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...quote from http://www.fractalforums.com/index.php?topic=4040.msg21503#new...

There's a confusing thing going on about the definition of fractals. 


Hey, my cat said it was a fractal!   j/k

Couldn't it be whatever actions lead to developing a fractal dimension near self-similar art be considered a fractal?  Mandelbrot also said that the most interesting fractals have a chaotic attribute to them.

 I'm somewhat frustrated by (present company excluded) mathematicians only explaining fractals in mathematical language.  Then they say it can only be explained that way.  As my friend who laughs at me when I try to learn the language of math, does.  It's far beyond me some times.

 I have a book that explains fractals in music and explains fractals by scanning images, shrinking them down, making x number of copies, placing them back on the scanner, shrinking down the same way, making the same number of copies, and then repeating the process the same way at least 3 more times.  I get the idea of applying a pattern (idea) unto itself is a fractal.  It creates self-similarity and dimensions of itself at many areas of itself, like my photoshop fractals and Matty's fractals. So my simpler understanding of what fractals are, is an idea, theme, or action made up of itself and refers to itself. 

Now that is an equation right, but explained without the fancy numbers and symbols that take me forever to memorize and understand.  Believe me I love math and the concepts of number theory and all of it, but it is taking me forever to understand and if ever catch up with the latest mathematical symbols and concepts.

I admit I made many mistakes in referring to a thing as a fractal when it isn't.  Such as the Moire Effect and the Fibonacci Sequence.  These are all things made up of itself but the chaotic aspect is not there.   IFS is not necessarily chaotic either though, right?  So this is where I get a little confused.

Okay, if I am wrong about all of this and the concept of fractals, can someone please make it clearer, because I really intend to learn it all.  If only I had more time and more brain power.

I am currently reading: Godel, Escher, Bach: an Eternal Golden Braid by Hofstadter.
It's taking up all my free time to read it and research to understand it.  Plus I'm going through Gleick's Chaos, Madden's Fractals in Music, Chaos and Fractals: New Frontiers of Science, the famous Mandelbrot's book, The Fractal Geometry of Nature, DVD teaching company lessons on Geometry, Algebra, Calculus, Trigonometry, Science.... etc...

I feel I have lost all highschool knowledge since 1996 and my BA degree was only music.  Not one math class was taught at Cornish where I graduated (exactly how is that possible?).  So when I worked on fractal music, due to boredom of only classical music and jazz,  I decided to learn all I can.

Sorry for the long winded rant but I feel this is the only place where I can get support but yet, I feel out of place for not being up on my math skills.  I can't hold a mathematical discussion here with anybody, because it's beyond me. Which is why I hardly respond to some comments that don't make any sense to me for fear I may make myself look stupid as I may have already.

Thanks all for doing such great work on applications and new ideas of fractals and 3D, 4D(That blows my mind), and perhaps maybe soon we will transcend beyond time.  Time is the 4th dimension right?

David, you are so kind.  I agree with you 100%. 

Just as I noticed many issues floating around this world, everybody keeps trying to categorize things as just one thing only and any mix is not allowed.  But as most scientists in this modern world realize is even the minutest thing effects the greatest thing (butterfly effect).  So when we try to classify things as one thing only; we miss the general aspect of it all. (I learned this from what I have read in GEB by Hofstadter).

I'd say that fractals tell us there is more to a thing then we can see.  We have to examine every aspect to truly understand one thing and each aspect to one thing is infinite.  Unless we can live forever, we will never be able to understand it all.

Understood!

Nahee, you represent knowledge but you don't reveal it, per se.  Interesting "per se" means of itself, that is a fractal huh?

My favorite Quote!

Thanks, I guess I made it out to be too big of a deal.  Just like the square-root of -1, it's not that hard to understand.  It just takes me longer to figure that out.

  Fractals are fractals man.  It's that simple.  You know, even the word makes different patterns in different minds, so it's fractaling the hell outa a bunch of gonzo freakazoid tube spazzers.  Not that it's any different from any other word out there....

http://www.etymonline.com/index.php?search=fractal&searchmode=none

  But then again, it's a newish word, with not a lot of history.  Does there need to be a definition?  Well, look at all the bullshit arguments that the dual definition of "Free Will" has caused, one side arguing that people do stuff of their own volition (true: I am writing this willingly) so free will exists (as per the pertinent definition), and the other side arguing that there are prior factors that determine our decisions (true: natural law, existence of stuff, etc.) so free will doesn't exist (as per the other definition pertinent to this argument).   Blehhh...

  Hahaha... well, this is a 5d video, although the 4th dimension is static, the 5th varies:
<a href="http://www.youtube.com/v/XtXyUOXWZfw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/XtXyUOXWZfw&rel=1&fs=1&hd=1</a>

F is for all the friends I made here.
R is for all the responses I have gotten.
A is for the apple computer I use.
C is for the care there is here.
T is for all the tea I drink
A is for the A's I got in college
L is for all the ... guess...


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LIMA BEANS!

Thanks!

I've been redefining fractals with Lissa's images for years now  (even if it's a bit hard to tell those are her feet!)  (I mean...  just because *I'd* know them anywhere, doesn't mean others would   ).

But that is a favorite of mine - if only because it took 5 Different Programs to make happen!  (Mutatorkamer, Chaos Pro, Bring It In, Particle Illusion, and ULead gif Aimator)

There was an episode of NOVA called Hunting The Hidden Dimension which put it all together quite well in layman's terms  (even has interview segments ith Benoit Mandelbrot!).

http://www.pbs.org/wgbh/nova/fractals/

That may help