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what is a fractal
what is not a fractal
fractals get more complicated the closer you look at them, but why so

"they say" fractals exist in greater dimensions then the two-dimensions we make them in.  Maybe like, two and a half dimensions almost, there the going between dimension 2 and 3 has to be difficult for the fractal to maintain,,  what do you think?

(btw I am Bill Newbold)
I have studied fractals since 1988 yep we made fractals on the 286 ibm machine when that was the new machine...
in the computer video art lab at college,,,

I am from New Jersey.  I am 49 years old, I make fractals usually lots of them...

see my fb photos for the fractals I have made..

hello and welcome to the forums!

everything is fractal ;) just euclidean math is not :D

The embedding space of a Cantor dust may be only one dimension.  A Cantor dust constructed by beginning with a line, dividing into three equal parts, removing the middle, and at each successive generation doing the same with the lines that are left has a Hausdorff dimensionality of Log(2)/Log(3), or roughly 0.631.  The boundary of the Mandelbrot object is embedded in two dimensions, but has been proven to have a fractal dimensionality of 2:

Shishikura, Mitsuhiro. "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets." Annals of Mathematics (1998): 225-267.
http://arxiv.org/abs/math/9201282 (http://arxiv.org/abs/math/9201282)

... although the area of the boundary is believed to be zero.

As for maintaining a constant fractal dimensionality, yes, of course, the fractal structure of natural objects necessarily breaks down at some point.  Things are after all composed of atoms and subatomic particles.  However, given the appropriate dynamics, a fractal structure is actually easier for a biological system to maintain than other structures given its scale independence.  You can see that given the simple set of rules for constructing a snowflake curve or Cantor dust.  Thus scale independence means less information needs to be encoded.  But at the same time, the fractal structure of one part or another of a biological system will usually break down after three or four levels.  A different dynamics takes over.

The question of dimension I have found to be difficult in small ways.

Thanks for the link through to the Archive site, I usually go there several times in one month..
I think if we look into the Hausdorff dimension there can be no exact number translation into real numbers.  It is like the eigenvalues that remain the numerical vector solution to second order differential equations.  we can have two dimensional numbers as easily as fractional dimensioned numbers... these are also able to be represented by the Hausdorff dimensions.  It starts with complex number theory, where the number has various parts to it.  So a fractal is functionally mapped into two dimensions from a greater dimension.  The irrational number can be of one dimension or of multiple values..  ..there is a loop going on but I just ignore that kind of thing.  The loop seems to cancel itself out when working into the new realities we create in the fractal universes.

Greetings, and welcome to this particular forum !!!     :D

Visited your Facebook page and saw some of your fractals.  Was wondering what rendering programs you use, and like using the most??
 

Thank you,..

I have fractals I have made in FE 2.02 I like the simple program interface and its workings for applying complex values in fractal form.  I am now looking to spend money on a Fractal program and most likely I will find that program in a tread of this forum...  As of late I have been trying to upgrade my computer, as it is the sound card I am having difficulty with.  There seems an endless amount of difficulties that I can't overcome... There really must be a simpler way with images and sound work, or so I think.

I also will map images with Apophysis but I still need to work on the motion mapping into videos that is possible but not implemented entirely,..

Sorry for a delay in response, life has become overwhelming more of the time then not.

Bill

With well over 600 fractal rendering applications available, and the majority of them may be downloaded for FREE, there really is no need to spend money to purchase one.
 

Best username ever? ::) ;D ;D ;D :beer: welcomies

yeah the name/number thing is number one in my book :)

so yeah back and all... sorry for the delay I was trapped in another body .,, I think?