Talk:Iterated function system/Archive 1

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)

The fern example would be even better (I think it is great already!) if the "green line" in the picture would be a little darker. For me it is hardly visible unless I click the picture to see the full resolution version. I couldn't see it at all in my first read-through of the example. —Preceding unsigned comment added by 212.73.171.132 (talk) 09:41, 7 August 2008 (UTC)

Proposal: split section Iterated function system#Example: a fractal "fern" to Barnsley's fern

IMHO it would be better if the section were moved into its own article, as it seems to fulfil the criteria of "a section of an article has a length that is out of proportion to the rest of the article". David Roberts (talk) 06:16, 25 April 2009 (UTC)

yes please! 72.229.20.206 (talk) 01:28, 15 September 2009 (UTC)

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. Esthefan. 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.

Esthefan 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. Esthefan 2007.06.02

So there is no answer since 2 year. I suppose we can declare this discussion closed and out-of-date. May I remove this whole section? Esthefan - maintainer of (IFS illusions) 2009.06.21

If by "this section" you mean this thread in the talk page, then, no, it is not good practice to remove it. Talk pages are useful historical records of discussions. If a talk page becomes too long then material can be archived, but threads are not usually just deleted. See WP:TALK for more guidelines on using talk pages. Gandalf61 (talk) 09:46, 21 June 2009 (UTC)

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.

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)

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:

1. 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.
2. Your version does not explain what the alternative construction methods are.
3. 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)

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)

Construction

Ifs Construction IFS being made with two functions.

I propose adding the image on the right, with some text, possibly replacing the fern as the example. Spot 01:52, 30 May 2007 (UTC)

Properties

Several things wrong here I fear.

• "In general, if there are p functions, then one may visualize the composition as a p-adic tree.". Link to p-adic takes you to p-adic numbers, not the same thing (see below), this is a full K-ary tree with K=p, ie each node has p immediate descendents.

• Confusion about the monoid (which consists of finite strings) and the tree (which has all infinite paths in it). The monoid can't consist of infinite strings, at least, not indexed by natural numbers: how could you compose the all L word with the all R word?

• Link to dyadic monoid redirects to modular group, presumably intended to R to section Dyadic monoid. See Talk:Modular group for what I think is wrong there.

• "the elements of the monoid can be seen to be isomorphic with the p-adic numbers; that is, each digit of the p-adic number indicates which function is to be composed with." Not so. (1) The p-adic numbers form a ring, not a monoid. (2) the p-adic numbers have an infinite sequence of base p digits, the elements of the monoid are finite strings (3) the p-adic numbers are usually only defined for prime values of p (4) composition of finite p-ary strings is not isomorphic to either of p-adic addition or multiplication (5) the monoid is countable, the p-adic numbers are uncountable ...

• "The automorphism group of the dyadic monoid is the modular group". No, the automorphism group of the dyadic monoid is just the cyclic group of order 2. Proof. The monoid is generated by two elements L and R. The image of each under an automorphism must be a word of length 1 (otherwise the alleged automorphism would not be invertible) and so the automorphism is either L,R goes to L,R or R,L.

Would someone completely rewrite -- or delete -- this section please? Richard Pinch (talk) 22:40, 15 July 2008 (UTC)

Yes, I think you are right. Any mention of p-adic numbers in this section is mostly misleading (or at least would require a lot of explanation to clarify the point being made), so that should be left out. And the whole "dyadic monoid" bit is confusing. I have cut down the section by removing most of these confusing references. There is still an outstanding point around the subtle distinction between the monoid which contains only finite strings and the limit object which contains countably infinite strings or sequences of functions - I may try to add some further explanation when I have more time. Gandalf61 (talk) 10:48, 16 July 2008 (UTC)

I think the point is that the monoid (finite strings) acts on the tree (infinite paths). Richard Pinch (talk) 20:08, 16 July 2008 (UTC)

Further points

1. The article needs references. I believe that the 1981 paper of Hutchinson is Hutchinson, John E. (1981). "Fractals and self similarity". Indiana Univ. Math. J. 30: 713–747.. See ZMATH.
2. The link to John Hutchinson points to a disambiguation page and I don't think any of the articles referred to there can be the right one.
3. The redlink Hutchinson set Hutchinson operator needs to be turned blue, or supplemented by a brief explanation or of course both.
4. "S is the fixed point of a Hutchinson operator, which is the union of the functions fi" might read better as "S is a set fixed under the action of any of the functions fi." supplemented by adding the following
5. "One way of constructing such a fixed set is to start with an initial point or set S_0 and iterating the actions of the f_i, as S_{n+1} = \bigcup_i f_i[S_n], then taking S to be the union \bigcup_n S_n. Random elements of S may be obtained by the "chaos game", see below. Hutchinson showed that the system {fi} has a unique closed bounded fixed set, which is the closure of the sets obtained by these iterations.
6. There's an issue with closure here. If the fi are closed and continuous then taking the closure of a fixed set is again a fixed set.
7. Hutchinson's paper requires the mappings fi to be contraction maps, not alluded to here.
8. "Iterated function systems are a generalisation of the Cantor set, first described in 1884, and of de Rham curves, a type of self-similar curve described by Georges de Rham in 1957." This needs some justification. I see that the Cantor set can be obtained as a fixed set of the functions f1(x) = x/3 and f2(x) = (x+2)/3 starting with the set {0} provided that we then take the closure. I'm not sufficiently familiar with the de Rham curves to expand on those. But anyway folks, we need references here!

Enough for now ... Richard Pinch (talk) 20:52, 16 July 2008 (UTC)

ad (3) Done but it's the merest of stubs so far. Richard Pinch (talk) 17:09, 19 July 2008 (UTC)

Contraction mappings

The sentence "Although the theory of IFS requires each function to be contractive, in practice software that implements IFS only require that the whole system be contractive on average." does not appear to be supported by an appropriate reference. Richard Pinch (talk) 18:36, 18 July 2008 (UTC)

page 3 of Draves and Reckase, the first reference listed.Spot (talk) 20:15, 18 July 2008 (UTC)

I have to point out that's by you yourself (a point you might have made) -- I think the onus is on you to show that it is appropriate in the light of WP:V#SELF or, preferably, find another, third-party, reference. Richard Pinch (talk) 21:09, 18 July 2008 (UTC)

The same material has been published in regular scientific channels, eg Applications of Evolutionary Computing, 2005, LNCS 3449 http://www.springer.com/computer/foundations/book/978-3-540-25396-9 and ACM Non-Photorealistic Animation and Rendering; The Electric Sheep and their Dreams in High Fidelity; Scott Draves (invited keynote) June 2006 http://www.siggraph.org/events/symposia/npar2006 But the Flame paper linked here is more accessible and complete. And if you google for "contractive on average" you will see others using this phrase for IFS. The reference was already in the bibliography I am just letting you know what page specifically... Spot (talk) 22:22, 18 July 2008 (UTC)

References published in regular scientific channels would be the appropriate ones to add. If you have one which defines "contractive on average" then by all means add that too. Bear in mind that WP:V#Burden of evidence puts the onus on you to do that when you add material. Richard Pinch (talk) 22:38, 18 July 2008 (UTC)

I didn't add the reference, it has been there for years, I'm just telling you on what page you can find the statement in the references already used that backs up the edit in question. Do the references really have to define it or just use the phrase? This is a statement about the computer graphics technique of IFS, not the mathematical objects, maybe it should just go into the section on constructions, which also includes implementation info such as the effect of zooming. I think that would be an best what do you think? Spot (talk) 22:54, 18 July 2008 (UTC)

Looks like this paper defines it: http://ace.acadiau.ca/math/mendivil/Papers/infifs.ps Spot (talk) 00:15, 19 July 2008 (UTC)

Contraction on average requires a notion of probability on the infinite k-ary tree and so really has to be defined after the description of the "chaos game". References that seem good to me are Persi Diaconis (Mar 1999). "Iterated Random Functions" (PDF). SIAM Review. 41 (1): 45–76. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help) and Thomas Jordan (2008). "The Haussdorff dimension of measures for iterated function systems which contract on average" (PDF). Discrete and Continuous Dynamical Systems. 22: 235–246. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help) Richard Pinch (talk) 09:05, 19 July 2008 (UTC)

Possible Outside Link

I wanted to volunteer a link to my IFS fractal "breeding" website, the Fractal Farm, so I'm following the instructions in the External Links section and posting the link here for feedback: http://www.davidaspitzley.org/FractalFarm/ . The site is free to use, though not open source (mainly because I haven't seen much point). If folks feel it isn't useful enough to justify a link, that's fine, but I thought it worth checking. David A Spitzley (talk) 17:30, 22 July 2008 (UTC)

David, thank you for following the instructions. The Fractal Farm does not look like anything listed in the "What should be linked" WP:ELYES so I would prefer to keep it out. Spot (talk) 01:00, 27 July 2008 (UTC)

IFS Tools (Possible outside link)

There is an interesting project hosted on sourceforge called IFS-Tools, that consists of several open source java appplets that let a user create iterated function systems interactively via a graphical interface. A direct link is here. I intended to just add it as an external link, but ran into the giant warning comment. Is that a result of the link war mentioned below? The applets at ifs-tools are a whole lot more interesting/comprehensive than the stuff at cut-the-knot IMHO OSJ1961 (talk) 23:27, 12 March 2009 (UTC)