# Fractals Project - Phoenix

Fractals Project Natalie Rowe Types of Fractals

Mandelbrot Set Pythagoras Trees Sierpinskis Triangle Plasma Fractals Star Fractals Circle Fractals Lorenz Fractals Levy Curve The Golden Ratio

Snowflakes Crystals Dragon Fractal Julia Sets Newton Fractals Pascals Triangle Peano Curves Formula Fractals Ginger Fractals Orbital Fractals Quaternion Mandelbrot Set

Mandelbrot sets are mathematical sets of points closely related to a general class of fractal. This fractal is closely related to the Julia set. The Mandelbrot set was named after mathematician Benoit Mandelbrot in 1978. http://www.youtube.com/watch?v=G_GBw uYuOOs Julia Sets The Julia Set was discovered by Gaston Julia early in the century. The Julia set is mostly found in a modified Mandelbrot set.

http://www.youtube.com/watch?v=NGwim 5kxRUM&feature=related Pythagoras Tree Pythagoras Tree was invented by mathematician Albert E. Bosman in 1942. It is constructed by squares, each triple square touching on another encloses right triangles. By using 30-60-90 degree triangles it can make the tree bend one side called Lopsided Pythagoras tree which also creates a Levy Curve. http://www.youtube.com/watch?v=B0YM_jkmv8A Levy Curve

The Levy Curve was analyzed by Ernesto Cesro in 1906 and G. Farber in 1910, but now bears the name of French mathematician Paul Pierre Levy, who was the first to describe its self-similarity properties. The Levy Curve also known as the C-curve. The C curve is built using 45* isosceles triangles. It can be used at any degrees other then 45* but below 60*. Angles less then 45* make a fractal that is tightly curled. http://scratch.mit.edu/projects/ngmr/34534 Sierpinskis Triangle Sierpinskis Triangle was discovered by

mathematician Waclaw Sierpinski in 1916. Its a process of subdivision; with screen revolution it can be seen to continue indefinitely also known as the chaos game. The Sierpinskis triangle starts with a normal equilateral triangle. Then connect the midpoints of each side to form four separate triangles and cut out the triangle in the center. For each of the remaining triangles perform this act indefinitely. Plasma Fractals Due to their randomness, plasma fractals closely resemble nature. Plasma Fractals are really useful to use in

making landscapes and cloud like features. By using the atlas colors we can tell the height of the colors to make a 3D landscape. http://www.youtube.com/watch?v=5fFHAmcQdvI Star Fractals Star fractals are formed by taking a 5-corner star and connecting the stars that are 3 times smaller to every corner. Which makes the process an act of Iteration. A repeated process with the aim of approaching a target. There are different types of star fractals such as: the Pentagon fractal that's made up of many

pentagons, another of triangles and the other one as squares. Circle Fractals Circle fractals was introduced by Apollonius of Perga. Circle fractals are based on repeated placement of two equal tangent circles within each circle of the figure. Circle fractals are closely resembled to the Cantor set. Cantor Set The Cantor set was introduced by German

mathematician Georg Cantor in 1833. It was originally discovered by Henry John Stephen Smith in 1875. Van Koch Line Fractal Van Koch line fractal involves a line that is breaking into segments to produce a pyramid like segment. First you start with a line, break it into 3 segments (AC,CD,DF), bring the middle segments (CD) up, then connect B to AC segments and E to DF segment. Repeat the process and the Van Koch line fractal is started.

Snowflakes The Koch snowflake is based on the Koch Curve which was described by Helge Von Koch in 1904. It is built by starting with an equilateral triangle and removing the inner third of each side and building another equilateral triangle at the location where it was removed, the process in repeated indefinitely. Crystals Fractal crystals is most constructed by

starting with a first generation cube and placing a half-scale cube on the center of each face. The second-generation cubes have the same orientation as the firstgeneration cube and so on indefinitely. http://www.youtube.com/watch?v=uGhtt4OB yoU Heres also a cool link to play with fractal cubes. http://www.coolmath.com/fractals/tmapcube/i ndex.htm Dragon Fractals A dragon curve is a repeated nonintersecting curve whose name comes from its resemblance

to a certain mythical creature the Dragon. Imagine taking a strip of paper in half, and then unfolding it to that angle formed at 90 degrees. Then consider folding it twice and three times and then infinitely. http://www.youtube.com/watch?v=ZBOE4Tt4OQ o&feature=related Pascals Triangle Pascals Triangle was named after French mathematician Blaise Pascal. The Pascals triangle starts with number 1 at the top, then continue placing the number in a triangular pattern.

Each number is just two numbers above it added together (except the edges which are all number 1). Peano Curve In 1880 Italian mathematician Giuseppe Peano constructed the Peano curve. The Peano curve is mostly known as the space-filling curve. Its a curve that has a range that contains an entire 2-dimensional. http://www.youtube.com/watch?v=4RQmL Na5ZNo

Quaternion Quaternion are number of systems that extends the complex numbers. It was first described by Irish mathematician Sir William Rowan Hamilton in 1843. Its applied to mechanics in 3-dimensional space. Unit quaternion provide a convenient mathematical notation for representing orientations and rotations of objects in 3dimension. Software for Fractals Mandelbulber- is an easy to use software that helps you design 3D Mandelbrot sets. Free to download. XenoDream- has unique 3D graphics which allows

you to explore or create your own fractal. It allows you to create different lighting and textures. You can also make animations. These are only a couple of softwares that you can use. There are a lot more you can use, heres a link I found with more software programs. http://fractalfoundation.org/resources/fractal-software/ Resources

http://www.olympus.net/personal/dewey/mandelbrot.html http://mathworld.wolfram.com/MandelbrotSet.html http://library.thinkquest.org/26242/full/types/ch5.html http://www.mcgoodwin.net/julia/juliajewels.html http://library.thinkquest.org/26242/full/types/ch11.html http://www.phidelity.com/blog/blog/nerdy-stuff/fractal/pythagoras-tre e/

http://library.thinkquest.org/26242/full/fm/fm18.html http://scratch.mit.edu/projects/ngmr/34534 http://serendip.brynmawr.edu/playground/sierpinski.html http://www.zeuscat.com/andrew/chaos/sierpinski.html http://library.thinkquest.org/26242/full/types/ch10.html http://bocoup.com/processing-js/docs/index.php?page=Plasma%20 Fractals More Sources

http://library.thinkquest.org/26242/full/types/ch13.html http://www.tnlc.com/eep/circles/ http://mathworld.wolfram.com/CantorSet.html http://www.tgmdev.be/curvevonkoch.php

http://library.thinkquest.org/26242/full/fm/fm16.html http://www.coolmath.com/fractals/tmapcube/index.htm http://cloudscape.blogspirit.com/archive/2009/12/20/crystal-fractals. html http://library.thinkquest.org/26242/full/fm/fm8.html http://ptri1.tripod.com/ http://planetmath.org/encyclopedia/PeanoCurve.html http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/ quaternions/index.htm http://fractalfoundation.org/resources/fractal-software/

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