Talk:Iterated function system

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1 Ferns
2 Edit War
3 Definitions
4 Dimension
5 Chaos Game
6 video feedback as IFS
7 Construction

[edit] Ferns

Does anyone know where the values in the fern IFS come from? For example, the map to draw the stalk is rather counterintuitive, because it seems to draw along the y-axis, whereas the actual stalk itself is made up of several segments increasing in their x-values. How would you go about deriving the values in the IFS (0.16 etc) if you didn't already know them, and what relations exist between them (e.g. if you changed one, how would you need to change the others to keep the fern "together")? I know Barnsley's Collage Theorem may be involved, but I'm not sure to what extent. Kidburla2002 00:04, 11 May 2007 (UTC)

I agreee, that's why i propose replacing it with the much simpler spiral at the bottom of this page. This IFS has simpler equations and fewer transforms, and the illustration includes several steps. The fern example is good for showing how complex natural shapes can be reduced to IFS, not for understanding IFS. Spot 19:24, 18 August 2007 (UTC)

[edit] Edit War

We seem to have an edit war with Hristos, who repeatedly inserts a link to this external web page IFS Illusions. TheRingess, Gandalf61 and I keep removing it. To me the link appears to be a BSP to a non-free derivative work that does not credit its sources. Hristos, can you please explain here why you think this link belongs on this page? thanks, Spot 19:47, 10 March 2007 (UTC)

Hi! I'm the author of IFS Illusions. Can you tell me why you and TheRingess keep saying that this software is non-free? Have you tried to download it? Thanks. Simzer. 2007.05.25

May I answer instead of Hristos? There were two reasons why we thought that the link belongs to this page.

1. There were a branch of IFS generator among the external links. Interesting detail, that when TheRingess removed the link of IFS Illusions with apostrophising it to non-free software incorrectly there were real non-free softwares in the list constantly unremoved.

2. We thought that the readers maybe interest to our software and our gallery. Now I see, that this is not the potent which forms this article.

Simzer 2007.05.28

IFS Illusions does not come with source code and its use is restricted to noncommercial, so it is not free. The reason I removed the link and left Xenodream (the other commercial link) because it was there as long as i can remember and at least offers something unique whereas IFS Illusions appears derivative of Apophysis/FLAM3. The Xenodream link is now gone too. Spot 23:22, 29 May 2007 (UTC)

A software is open source if there is a community, which develope it. It is not condition of free. Anyway why would be IFS Illusions open source? I developed it myself and nobody have offered his help to improve it and asked the source yet. Restriction of usage to noncommercial isn’t condition of free too. Just for your guidance: IFS Illusions is freeware, and freeware doesn't meant non-free.

That you think IFS Illusions is a derivate of Apophysis proofs that you don’t adept on IFSs. Yes, my software render iterated function systems too. There are just some little difference. For example: different function types and coloring model used, and a branch of attribute of rendering developed, etc. The user interface is also not like Apophysis as i haven’t seen it before I had made the software. And yes, there was ideas get from Flames like conform functions, but that is not the main functionality of the software.

So your last reason for removing a link of a free software instead of a commercial one and mark it non-free is that the commercial one was there as long as you can remember. In sight of these negligence and dilettantence i don't understand why are you editing this article. Thank you in advance. Simzer 2007.06.02

[edit] Definitions

The iterated function system or IFS should be defined as a dynamical system. Then the fractal sets may be defined as the invariant sets of IFSs.

[edit] Dimension

Aren't fractals represented as 2 or 3 (or X) dimensional, but in actuality of fractional dimension? If so, this should be clarified in the article. Hyacinth 00:43, 8 Feb 2005 (UTC)

[edit] Chaos Game

the article says "An IFS provides a global construction of a fractal by examining the backward orbits of points." i don't understand that, can you clarify?

then it says "Where a high degree of detail in a small area of the fractal is required, local methods based on calculating forward orbits and the fate of individual points may be more efficient." what methods are these? please provide a reference.

I added these sentences to the article, in an attempt to clarify a comment inserted by another contributor, which basically said "you cannot zoom into an IFS". Let me try to explain in more detail with an example. Suppose you want to plot the Julia set of the dynamical system

f (z) = z 2 + c

i.e. the Julia set that lies "behind" the point c in the Mandelbrot set plane. There are two different ways of doing this.

One method is to use an IFS approach. Start with a random point z; iterate the inverse functions $g(z)=\sqrt{z-c}$ , taking one of the two values of the square root at random; throw away the first 10 or so iterates then plot the rest. The iterates lie in the backward orbit set of the initial point and they converge to the Julia set, because the Julia set is the limit set of the backward orbit set of any point.

The second method is to iterate

f (z) = z 2 + c

for each point in a lattice. If the iterates diverge to infinity, that point is not in the Julia set; if they stay bounded then it is, because the Julia set is invariant under iterations of f(z). In practice, you pick a threshold magnitude and plot a point z if

| f n (z) |

is still less than this magnitude after, say, 10 iterations. This method examines the forward orbit of z.

If your viewing window covers the whole Julia set, then the IFS method is more efficient - it will give you an outline of the Julia set very quickly, although it takes time to fill in detail. If your viewing window is just a small area of the Julia set then the forward orbit method is more efficient, because most iterates of the IFS method will fall outside of the viewing window, and so are thrown away. I don't have a reference for this to hand, but I would guess Barnsley's Fractals Everywhere most probably covers this.

Does this explanation make things any clearer ? Gandalf61 10:13, 20 June 2006 (UTC)

yes but it only works for a few special cases, not IFS in general.

Yes, which is why the article says that local methods based on forward orbits may be more efficient. It does not claim that local methods exist for every IFS. Gandalf61 12:57, 26 June 2006 (UTC)

yes, but "may" is one tiny word at the end of a heavy paragraph. i'm not aware of any IFS implementations that do that, are you? i would say that's an interesting research idea, but not relevant to the point of the paragraph: how IFS are drawn, how that differs from the stereotypical 2D fractal algorithm, and the implication of this (zooming is hard).

Some IFSs produce the Julia sets of dynamical systems (

f (z) = z 2 + c

is one example) and the same image can then be produced by tracing forward orbits - that's fact, not a research idea. However, if you want to rewrite or remove the whole paragraph, that is fine with me. I did not add this paragraph in the first place - I just tried to clarify a couple of sentences added by another contributor - so I don't feel strongly about it at all. Gandalf61 11:26, 27 June 2006 (UTC)

Hi Gandalf, why do you keep reverting my work on the Iterated Function System page? The text you defend is misleading and nearly opaque. My version is correct and clear. I know this because I teach people about IFS all the time. You said "if you want to rewrite or remove the whole paragraph, that is fine with me. I did not add this paragraph in the first place - I just tried to clarify a couple of sentences added by another contributor - so I don't feel strongly about it at all. " but you persist in using your text. i do feel strongly about this and i know what i'm talking about. my text is shorter, uses less jargon, addreses the issues that concern and confuse readers, and is correct. what was inaccurate? please explain. -spot

I reverted your version of the paragraph about the shortcomings of the IFS method of constructing fractals because:

Your version uses the term "IFS fractal". There is no such thing. An IFS is a method of constructing a fractal, not an attribute of the fractal itself.
Your version does not explain what the alternative construction methods are.
Your version uses the second person - "you cannot easily zoom into ...". WP:STYLE says that use of the second person is discouraged because it sets an unencyclopedic tone.

Gandalf61 10:57, 2 August 2006 (UTC)

[edit] video feedback as IFS

i would prefer to mention another implementation of IFS: video feedback. —Preceding unsigned comment added by 69.109.182.150 (talk • contribs) 07:07, 27 June 2006--LutzL

Yes, that's a nice passtime to confuse shopkeepers. It's chaotic, but could you please explain in which sense this slightly perturbed affine linear map constitutes an IFS? Or any link detailing this?--LutzL 10:04, 27 June 2006 (UTC)

see here: http://www.physics.gla.ac.uk/Optics/projects/fractalVideoFeedback/ and it's mention here: http://en.wikipedia.org/wiki/Optical_feedback Spot 02:00, 10 March 2007 (UTC)

Yes, nice descriptions of the effect. But neither page describes a relation to IFS. The other problem is that color is involved, or at least different shades of gray. An IFS is only capable to generate black-white images as representations of the fix-point set. As in the fractal flames example, optical feedback needs a generalization of IFS to something like self-similar functions (Cabrelli/Molter (1996): Generalized Self-Similarity).--LutzL 08:16, 29 May 2007 (UTC)