fractals
DESCRIPTION
Fractals. Laura Wierschke Libby Welton. History of Fractals: Julia Sets. Gaston Julia (1873-1978): French mathematician who worked with fractals Made fractals that were named after him called the Julia Sets Two types Connected sets Cantor sets Had disadvantage to Mandelbrot - PowerPoint PPT PresentationTRANSCRIPT
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FRACTALS
Laura Wierschke
Libby Welton
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HISTORY OF FRACTALS: JULIA SETS
Gaston Julia (1873-1978): French mathematician who worked with fractals
Made fractals that were named after him called the Julia Sets
Two types Connected sets Cantor sets
Had disadvantage to Mandelbrot No computers
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DIVERGENT FRACTAL
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MANDELBROT SETS
Benoit Mandelbrot (1924-present): Polish mathematician who studied fractals
Able to use computers Found a simpler equation to the Julia sets
that included all Julia Sets These sets called Mandelbrot sets Julian and Mandelbrot worked with non-
Euclidean geometry Made fractals that could easily represent things
like snowflakes and coastlines- something not easily done with Euclidean geometry
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CONVERGENT FRACTAL
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WHAT IS A FRACTAL?
Self-similar figure that repeats over and over in infinite iterations Iteration: Every time the pattern is repeated Axiom: Beginning of fractal Recursion: the rule at which the fractal is
repeated Magnifying a fractal will give a smaller, but
similar fractal Graphed on complex number plane
X-axis is real numbers Y-axis is complex numbers
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FRACTALS IN NATURE Iterated Function System Fractals (IFS)
Snowflake Fern Maple Leaf Coastlines Silhouette of tree
Koch’s Snowflake
Fern
Maple Leaf
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L SYSTEM FRACTALS
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KLEINIAN GROUP FRACTALS
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KLEINIAN FRACTAL
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JULIABROT, QUATERNION AND HYPERCOMPLEX FRACTALS
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Circle and Sphere inversion fractals
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Hyperbolic Tessellation Fractals
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Hyperbolic Tessellation
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STRANGE ATTRACTORS
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WORKS CITED Apollonian Gasket. May 31, 2009. Mathworld Team. June 2, 2009. mathworld.wolfram.com/ApollonianGasket.html
Chalk River Graphics. Castle One. 2008. June 2, 2009 http://www.fractalpalace.com/Details-CK1.php
Chalk River Graphics. Centipedius Kleinianus I. 2008. June 2, 2009 http://www.fractalpalace.com/Details-CK1.php
Chalk River Graphics. Eggs Hyperbolic .2008. June 2, 2009. http://www.fractalpalace.com/Details-EH.php
Chalk River Graphics. Hyperbolic Tessallation I. 2008. June 2, 2009. http://www.fractalpalace.com/Details-HT1.php
Chalk River Graphics. Pizza Bug .2008. June 2, 2009. http://www.fractalpalace.com/Details-EH.php
Circle and Sphere Inversion Fractals. June 2, 2009 http://www.hiddendimension.com/CircleInversionFractals.html
“Convergant Fractals.” Mathematics of Convergent Fractals . June 2, 2009 http://www.hiddendimension.com/Convergent_Fractals_Main.html
"Fractal Mathematics Main page." Hidden Dimension Galleries. 03 June 2009 <http://www.hiddendimension.com/Mathematics_Main.html>.
"Fractals: An Introductory Lesson." Arcytech Main Page. 03 June 2009 <http://www.arcytech.org/java/fractals/>.
“JuliaBrot, Quaternion and Hypercomplex Fractals.”Mathematics of JuliaBrot, Quaternion and Hypercomplex Fractals. June 2, 2009 http://www.hiddendimension.com/JuliaBrot_Fractals_Main.html
“Kleinian Group.” Kleinian Group Fractals. June 2, 2009. http://www.hiddendimension.com/KleinianGroup_Fractals_Main.html
L-System Fractals. August 27, 2008. Soltutorial. June 2, 2009. sol.gfxile.net/lsys.html
McWorter, William. Fractint L-System True Fractals. January 1997. June 2, 2009. http://spanky.triumf.ca/www/FractInt/LSYS/truefractal.html
Morrison, Andy. June 2, 2009 http://www.dannyburk.com/red_maple_leaf_4x5.htm
Seirpinski. Seirpinski’s Triangle. November 27, 1995. Chaos. June 2, 2009. www.zeuscat.com/andrew/chaos/sierpinski.html
Strange Attractors. 2009. Fractal Science Kit. June 2, 2009 www.fractalsciencekit.com/types/orbital.htm
Thelin, Johan. Attracting Fractals. June 2, 2009http://www.thelins.se/johan/2008/07/attracting-fractals.html
Vepstas, Linas . The Mandelbrot Set as a Modular Form. 30 May 2005. June 2, 2009 linas.org/math/dedekind/dedekind.html