Talk:Iterated function system
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[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)
[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) = z2 + 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
, 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) = z2 + 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 | fn(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) = z2 + 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. —The preceding unsigned comment was 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)
