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I had a few free minutes this afternoon so I thought I'd log in and peruse some of the topic areas I don't normally visit much...

This question, "Is this fractal really art?" (or the more general question "Is any fractal really art?") has always bothered me -- usually I have no problem accepting a fractal image as art. The question I've found myself asking far more often is, "Is this art really a fractal?"

The scope of the term "fractal" seems to have expanded to include anything that has any kind of periodic pattern repetition, spiral, swish, curlicue, or radiating lines. Or anything that was generated by or edited with UltraFractal.

I can't provide examples right now (only a few free minutes right now), but I would bet that most people have seen things like this.

Ah, the age old questions concerning...   What is "art"?  and  What is a "fractal"?      :death:


Yes, the UF "bigots" seem to think the application was sent from Heaven like manna, and those that use it sit on the right-hand of GOD.      :evil1:   :evil1:

Personally, I do not feel that all mathematical formulae which can be used within UF should be considered as fractal.  Nor do all images, coming from such a graphic editor as UF is, should be considered as fractals.

Once someone starts layering, masking, merging colors, and using many of the other graphic editor functions, how much of the resulting image truly should be considered as "fractal" ??


More than I care to think about.  And it seems to be growing exponentially.    :ugly:

I agree, some "fractal" applications such as Ultra Fractal are quite capable of producing images that are not fractal - even Fractint could be used to do so :)

Just to point out that I'm not a UF "bigot" - I'm an ego-centric fractal formula writer, it just so happens that I write my formulas for UF :)
I would recommend other fractal software for certain things - Incendia for general 3D fractals, Xenodream for 3D IFS (non-zoomed or non-affine), Chaoscope for strange attractors, software by Terry Gintz for quaternions etc., and Apophysis if you just want to do flames but for general "normal" escape-time fractals then I would recommend Ultra Fractal - and for affine 3D IFS with zooming possible then I'd recommend my own mmf4.ufm:3D IFS formula for Ultrafractal ;)
I confess I haven't tried the Fractal Science Kit in earnest but my impression of version 1.0 so far is that it's comprehensive in approach and a reasonable GUI but is relatively very slow at rendering.

is an image really fractal? simple test: look for self-similarity.

that is all, surely?  O0

Paul, you are not a Ultra Fractal lover, I see :-).

My real love is for Fractal Explorer, but it can't be updated anymore... it will disappear soon. UF is a nice program, but I don't consider this a pure fractal program. I can do nice postprocessing with it. Most things I could do with PSP, but this is more direct versatile. For me it is of no importance if it is a real fractal or art or whatever. I enjoy playing with the possibilities of fractalprograms.

I think it's clear that many images made by Ultra Fractal and FractInt (and probably many other fractal programs) are not, strictly speaking, fractals.  But, does it matter?  Probably not, unless you're doing mathematical (as opposed to art) work with the program.

i for myself like it the most if you can not resemble the 'classical' fractal structure, if the self similarity is hard to guess,
and a good use of layering techniques is also very welcome, but i for myself prefer to say it is procedural, and not textural (?) ...
i like if the whole result can be computed from formulas, like ultrafractal does it .... in a way it is a method of compressing the whole image
( the formula takes 2kb , and the printable image would eat easily 10mb of data )

 O0

As I understand Fractal Explorer was coded in Delphi.

The last I used Delphi was around 2004 I think.   If Fractal Explorer is written in Delphi and the source code is available there exists the possibility of translating to a different programming language.

Delphi was based on the Pascal language.

I enjoyed using PlantStudio to create scenery for POVray, but it's a Windows program, just like Fractal Explorer, only because unfortunately it also was written in Delphi, and the creators don't have the resources to update it.

They've made the source code available and have translated around 75% of it to Python.
(I'd consider helping out, but my knowledge of Python is not up to it right now)

At that point they got stuck on the GUI part, and tried some solutions like  Jython, Tk, wxWidgets, but they couldn't sort it out.

I think using the non-standard, non-cross-platform solutions such as Delphi is a huge mistake.

Plant Studio grew out of around 6 years of work by the authors. 

It's a shame such great programs with so much work behind them become obsolete.

Hi iteron,

The author of Fractal Explorer gave me the source code... He told me that if I could find someone that could update it, I could give it to him or her...
He told me too it would be a big job.
Please write me your own mailaddress if you want to discuss this further.

As with many things, the question should perhaps not be "is xyz a fractal", but rather how fractal-like is it. There are many shades of grey - for example, a repeating pattern with just 10 copies of a shape with each one rotated by 5 degrees is far less fractal-like than one which recurses off to an infinity small point, especially when such an area is properly 'space-filled' like the mandelbrot is, (rather than being very sparse).

As for whether fractals are art, a better question is how *good* is it.

I think a lot of what defines is art is being able to extract meaning from a picture. Although that can be cool sometimes, different people find different meanings (i.e. events/thoughs that the picture happens to remind them of), and although fractals have little of this 'meaning' thing, they have the far deeper, more timeless/universal quality which doesn't have to rely on potentially fickle relations to someone's past experience.

In other words, fractals are cool intrinsically for what they are, rather than for what they remind people of.

There is a formal definition of what is a fractal. A fractal is an object with fractal (i.e. non-integer) dimension. Unfortunately, a lot of images are called fractals but they are not pure mathematical fractals. Such images explore semi-chaotic-semi-ordered shapes and patterns. These shapes are close to some dynamic systems (like turbulent streams). Fractals are also tightly related to dynamic systems, but they are not the same.

However, if we forget about the mathematical root of fractals, we could consider many ambient art works to be fractals, especially if they have hundreds of elements (balls, threads, etc) at different scales which are spread in a chaotic manner but still show some inception of order.

Personally, I would prefer to use "fractal" for mathematical fractals, and "fractal art" for artistic interpretations which look like fractals or for fractals that have been modified artistically.

BTW sometimes it is hard to tell whether a piece of fractal art is a true fractal. Its dimension must be calculated in order to be sure about this.

I've never liked that definition of fractal. By that definition, first of all, a fractal must be a set - in other words, a complex coloring algorithm that produces fractal shapes and whatnot without the use of a formula... would not even make any sense as a fractal. Secondly, it ignores all fat fractals (that is, fractals with area or volume, dense within some neighborhood). This means that the Mandelbrot set wouldn't even be a fractal. Even if you extended that definition to "A set with a fractional dimension, or whose boundary has a fractional dimension" you would still not be including the Mset, because it's boundary is so erratic that it's actually 2 dimensional. Even the Sierpinski tetrahedron has an integer number of dimensions. Only the first types of fractal conceived, such as the Cantor set or Koch curve, didn't have an integer dimension.

I think the best strict definition is this: Wikipedia.

This includes the boundary of the Mandelbrot set, despite it having an integer fractal dimension.
And strictly speaking the Mandelbrot set isn't a fractal. It is a set of points, just like a disk is a set of points. The boundary is a fractal, since it is topologically 1d (a line) but has fractal dimension 2. Equally, the Mandelbulb isn't strictly a fractal, but its surface is.

However, in Mandelbrot's Interview (http://www.fractalforums.com/index.php?topic=2838.0) (in the links section) you can see that he is accepting of 'fractal' being used in much looser ways, e.g. a coastline or a work of art being a fractal.

Just because it's a "set of points" doesn't mean it isn't a fractal. A line - or a Koch Curve - is also a set of points. A ball of crumpled paper, or a 3D Koch surface, both are fat "Surfaces". And that definition doesn't even include the Cantor Set - it's Hausdorff dimension is less than it's Topological dimension.

My definition of "fractal" is as loose as it can get - *everything* is fractal ;)

I think the topological dimension of cantor dust is 0, it is made from 0 dimensional points/dust. Its fractal dimension is about 0.63.
The Mandelbrot set is the set of interior points. They fill an area, and just like a disk, if you bring it twice as close it fills 4* as many pixels. Its topological dimension is 2, and its fractal dimension is 2. So the 'set' isn't fractal by Mandelbrot's 1975 definition.
The border of the set is a line, which is 1 dimensional, but if you bring it twice as close it fills 4* the pixels to draw the border, so its fractal dimension is 2, larger than its topological dimension, so a fractal. This is why Wikipedia is careful to say "the boundary of which forms a fractal."

But that's being fussy, everyone knows it as a fractal :)

Warning, unfounded philosophical babbling ahead!

I regard the Mandelbrot set as an example of a battle between two conflicting forces. One force tries to attract the orbits, another force tries to repel them. The areas held by either force, i.e. the inside and the outside of the set, are fairly boring, ordinary 2 dimensional planar sets. But the front line between them, that's the place where chaos reigns.

Two forces aren't really enough for chaos to happen (that would just be z^2), but some small third force is needed that disturbs the two great armies (the + c part). But that doesn't change the general notion that chaos always happens - if it does happen at all - at some border between conflicting forces.

Well, I can't help with What is a "fractal"?  Too many definitions out there...

But I can babble with the best of them about What is "art"?

There is no criteria which can be used as a blanket statement to define whether anything is "Art" or not.

Art is an Intent and an Act of Creating Something. Not a finished item.

It is a Process, not a material object.

It is a Thing To Do, not a Thing.

It is a Verb, not a Noun!

Sometimes the finished product is not the point at all, but merely the by-product of the Art.

Hobold, did you steal that from somewhere within the pages of "The Beauty of Fractals"?  :dink:

Socratease, that's a very nice way of describing things. I think the same might be said of cooking, to some extent: Sure, everyone might be enjoying the finished product, but the part where your heart is really in it is while you're stirring through the batter.  :)

There is certainly a danger that this idea infected me when I read "The Beauty of Fractals" back in my school days. But I have no conscious memory of such a quote in that book. The book did profoundly impress me, though, and was a big part of the reason why I chose to study mathematics, and do that at the University of Bremen. Funnily enough, I then proceeded to never meet Professors Peitgen or Richter during all of my education. :)

I don't regret the path I have taken, though. And I did get to meet some some of the " fractal celebrities" eventually.

Whom have you gotten to meet?

I think that, especially in the sections about Newton fractals and the Volterra-Lotka equation, it talked about how in some sense there are several attractors, each pulling on the point. The Mandelbrot set is somewhat like a plot of all the different ways that the small attractor would win; it's complement is all the ways it would lose. In the Volterra-Lotka dynamics, you have the predator vs. the prey, but there is also some strange force trying to make them battle for eternity, and one trying to make them live in harmony... or something like that. It's a great book.