Learning Resources for Students, Families and Teachers

Search over 100,000 research quality URLs

StudySphere provides fast, easy and free access to a wide variety of research-quality child-safe websites organized for education online from home, school, study abroad and home school. StudySphere’s goal is to help students, teachers, librarians, and other researchers find both highly targeted and closely related information quickly.

Tutorials

/Home/Mathematics/Advanced Math/Fractals/Tutorials


		About Fract-ED ^Votes:0 The Fract-ED Information Pages LinkExchange Member Thank you for visiting the Fract-ED pages. Herein are presented excerpts from the first installment of Fract-ED, along with descriptions and sample images from some of the forthcoming additions to the series. What is Fract-ED? Fract-ED is an introductory fractal tutorial intended for high school or college entry-level students. It is an informal discussion of some of the elements of fractal geometry, and includes interactive programs which demonstrate the techniques of fractal generation. Please be aware that these documents are incomplete in their HTML form. Additional links need to be made, and I will continue to update them as time allows. Contents From the Author ... Introduction What is a fractal? A Modern Tool Iteration - A 'popular' Read More Go to Site


		Exploring Fractals ^Votes:0 Exploring Fractals by Mary Ann Connors publications and photos Department of Mathematics and Statistics University of Massachusetts Amherst This World Wide Web project commenced in July 1994. It is is based on a curriculum, entitled "Exploring Fractal Dimension," developed by Mary Ann Connors and Anna Rose Haralampus at an NSF funded Institute for High School Mathematics Teachers at Georgetown University July - August, 1991. Its revision entitled "Exploring Fractals: From Cantor Dust to The Fractal Skewed Web" has been edited by Mary Ann Connors 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, and 2004. (c) Copyright 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, and 2007 by Mary Ann Connors. All rights reserved. Exploring Fractal Dimensions of Str Read More Go to Site

		Fractal Explorer: Mandelbrot and Julia sets (by Fabio Cesari) ^Votes:0 Keywords: fractals, mandelbrot set, fractal, julia sets, quaternion, quaternion julia sets, Mandelbrot, Julia Your browser doesn't support frames. This site is best viewed with Netscape 3.0 , or an equivalent browser that supports JavaScript and frames . You can always access this no-frames version of this site. If you have troubles accessing it, please let me know Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms, how the Mandelbrot set and Julia sets are generated. This document provides an informal introduction to these subjects, and is only intended to be a starting point to learn more about fractals and fractal geometry. You can contribute to the future development of this site by fillin Read More Go to Site

		Fractal Ferns ^Votes:0 This page has nothing whatever to do with real ferns except the beauty of likenesses you can create of them. Like many people, I've been fascinated by the images of ferns generated by computer using the mathematics of fractals. When I mentioned to a friend that I was developing a series of Web pages on ferns, he suggested I also include a piece on fractal ferns (thanks HR). This page is the result. Put simply (probably a gross oversimplification), fractals generate points to plot on a graph that are the result of iterated calculations. The answer from one calculation is used as the input value to the next calculation. The beautiful Madelbrot images are generated by programs that assign a colour to any point on the graph, depending on how that point behaves when it is used as a starting poi Read More Go to Site

		Fractal Frequently Asked Questions and Answers ^Votes:0 MultiPage Fractal Frequently Asked Questions and Answers There are reader questions on this topic! Help others by sharing your knowledge From: stepp@muvms6.mu.wvnet.edu (Ermel Stepp) Newsgroups: sci.fractals Subject: Fractal Frequently Asked Questions and Answers Date: 23 Apr 1995 04:36:54 GMT Message-ID: <fractal-faq_798611453@rtfm.mit.edu> Reply-To: stepp@marshall.edu Summary: Fractal images, software, algorithms, definitions, and reference Keywords: fractals, chaos, complexity, Mandelbrot X-Last-Updated: 1995/02/20 Archive-name: fractal-faq Posting-Frequency: monthly Last-modified: Mon, 13-Feb-1995 Version: v1n1 FRACTAL FAQ (FREQUENTLY ASKED QUESTIONS) ___________________________________________________________ ISSN Pending Volume 1 Number 1 February 13, 1995 _____________________ Read More Go to Site

		Fractal Gallery: What Is a Fractal? ^Votes:0 [an error occurred while processing this directive] What Is a Fractal? And who is this guy Mandelbrot? Images and text by Alan Beck The word "fractal" was coined less than twenty years ago by one of history's most creative mathematicians, Benoit Mandelbrot, whose seminal work, The Fractal Geometry of Nature , first introduced and explained concepts underlying this new vision. Although prior mathematical thinkers like Cantor, Hausdorff, Julia, Koch, Peano, Poincare, Richardson, Sierpinski, Weierstrass and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fruitful discipline. Lamp (63 k / jpg) Mandelbrot derived the term "fractal" from the Latin verb frangere , Read More Go to Site

		Fractal Terrains in Bryce 2 ^Votes:0 Fractal Terrains in Bryce 2 By Steve Lareau Hilltop Design This tutorial is on how you can turn a fractal into a terrain in Bryce from Metatools, although this concept can be applied to most other graphics programs. I'm assuming that you've already spent time tinkering with Bryce, and if this is the case, this should be a snap. (By the way- this tutorial was created in Bryce 2 for Windows; this will work in Bryce 3D as well, you'll just have to adjust to the different interface.) I've included everything in this tutorial- the images found here, as well as the scene file I used for this tutorial in a ZIP file which you can open up in Bryce 2 and Bryce 3D so you can study it. Scroll to the bottom of this page and start your downloads, then come back here and start doing some reading. Before Read More Go to Site

		Fractal Tutorial Page ^Votes:0 Fractal Tutorial Page LINK PAGE <<< Back to Koski's > >> HOME PAGE -P1 PI PAGE -P3 MATH ACTIVITY PAGE -P5 GAME PAGE -P4 Fractal Fun Page Fractal Gallery Page I bet you are wondering what a fractal is! A fractal is basically a small piece of an object that mimics that of a larger portion of that object. Can You Picture It ?? Lets think of some real life fractals! Hmmmmmmm!!!! Snowflakes ..... Mountains ..... Crystals .... Ferns ... Coastlines Nature is FULL of Fractals! OK .... So what is the big deal. Well, fractals have been found to exist in the real WORLD and they posses a unique quality that is quite intriguing. Currently fractals are a major issue of study for Mathematicians around the world !!! Studies are being conducted about this marvelous mathematic phenomenon. Read More Go to Site

		fractalprogression ^Votes:0 Announcing! A fractal tutorial. It's made for kids, but take a look, you might even learn about fractals... Here All images on this site are the copyrighted property of dwarvenkind. Any commercial use of these images without permission of the artist is strictly prohibited. My e-mail link Welcome to my website. This site is a visual experience. If you are looking for a scientific explanation of fractals, mathematics and color point expression... Search elsewhere. If you like color, symmetry, chaos, order or just want a good visceral, visual experience. I welcome you. The fractals on this site were created using many different programs. For more information about Fractal Explorer or how I create the artwork on this site, here's a link to some of my ramblings on the subject; otherwise, check Read More Go to Site

		Fractals & the Fractal Dimension ^Votes:0 Fractals and the Fractal Dimension Mandelbrot and Nature "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."(Mandelbrot, 1983). The Concept of Dimension So far we have used "dimension" in two senses: The three dimensions of Euclidean space (D=1,2,3) The number of variables in a dynamic system Fractals, which are irregular geometric objects, require a third meaning: The Hausdorff Dimension If we take an object residing in Euclidean dimension D and reduce its linear size by 1/r in each spatial direction, its measure (length, area, or volume) would increase to N=r D times the original. This is pictured in the next figure. We consider N=r D , take the log of both sides, and get Read More Go to Site

		Fractals: An Introductory Lesson ^Votes:0 Fractals: An Introductory Lesson Fractals -- An introduction A Process to Generate Fractals A bit of Fractal Math The Koch Curve Fractal The Sierpinski Triangle Fractal The Dragon Curve or Jurassic Park Fractal L-System Based Fractals -- with many fractal examples Check awards and feedback Last Updated: Friday, 11-Aug-2000 22:59:35 GMT Arcytech Java Home Page Provide Feedback Read More Go to Site

		FRACTINT L-systems tutorial ^Votes:0 Fractint L-Systems Tutorial A tutorial by William McWorter mcworter@midohio.net version 1.4 January 1997 WHAT ARE L-SYSTEMS PLANTS TILINGS SPACEFILLING CURVES TRUE FRACTALS VARIATIONS FURTHER INFORMATION Back to The Fractint Home Page. or back to The Fractint Index Page. This page maintained by Noel Giffin, noel@triumf.ca Read More Go to Site

		Kerry Mitchell ^Votes:0 Kerry Mitchell Book Sixteen Variations on a Single Theme Galleries nineteen eighteen seventeen sixteen fifteen fourteen thirteen twelve eleven ten nine eight seven six five four three two one Other Stuff Tutorials Fractal Articles My Ultra Fractal Help Files Contact me or buy prints All images © Kerry Mitchell Read More Go to Site

		Making Order Out of Chaos ^Votes:0 Making Order Out of Chaos Making Order out of Chaos This page is best viewed with Netscape Navigator. You can also view the no frames version, without the table of contents. Read More Go to Site

		Mandelbrot and Julia Set Explorer ^Votes:0 Julia and Mandelbrot Set Explorer David E. Joyce 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 . Also, check out the Applet to explore the Mandelbrot set . I recently stumbled upon StumbleUpon that helps you discover and share great websites. You can create a public blog of websites you like and find other websites like those you like. You'll need either a Firefox browswer or a Mozilla 1.5-1.8 complient browser. Mandelbrot Set : x in [-1.0,2.0]; y in [-1.5,1.5]. Parameters Clicks on the Mandelbrot set image will get a Julia set magnify the Mandelbrot set by a factor of Alternate Mandelbrot parameter plane mu lambda (mu = lambda^2/4-l Read More Go to Site

		Math Forum - Ask Dr. Math Archives: High School Fractals ^Votes:0 Ask Dr. Math High School Archive Dr. Math Home \|\| Elementary \|\| Middle School \|\| High School \|\| College \|\| Dr. Math FAQ TOPICS This page: fractals Search Dr. Math See also the Internet Library : fractals HIGH SCHOOL About Math Analysis Algebra basic algebra equations/graphs/ translations linear algebra linear equations polynomials Calculus Complex Numbers Calculators/ Computers Definitions Discrete Math permutations/ combinations Exponents Logarithms Fibonacci Sequence/ Golden Ratio Fractals Functions Geometry Euclidean/plane conic sections/ circles constructions coordinate plane triangles/polygons higher-dimensional polyhedra non-Euclidean practical geometry symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzle Read More Go to Site

		Suzanne Alejandre - Fractal links ^Votes:0 --> Suzanne's Math Lessons Fractals Suzanne Alejandre Magic Squares \|\| Multicultural Math Fair \|\| Polyhedra \|\| Tessellations What is a fractal? From the Fractal FAQ: "A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale." "There are many mathematical structures that are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set, and Lorenz attractor. Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes." The Fractal FAQ was created and edited by Ken Shirriff through September 26, 1994. The current editor i Read More Go to Site

		The Fractory: An Interactive Tool for Creating and Exploring Fractals ^Votes:0 A ThinkQuest project by David Green , Alex Kulesza , and Keith Bergstresser Welcome to The Fractory! This page will help you learn about fractals: what they are and how to design them, but it will also let you discover more on your own. Fractals are just now emerging as a science. They show an order in seemingly random things, and give us tools with which we can predict the weather, render natural looking objects, and help understand the order in our chaotic lives. You will also play a part in our interactive fractal creation center, designing and displaying fractals you have invented. You can even post your coolest fractals on our fractal message board. How to Understand Fractals Fractals can be understood on many different levels. We have separated the information on this page into the f Read More Go to Site

		Tiera-Zon Fractals Tutorial ^Votes:0 Since you are visiting this tutorial, I suspect that you may have been bitten by the "fractal bug". This tutorial is written for a freeware fractal program called Tiera-Zon . Go download the program if you don't already have it since you will need it for this tutorial. This program is not exactly "intuitive" so I have written this tutorial to help you get familiar with the program and how it functions. So, lets get started. Open a new document (CTRL N). Up pops your basic fractal starting point. You might want to open another at this time so you can have two images to work on at the same time. Now, before you jump right in it's best if you learn how things work. The first thing you might want to do is to change the size of your fractal image. To do this, click on the button on the left too Read More Go to Site

		Welcome to Fractal World! ^Votes:0 You are visitor number since May 15, 1997. Back to Projects Welcome to Fractal World! On this web page, you will be introduced to the mysterious world of fractal geometry. You have the choice to learn about three major topics of fractal (see chart below).By clicking on "What is a Fractal?" , you will find basic information on the formulas and origins of fractal geometry. Under "What is a Fractal? 2" , I've included more complicated information like the Mandelbrot function, and imaginary numbers. Click on "Fractal Links" , and you will find a list of other fractal related sites across the Internet. Finally, view some very appealing computer generated fractals under "Sample Pictures" . So, prepare to be shocked as you enter the great Fractal World! &qu Read More Go to Site

StudySphere is an outstanding resource for homework help, special education, music school, cooking school, charter schools, art schools, technical schools, traffic school, film schools, catholic schools, etc.