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Topic: Julia set


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  Julia set - Wikipedia, the free encyclopedia
Julia sets, described by Gaston Julia, are fractal shapes defined on the complex number plane.
Since (in general) the Julia set is the boundary between basins of attraction, the Julia set is sometimes described as being a repeller because all orbits tend away from it.
Julia sets typically (though not always) have a fractal structure, and Julia sets can be associated with fractals such as the Sierpinski triangle and the Cantor set.
en.wikipedia.org /wiki/Julia_set   (1472 words)

  
 Julia set -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-06)
Julia sets are closely related to the (A set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration) Mandelbrot set which is the set of all values of c for which z
Like the Mandelbrot set, the Julia set is often (A secret scheme to do something (especially something underhand or illegal)) plotted with different colors signifying the number of iterations carried out before the modulus of z becomes larger than 2.
At c = 1/4, the (Small elevation on the grinding surface of a tooth) cusp at the set's mouth, the Julia set outline is a closed curve with cusps all around.
www.absoluteastronomy.com /encyclopedia/j/ju/julia_set.htm   (1534 words)

  
 Mandelbrot set - Wikipedia, the free encyclopedia
In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence:
The Mandelbrot set was created by BenoƮt Mandelbrot as an index to the Julia sets: each point in the complex plane corresponds to a different Julia set.
The Mandelbrot set is compact, and thus measurable; its area was estimated as 1.5065918 by Hill [1].
en.wikipedia.org /wiki/Mandelbrot_set   (2033 words)

  
 Julia set
Julia sets are closely related to the Mandelbrot set, which is the set of all values of c for which z = 0 + 0i doesn't tend to infinity through application of the recursion.
If c is on the boundary of the Mandelbrot set, but not a waist point, the Julia set of c looks like the Mandelbrot set in sufficiently small neighborhoods of c.
Julia sets are named after the French mathematician Gaston Julia (1893-1978), whose most famous work, Memoire sur l'iteration des fonctions rationnelles, which provides the theory for Julia sets before computers were available to computer or represent them, was written in a hospital in 1918 at the age of twenty-five.
www.daviddarling.info /encyclopedia/J/Julia_set.html   (377 words)

  
 Julia set - Term Explanation on IndexSuche.Com   (Site not responding. Last check: 2007-10-06)
Julia sets are closely related to the Mandelbrot_set which is the set of all values of c for which ''zn'' = ''zn-1''2 + ''c'' does not tend to infinity through application of the recursion with ''z0'' = 0.
Like the Mandelbrot_set, the Julia set is often plotted with different colors signifying the number of iterations carried out before the modulus of ''z'' becomes larger than 2.
For example, the Sierpinski_triangle is a fixed point set of three maps, each of which maps the triangle to one of the corners, shrinking by a factor of 1/2.
www.indexsuche.com /Julia_set.html   (537 words)

  
 Fabio Cesari: Fractal Explorer
Julia sets are strictly connected with the Mandelbrot set.
The following algorithm produces the Julia set associated with C: given a generic point Z on the complex plane, this algorithm determines whether or not it belongs to the Julia set associated with C, and thus determines the color that should be assigned to it.
In the first case, it belongs to the Julia set; otherwise it goes to infinity (infinity is an attractor for the point) and we assign a colour to Z depending on the speed the point "escapes" from the origin.
www.geocities.com /CapeCanaveral/2854/julia.html   (560 words)

  
 FRACTINT Julia Sets   (Site not responding. Last check: 2007-10-06)
These sets were named for mathematician Gaston Julia, and can be generated by a simple change in the iteration process described for the Mandelbrot Set.
In fact, all Julia sets for C within the M-set share the "connected"; property of the M-set, and all those for C outside lack it.
Historically, the Julia sets came first: it was while looking at the M- set as an "index" of all the Julia sets' origins that Mandelbrot noticed its properties.
spanky.triumf.ca /www/fractint/julia_type.html   (701 words)

  
 Fractals   (Site not responding. Last check: 2007-10-06)
The Julia set is the set of all z in the complex plane such that the limit of the sequence f(z), f(f(z)), f(f(f(z))), f(f(f((f(z))))...
Julia set with in alpha = 0.22 + 0.44 i
The Mandelbrot set is the set of all z in the complex plane such that the limit of the sequence f(z), f(f(z)), f(f(f(z))), f(f(f((f(z))))...
www.cecm.sfu.ca /~kghare/numeric/fractal.html   (387 words)

  
 Encyclopedia article on Julia set [EncycloZine]   (Site not responding. Last check: 2007-10-06)
The "normal" Julia set J_c is the edge of the filled-in Julia set.
The set of all points z_0 with orbits that are "attracted to" infinity makes up the basin of attraction to infinity.
If this second attractor does exist for a particular c, then the Julia set is topologically connected, and is in fact the boundary between the basin of attraction to infinity and the basin of attraction to the finite attractor.
encyclozine.com /Julia_Sets   (1520 words)

  
 Fractals: Julia Sets   (Site not responding. Last check: 2007-10-06)
If the number does not go to infinity it is in the set so colour it fl Otherwise, you can colour the original z depending on how quickly it went to infinity (All the points the same colour require the same number of iterations to reveal that they are attracted to infinity).
The way a Julia set looks depends on whether its constant c is located on the Mandelbrot set with a corresponding formula.
If the constant is located on the Mandelbrot set, the Julia set will be a completely interconnected figure.
www.bath.ac.uk /~ma0cmj/JuliaSets.html   (358 words)

  
 [No title]
There is a Julia set corresponding to every point on the complex plane (an infinite number of Julia sets).
The most visually attractive Julia sets tend to be found for the C values equal to points of the Mandelbrot set just outside the boundary.
It was a while looking at the Mandelbrot set as an "index" of all the Julia sets' origins that Mandelbrot noticed its properites.
members.lycos.co.uk /ququqa2/fractals/Julia.html   (142 words)

  
 Embedded Julia Set, Mu-Ency at MROB
The size of an embedded Julia set is proportional to the size of its influencing mu-molecule, and inversely proportional to its distance from the influencing mu-molecule, or distance from other larger-size embedded Julia Sets (whichever distance is less).
The shape of the Embedded Julia Set is very close to (but never exactly the same as) the Julia set whose Parameter whose position relative to the Continent corresponds to the embedded Julia set's position relative to the influencing island.
The second component is a set of Filaments whose shape is very similar to the filaments adorning the influencing island, which in turn resemble the filament of which the influencing island is a part.
www.mrob.com /pub/muency/embeddedjuliaset.html   (1255 words)

  
 The Julia Sets   (Site not responding. Last check: 2007-10-06)
Julia sets and the Mandelbrot set are close relatives.
Julia sets take several different forms depending on the location in the plane of the fixed point k.
Each Julia set is contained in the same region of the complex plane as is the Mandelbrot set.
mcasco.com /jset.html   (528 words)

  
 Classic Mandelbrot/Julia Set
The Mandelbrot Set is probably one of the most well known fractals, and probably one of the most widely implemented fractal in fractal plotting programs.
Julia Sets are produced with the same formula as the Mandelbrot set, but the starting values are different.
By thinking of the Mandelbrot Set as an index for Julia Sets, the question comes up about what happens if a point on the edge of the Mandelbrot Set is chosen as the value of c.
www.jamesh.id.au /fractals/mandel/Mandel.html   (580 words)

  
 Julia set
Julia sets are closely related to the Mandelbrot set which is the set of all values of c for which z=0+0i doesn't tend to infinity through application of the recursion.
As the point crosses the boundary of the Mandelbrot set, the Julia set shatters into a Cantor dust of unconnected points.
If c is on the boundary of the Mandelbrot set, and isn't a waist, the Julia set of c looks like the Mandelbrot set in sufficiently small neighborhoods of c.
www.fastload.org /ju/Julia_set.html   (336 words)

  
 Some Julia Sets
The Julia set of f then is the set of all points of G, at which this sequence of iterated functions is not equicontinous.
The Julia sets are white, the Fatou sets fl.
In those pictures the Julia set ist defined as the set of all points, of which the iterated points do not converge to infinity, but remain bounded.
www.ijon.de /mathe/julia/some_julia_sets_1_en.html   (1022 words)

  
 Mandelbrot And Julia Set Explorer   (Site not responding. Last check: 2007-10-06)
It exists in the complex plane and is the set of all points that, after any number of iterations, do not diverge.
In this mode, when you click on the Mandelbrot set, a similar window will pop up that will let you view the Julia Set generated by using the complex point on which you clicked as the seed.
You will notice that if you select on a point that is in the Mandelbrot Set, the corresponding Julia Set is continuous, but if you select a point that is not in the Mandelbrot Set, the corresponding Julia Set is disjointed...
library.thinkquest.org /2647/cooljava/testmand.htm   (416 words)

  
 Fractal Geometry
The Julia set is the boundary of the filled-in Julia set.
Julia sets are either connected (one piece) or a dust of infinitely many points.
The Mandelbrot set is those c for which the Julia set is connected.
classes.yale.edu /fractals/MandelSet/welcome.html   (555 words)

  
 ipedia.com: Julia set Article   (Site not responding. Last check: 2007-10-06)
Given an iterated map of the complex plane to itself, or a collection of such maps, the Julia set for thi...
If this second attractor does exist for a particular, then the Julia set is topologically connected, and is in fact the boundery between the basin of attraction to infinity and the basin of attraction to the finite attractor.
It is also possible to generate Julia sets using a method derived from the IFS "random game" method.
www.ipedia.com /julia_set.html   (1384 words)

  
 Julia Set Fractal Image   (Site not responding. Last check: 2007-10-06)
This applet creates fractal images by plotting Julia sets derived from iterating complex functions of the form z^2 + c, varying z over the complex plane for a given value of c.
For each complex point z that is not in the set, the "escape velocity" of the point's orbit is represented by a shade of gray -- the more iterations, the darker the shade.
For each point z that is in the set, its color is determined by the modulus of the final computed orbit value.
www.apropos-logic.com /nc/JuliaFractal.html   (181 words)

  
 Julia - Wikipedia, the free encyclopedia
In Ancient Rome, women from all branches of the Julius family were called Julia (see Roman naming convention).
The Julia set, a set of fractals defined by Gaston Julia
Julia is the name of a fictional character from George Orwell's dystopian novel Nineteen Eighty-Four.
en.wikipedia.org /wiki/Julia   (286 words)

  
 Julia set fractal   (Site not responding. Last check: 2007-10-06)
The Julia set is named after the French mathematician Gaston Julia who investigated their properties circa 1915 and culminated in his famous paper in 1918.
Computing a Julia set by computer is straightforward, at least by the brute force method presented here.
A Julia set is either connected or disconnected, values of c chosen from within the Mandelbrot set are connected while those from the outside of the Mandelbrot set are disconnected.
astronomy.swin.edu.au /~pbourke/fractals/juliaset   (397 words)

  
 Julia Set Images
Consider a connected Julia set to be the cross-section of a long metal rod perpendicular to the X-Y plane.
If the set rod were to emit electrons, they would be attracted to the plus 1000 volt outer cylinder, moving slowly at first, and speeding up as they approach the cylinder.
The spiral arms, rotating about a sink-point in a set, reverse their direction of rotation from CW, clockwise, to CCW, counter-clockwise, when the sign of the y-component of C is changed.
home.att.net /~fractalia/jset/jset.htm   (1178 words)

  
 Julia   (Site not responding. Last check: 2007-10-06)
Many on both sides were wounded including Julia who lost his nose and had to wear a leather strap across his face for the rest of his life.
Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f
Although he was famous in the 1920s, his work was essentially forgotten until B Mandelbrot brought it back to prominence in the 1970s through his fundamental computer experiments.
www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Julia.html   (241 words)

  
 sci.fractals FAQ   (Site not responding. Last check: 2007-10-06)
Note that the Mandelbrot set in general is _not_ strictly self-similar; the tiny copies of the Mandelbrot set are all slightly different, mainly because of the thin threads connecting them to the main body of the Mandelbrot set.
The boundary of the Mandelbrot set and the Julia set of a generic c in M have Hausdorff dimension 2 and have topological dimension 1.
That is, the Mandelbrot set is in parameter space (c-plane) while the Julia set is in dynamical or variable space (z-plane).
www.faqs.org /faqs/sci/fractals-faq   (12472 words)

  
 Gaston Julia   (Site not responding. Last check: 2007-10-06)
As a result, he lost his nose, and despite several surgical interventions to remedy the situation, he had to wear a leather strap across his face for the rest of his life.
In that said article, Julia precisely described the set J(f) of those z in C for which the nth iterate fn(z) stays bounded as n tends to infinity.
Gaston Maurice Julia died in Paris the 19th day of March 1978 at the age of 85.
www.fractovia.org /people/julia.html   (337 words)

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