Fractalforums

  What's a fractal?
  Can you eat them?
  Wasn't someone born in a Menger? 

Linkback: https://fractalforums.org/meet-and-greet/4/hi-everyone-im-new-around-here-whats-a-fractal/238/

that depends on who you ask.
the opinions are all over the place and there is no real official definition.

to me the following attributes of an object are indicators that it very probably is a fractal:
-it is self similar across several scales. for me personally 3 scales are sufficient.
(like the fern leaf made out of smaller copies of itself)
-the pattern is caused by a compareably simple iterative process. in simpler word: what is happening when a tree grows, simple rule: branch into 2 smaller branches after a certain distance in a certain angle. repeat.


looking forward to read what a fractal is for others here..


and of course you can eat them!


or use them to drive to rome


or think with them:



but of course, I could be wrong: 

  I think I've seen that one, it's virtually impossible to zoom out of 

the question is, what is not a fractal?

Fractal Wrongness algorithm == Murphy's Law (or correlates somehow)

Saying that a fractal is self-similar actually detracts from the applicability of the concept.
Check out this video:
https://www.youtube.com/watch?v=gB9n2gHsHN4
For an excellent informal introduction to the mathematical definition of a fractal.

I have no idea but I think one thing that is missing is a self similarity scale. From the images above you can see the major difference between fractals is the amount each scale maintains the parent's "dna" but we rarely quantify it. 1 would be an exact copy and 0 would be no inheritance. Fractals are anything between??

Hi eiffie!

I think MB's OP was just his way of saying hello, I'm surprised this has grown this way but also interested,
 

1 would be an exact copy and 0 would be no inheritance. Fractals are anything between??

I think that sums it up, no similarity at any scale means no not a fractal. What about clouds? from a distance they have structure and shape but once you get close or beyond the surface they just fog and look nothing like the distant view.

that depends on who you ask.
the opinions are all over the place and there is no real official definition.

That's not right, unfortunately. Mathematically, a fractal is one or more points in a non-integer dimensional space (Bénoit Mandelbrot 1975)
Colloquially the pictures resulting from mathematical operations with it.

That's not right, unfortunately. Mathematically, a fractal is one or more points in a non-integer dimensional space (Bénoit Mandelbrot 1975)
Colloquially the pictures resulting from mathematical operations with it.

I would say that is not even wrong.

  What's a fractal?
 

In Gaston Julia's time, fractals were called "monstrous" or even "pathological" curves.
One attribute they used to judge such functions was whether or not they were "well behaved".
This doesn't answer the question but it does point to a  possibly religious origin of forbidden regions of math
or notions of angels dancing on a pinhead.

Certain areas of science are said to be pathological.