Talk:Fractal/Archive 4

Ghastly definition
Does the main definition seem poor to anyone else? >> "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole". This is a horrible definition, imo, firstly, because it references someone else's quote exactly, whereas a fractal means many different things to many people. A W article should be smarter than mindless parotting someone else's exact definition.(?).. Secondly, it's just plain dead wrong.

Let's say I have a circle filled with various colors, and I divide this into four even quadrants. Now I have four pictures resembling pieces of pie, none of which are a "copy" of a circle, not even approximately. They're a picture of a portion of the image, that's all, which would be saying like the front legs of a horse are a copy of the picture of a horse. If go further with this circle division, you're going to get pieces that are 100% solid colors, all of them non sequitur to each other (a picture of all blue, a picture of all yellow, a picture involving green and purple, etc.), just like they're non sequitur to all the little pieces photographing the edges of the circle. Some will be open space and have no color or curvature at all.

Now, if this circle shape is really a fractal, we're generally going to see lots of self-similiarities as we go deeper; we may see very similar "copies" to our original picture, yes, but there are still all those other pieces that are not copies. In fact, there are some cases we won't even see anything like the original shape, a circle created by a jagged triangular outline. So there cases where NO parts, not even one, is a "copy" of the original image, even if you assume that "split into parts" is just talking about taking particular portions, not dividing the image in such a way where every piece left over is also supposed to be a copy.

Further, a fractal isn't necessarily "rough" or "fragmented", given fractals are used in art to create flowing, fluid shapes, that not only utilize fractals, but of which the end result is quite definitively called a fractal. Being a mathematical-oriented definition, this doesn't cover the elegant fractals that have "evolved" in a sense from the basic math. (Not that they're "better" fractals, but they're certainly properly categorized as fractals.) "Fractal" is a very widely used adjective, used to describe end results only even partially based on the root mathematical core, which is sometimes just a tool or "paintbrush" of sorts. Artistic images properly labeled "fractals" may have no resemblance to their strict mathematical origin. Hence, even "shape" in this definition is incorrect in these cases, as these fractals are pictures, not just shapes.

I could go on, but I'm already exhausted. It's just plain horrid. Not my personal "original research" horrid. It's just plain strictly, verifiably horrid. Squish7 (talk) 16:49, 17 September 2011 (UTC)

Agreed. Self-similarity is a "striking feature defines the most common class of fractals", but by no means all. If we are addressing our intersubjective reality, there are a very few examples of existing objects we observe which exhibit any scaling self-similarity. When we do see such examples this property appears only over a very narrow scale range. The classic natural fractal example being broccoli romanesco. Such rarity demonstrates self-similarity in nature is an exception that proves the rule: natural objects are not self-similar. And yet, physical reality appears non-differentiable at any point. In no small part, this may be due to the fact that a point appears to be a purely hypothetical Euclidean ideation rather than something we can (could?) possibly observe. The cause of this misperception seems to derive from the overwhelming prevalence of computer generated fractals. It is completely natural for anyone whose entire exposure to fractals involve those created artificially to infer all fractals possess self-similarity.BurntSynapse (talk) 18:35, 6 May 2017 (UTC)

I agree the definition needs work, but I have reverted the latest edit which says that a fractal is a mathematical set "that often exhibits a repeating pattern displayed at different scales" for several reasons. If this property is not always true, then the reader is left wondering what exactly a fractal is. I think the problem editors are facing is that there are conflicting ideas of what a fractal is. The mathematical definition of a fractal and the idea of a fractal in nature are probably not quite the same. The opening sentence appears to be giving something resembling a mathematical definition and the wording "that often exhibits a repeating pattern displayed at different scales" is not a definition. If we go with a description of fractals in nature, then the opening wording describing it as a "mathematical set" would also need to be changed. (If we go in that direction, perhaps the article should even be split in two?) Correct me if I'm wrong, but I believe the current opening sentence does accurately describe mathematical fractals, even if it falls short of describing fractals as understood in nature or computer graphics. If it does not, then it should be replaced with an accurate definition. --seberle (talk) 17:37, 7 May 2017 (UTC)

The difficulties with definition are a major problem here. OTOH, the fact that some readers may be left confused doesn't seem to justify actually misinforming them with a claim that appears very much like a composition fallacy. Clarity on our concepts seems like a good idea. "Fractal" is a type of mathematical description created to address natural objects, as are the most basic math concepts: numbers and sets. For both, Wikipedia leads with functional definitions of what they do and how they're used. I've input this type of definition for consideration. Analysis invited. :) BurntSynapse (talk) 13:06, 12 May 2017 (UTC)

Where did that definition of "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole" come from? I searched Mandelbrot's 1977 and 1983 books, and it is certainly not there. Unfortunately it is now attributed to him everywhere on the Internet. This is a very serious and unfortunate consequence!

On the other hand, Mandelbrot (1983, p.15) DOES give this definition: "“A fractal is by definition a set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.”  2806:104E:16:9089:20AA:C125:7C3A:17B7 (talk) 01:19, 13 January 2022 (UTC)

This article needs a forum session.
Most of the time, science is concibed as a rigid field that can not be discussed with differents points of view. This is wrong due to what makes the science science, is the construction of one idea made of differents critical points, there is not only one way to think, there are many. For that reason it is important to make a forum to discuss non rigid topics about fractals. There are a lot of questions that are not made here in the main article because it is consider non important. For example, why people under psychedelics drugs perceives and watch fractals in their trips? Mariavictoria35 (talk) 08:42, 10 April 2023 (UTC)