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	Iterated function - Wikipedia, the free encyclopedia
		An iterated function is a function which is composed with itself, repeatedly.
		denotes the function composition of functions; that is,
		Iterated functions can be studied with the Artin-Mazur zeta function and with transfer operators.
	en.wikipedia.org /wiki/Iterated_function (253 words)

	Iterated function systems (Site not responding. Last check: 2007-09-11)
		Iterated Prisoner's Dilemma This site aims to be a comprehensive repository of information on the Iterated Prisoner's Dilemma, a major topic in artificial life, and a look at cooperation (and evolution of cooperation) between agents.
		PHP Function Table Handy PHP function reference which helps to quickly locate a desired function, to learn which PHP version it available in, and if it is documented.
		C++ Tutorial on Function Templates This tutorial covers function templates in C++, which provide a way to parameterize the arguments or return types of a function.
	www.serebella.com /encyclopedia/article-Iterated_function_systems.html (507 words)

	Iterated function system - Wikipedia, the free encyclopedia
		Iterated function systems or IFS, are a kind of fractal that was conceived in its present form by John Hutchinson in 1981 and popularized by Michael Barnsley's book Fractals Everywhere.
		The functions are normally "contractive" which means they bring points closer together and make shapes smaller.
		It consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system and drawing the point.
	en.wikipedia.org /wiki/Iterated_function_systems (324 words)

	Automatic Generation of Iterated Function Systems (Site not responding. Last check: 2007-09-11)
		A set of affine mappings with randomly chosen coefficients is repeatedly iterated numerically using the random iteration algorithm to produce an attractor with fractal characteristics.
		Results of evaluating 7500 iterated function systems, showing that the most visually appealing cases are those with large negative Lyapunov exponents (L) and with correlation dimensions (F) greater than one.
		Examples of iterated function systems produced by pairs of three-dimensional affine maps in which the color is determined by one of the variables.
	sprott.physics.wisc.edu /pubs/paper210.htm (188 words)

	Iterated function system - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-09-11)
		Iterated function systems or IFS, are a kind of fractal that was
		Iterated Function Systems and Permutation Representations of the Cuntz Algebra (Memoirs of the American Mathematical Society, 663)
		Subdivision schemes for iterated function systems (Research report RC.
	encyclopedia.worldsearch.com /iterated_function_system.htm (251 words)

	Iterated Function Systems (Site not responding. Last check: 2007-09-11)
		Iterated Functions Systems are a kind of fractal that wasconceived in its present form by John Hutchinson in 1981 andpopularized by MichaelBarnsley 's book Fractals Everywhere.
		The functions are normally "contractive" which meansthey bring points closer together and makes shapes smaller.
		It consists of picking a random point in the plane, then iterativelyapplying one of the functions chosen at random from the function system and drawing the point.
	www.therfcc.org /iterated-function-systems-87028.html (222 words)

	Collage Theorem, Iterated Function Systems
		Functions map points to points but also comprise (function) spaces where each is considered an indivisible one.
		Iterated Function Systems (IFSs) is another rewarding topic that capitalizes on the general theory.
		The algorithm is heuristic and sometimes is off by an iteration or two.
	www.cut-the-knot.org /ctk/ifs.shtml (980 words)

	Institut für Computergraphik und Algorithmen - Abteilung für Computergraphik (Site not responding. Last check: 2007-09-11)
		The theory of Iterated Function Systems is based on the contractivity but not on the linearity of the defining functions.
		Nonlinear Iterated Functions Systems are characterized by a higher degree of flexibility and greater modeling capability than their linear counterparts.
		Limit sets of 3D nonlinear Iterated Function Systems are either rendered by displaying approximating point sets (z-buffer approach) or through ray tracing an approximate set of 3D solids.
	www.cg.tuwien.ac.at /research/TR/94/TR-186-2-94-12Abstract.html (221 words)

	Iterated Function Systems (IFS) (Site not responding. Last check: 2007-09-11)
		An iterated function system is By taking a point and repeatedly applying these mappings you end up with a collection of points on the fractal.
		Iterated function systems can be used to make things such as fractal ferns and trees and are also used in fractal image compression.
		The simplest algorithm to display an IFS is to pick a starting point, randomly select one of the mappings, apply it to generate a new point, plot the new point, and repeat with the new point.
	fractals.iut.u-bordeaux1.fr /sci-faq/IFS.html (247 words)

	Iterated analytic function problem
		Author: existing If you consider a point in a space to represent a real-valued function can one generate an operator which takes a point in the space to another point such that the orbit generated when the operator is iterated covers a ball of points.
		Yes, an operator maps a function to a function; the operator you describe is very specialized, in that its "domain" is f, f(f), f(f(f)), etc. Thus, a given function f completely specifies both the operator and its domain.
		Of course in a count- able number of iterations you cannot get an uncountable number of points, and I am really not sure what it would mean to apply an uncountable number of iterations - iterations by there very nature seem to be countable.
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH130.HTM (633 words)

	Methods and apparatus for image compression by iterated function system - Patent 4941193
		The method of claim 47, wherein the iterated function system codes are the coefficients of a collage of contractive transformations applied to each of the selected geometric regions.
		In other words, the results of a first predetermined number of iterations are not displayed, in order to allow the attractor to begin stabilizing and to prevent the display of points in the output image which are randomly distant from the attractor's geometric location in the display space.
		After the system has completed its iterations and the attractor has emerged (assuming that we are still discussing the color map color encoding method), the values in the hit count RAM 61, divided by the number of iterations, will be numbers proportional to the probability of occurrence of a point in the color map.
	www.freepatentsonline.com /4941193.html (20366 words)

	Kevin Hickerson: Iterated Function Systems (Site not responding. Last check: 2007-09-11)
		Here are some examples of iterated function system renderings I made.
		An IFS (Iterated Function System) is any system which recursively iterates a function or a collection of arbitrary functions on some base object.
		I implemented my iterated function system as a 3-D object that could be plugged into a ray-tracer that I wrote in C++.
	www.ugcs.caltech.edu /~kevinh/iterated.html (636 words)

	IBM: Senile Depth First Search applied to Iterated Function Systems
		Disclosed is a deterministic, terminating method to mark the points in a quantized space, such as an array of pixels, according to whether or not a given iterated function system "hits" each quantized region.
		Since each of the iterating functions can be invoked to get to the next point, the depth first search will have at each node as many branches as there are functions.
		If the iterated function system is bounded in extent, the algorithm must eventually terminate because there are at most a finite number of pixels to plot.
	www.vm.ibm.com /devpages/GREER/SDFSIFS.HTML (636 words)

	IFS - Iterated Function Systems
		On every iteration each polygon is replaced by a suitably scaled, rotated, and translated version of the polygons in the generator.
		To run the system an initial point is chosen and on each iteration one of the transformation is chosen randomly according to the assigned probabilities, the resulting points (xn,yn) are drawn on the page.
		The initial conditions usually consist of a single square, the first iteration then consists of replacing this square by a suitably positioned, scaled and rotated version of the above generator.
	www.codenet.ru /progr/fract/intro7.php (477 words)

	Use of an Iterated Function System to Simulate the Behavior of a Time Series
		Iterated Function Systems, or IFS, are a set of equations that can be made to resemble almost any shape.
		This is a bitmap of the same algorithm with 10.000 iterations.
		This is a bitmap of the same result, at 100.000 iterations.
	www.mathcad.com /Library/LibraryContent/MathML/ts2ifs.htm (683 words)

	comp.compression Frequently Asked Questions (part 2/3)
		We could then construct a set of functions out of the sync functions at any level so that their total value at all higher levels is zero.
		The predicted value is a simple function of the already-transmitted pixels just above and to the left of the current one (for example, their average; 8 different predictor functions are permitted).
		It is comprised of portions of the attractor as it emerges during iteration.
	www.faqs.org /faqs/compression-faq/part2/index.html (14833 words)

	sci.fractals FAQ
		Iteration of this equation yields the period doubling route to chaos.
		Feigenbaum's constant is important because it is the same for any function or system that follows the period-doubling route to chaos and has a one-hump quadratic maximum.
		If this is written e^(n(lambda) for _n_ iterations, then e^(lambda) is the factor by which the distance between closely related points becomes stretched or contracted in one iteration*.
	www.uni-giessen.de /faq/archiv/sci.fractals-faq/msg00000.html (11976 words)

	Iterated Function Systems
		Basically, a contraction possesses the property that under iteration pairs of points are brought closer together - distances are scaled down by a factor k.
		Although iterated function systems could include any type of function, the most widely studied systems are comprised of affine transforms.
		Despite the use of random iteration, theory indicates that for each IFS Code there is a unique associated attractor-image and a unique associated measure on the attractor.
	chaos.phy.ohiou.edu /~thomas/fractal/ifs.html (1489 words)

	GI'97 Online Papers (Site not responding. Last check: 2007-09-11)
		Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations.
		A new, fast and image-based technique for determining the connectedness of an iterated function system attractor is introduced.
		For each shape interpolation, a two parameter family of iterated function systems is defined, and a connectedness locus for these shapes is plotted, to maintain connectedness during the interpolation.
	www.graphicsinterface.org /proceedings/1997/BurchHart (157 words)

	Larry D. Bradley: Iterated Function Systems
		Fractals reproducing realistic shapes, such as mountains, clouds, or plants, can be generated by the iteration of one or more affine transformations.
		An example of an iterated function system is the fl spleenwort fern.
		What is truly amazing is that only 28 numbers are necessary to generate this infinitely complex image: four 2 x 2 transformation matrices, four 2 x 1 translational vectors, and four weighted probabilities for the transformations (each attractor).
	www.pha.jhu.edu /~ldb/seminar/ifs.html (173 words)

	Iterated functions (Site not responding. Last check: 2007-09-11)
		If we compose a function with itself (using the output as the new input into the same machine), and keep inputting the last output over and over again, it becomes an
		Iterating the function f(x) = x + 2 with beginning seed 4 gives the sequence {4, 6, 8, 10,...}.
		For this function, all seeds generate sequences that get larger and larger with each term, slowly approaching infinity.
	math.youngzones.org /Math_2213_webpages/iterated_functions.html (279 words)

	Chaos and fractals exercises (Site not responding. Last check: 2007-09-11)
		Iterated Function Systems (IFS) are an elegant way for generating fractal images.
		In Deterministic Iterated Function Systems we use the "deterministic algorithm" (at each step, apply all the transformations to every point of the picture) to generate a variety of fractal images.
		In Random Iterated Function Systems we use the "random algorithm" (start with a point and apply the transformations one at a time, in random order, each time to the point produced by the previous application) to generate a variety of fractal images.
	www.math.union.edu /research/chaos/Ch2Ex.html (204 words)

	Iterated Function Systems
		For practical image compression, a number of restrictions on the mapping functions are imposed.
		For the next iteration, the new range image then becomes the domain image and the process is repeated.
		The range image converges to what is referred to as the ``attractor image'' as the number of iterations increases.
	www.uoguelph.ca /~rdony/ccece98/paper-node3.html (443 words)

	Fractal Questions and Answers - Iterated function systems and compression (Site not responding. Last check: 2007-09-11)
		The basic idea behind fractal image compression is to express the image as an iterated function system (IFS).
		Barnsley's company, Iterated Systems Inc, has a line of products including a Windows viewer, compressor, magnifier program, and hardware assist board.
		Algorithms are illustrated using source code in C. The October 1993 issue of Byte discussed fractal compression.
	www.softlab.ntua.gr /miscellaneous/faq/fractal/faq-doc-11.html (553 words)

	Nonlinear Iterated Function Systems (Site not responding. Last check: 2007-09-11)
		The existence and uniqueness of attractor A', however, depend on the contractivity of the functions but not on their affinity.
		Above an interactive program for the specification of 2D linear and nonlinear Iterated Function Systems is shown.
		An interactive program for the specification of 3D nonlinear Iterated functions Systems was implemented as well.
	www.cg.tuwien.ac.at /research/vis/dynsys/nifs/nlinifs.html (361 words)

	Iterated Function Systems: David Arnold
		The chaos game is actually a particular example of a more general class of processes called iterated functions systems.
		Iterated functions systems follow the same basic rules as the chaos game, but allow you more freedom in selecting and applying your transformations.
		If each transformation is equally likely to be selected at any iteration (each transformation has probability 1/5, or 0.2, of being selected), write a program that produces the image generated by this iterated function system.
	online.redwoods.cc.ca.us /instruct/darnold/ifs (2351 words)

	The Fractory: Fractal Gallery (Site not responding. Last check: 2007-09-11)
		This fractal was created by our team and is calculated by the following function: To begin, z=pixel, and c=pixel-sin(z).
		This is an Iterated Function System that was created by our team.
		It is the word Fractory, and each line is made up of the word Fractory, and each of those lines is also.
	library.thinkquest.org /3288/gallery.html (192 words)

	Iterated Function System (Site not responding. Last check: 2007-09-11)
		An Iterated Function System (IFS) is a recursive algorithm for generating a sequence of points, usually in two dimensions.
		Iterated Function Systems are discussed in detail in Chapter 9, but we won't be covering that chapter in this course.
		We are using Iterated Function Systems so that you will produce some cool graphics.
	www.ma.iup.edu /~hedonley/cosc355/class/ch2/ifs.html (158 words)

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