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For background on Julia and Mandelbrot sets, see the introduction. There is detailed help available for using this form. For more information on complex numbers, see Dave's Short Course on Complex Numbers. ... Clicks on the Mandelbrot set image will get a Julia set magnify the Mandelbrot set by a factor of...
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aleph0.clarku.edu/~djoyce/julia/explorer.html
aleph0.clarku.edu/~djoyce/julia/explorer.html
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We have begun to explore the complex Julia set for this function, but only just begun. Let's try another complex number for a0. ... This was a quadratic function gave an interesting Julia set. Linear functions like f(z) = 3z + 5 don't yield interesting partitions of the complex plane, but quadratic and higher degree...
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aleph0.clarku.edu/~djoyce/julia/julia.html
aleph0.clarku.edu/~djoyce/julia/julia.html
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The constant c can be any complex number, and every complex number produces a different Julia Set. What is even more interesting is that the same formula with different constants can produce fractals that look nowhere close to each other:
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library.thinkquest.org/26242/full/types/ch5.html
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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. While the Julia set is now associated with a simpler polynomial, Julia was interested in the iterative properties of a more general expression, namely z4 + z3/(z...
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local.wasp.uwa.edu.au/~pbourke/fractals/juliaset/
local.wasp.uwa.edu.au/~pbourke/fractals/juliaset/
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is the boundary of the filled-in set (the set of "exceptional points"). There are two types of Julia sets: connected sets (Fatou set) and Cantor sets (Fatou ...
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mathworld.wolfram.com/JuliaSet.html
mathworld.wolfram.com/JuliaSet.html
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Click in the image of the Mandelbrot Set below to generate the corresponding Julia Set. ... Each Julia Set generated here corresponds to a complex number c. The Mandelbrot Set lives in the complex plane and is related to the generated Julia Sets. You may choose the complex number c by clicking on the image of the...
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www.unca.edu/~mcmcclur/java/Julia/
www.unca.edu/~mcmcclur/java/Julia/
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Time escape Julia set from coordinate (phi-2, phi-1) ... Julia set for c=i made with IIM ... English: The Julia set is a fractal. It was first created by the French mathematician Gaston Julia. The set was then long forgotten until Benoît Mandelbrot (who was taught by Julia in the 40s), made a work about it in the early 1980s.
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commons.wikimedia.org/wiki/Julia_set
commons.wikimedia.org/wiki/Julia_set
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When we generate Julia set fractals, we use functions of a complex variable. The convention has been to use the letter z to represent a complex number or variable. As before, a complex variable is the sum of a real variable and an imaginary variable.
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www.lifesmith.com/makjulia.html
www.lifesmith.com/makjulia.html
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Created by James Denvir. ... We welcome your feedback on these applets. Please send any comments or suggestions to Robert L. Devaney at bob@bu.edu. ... How to use this applet...
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math.bu.edu/DYSYS/applets/JuliaIteration.html
math.bu.edu/DYSYS/applets/JuliaIteration.html
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