that recursion is just a process, no other entity, and can be applied anywhere, with or without sense, geometrically recursion is always an extended spiral over time.
    Let's separate then what is a process in time, recursion or fractalization, from what you apply it, and to apply the recursion to something, we need the gnomon, ie, a way to connect the recursion and the object to which we apply it.
    Not quite sure how to relate this with music but I´m sure it will make sense for you  if you can translate this into your own terms.
    Probably there´s no name for this thing since it does not exist, gnomon, or better gnomonic, it´s a word wich describes its behaviour.
« Last Edit: February 02, 2014, 03:41:17 PM by stereoman » Logged
stereoman
Fractal Lover
**
Posts: 221


« Reply #14 on: February 02, 2014, 01:01:46 PM »

I think this may help.
  This is the  gnomonic structure of the human brain , although it is too complex for it to start, it may serve to understand how nature Works, and what the aim is.
  The front section shows the  gnomonic development and the side view it´s logarithmic growth .
  The final result would be a flexible spherical gnomon wich can be edited at polygon, edge  or vertex level, both graphically and by numbers, then , you can apply recursions at different levels and see what happens.
   Of course, this allows to create transparent layers, , rigid or flexible, forms within forms, animations and a lot  of options to develop new ideas.
   I want to make it as clear as posible, I hope this way we will know if this thing can be done or not, so, I´m grateful to questions.
  
 


* gnomon-04.jpg (72.28 KB, 442x394 - viewed 484 times.)

* gnomon-05.jpg (56.57 KB, 479x378 - viewed 511 times.)
« Last Edit: February 02, 2014, 02:19:49 PM by stereoman » Logged
Pages: [1] 2 3   Go Down
  Print  
 
Jump to:  


Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.197 seconds with 23 queries. (Pretty URLs adds 0.009s, 2q)