Fractals

The Dance of Chance exhibit. Patterns in nature.
http://polymer.bu.edu/museum/

Polygonal. Change the parameters to create a new fractal. You need Java software in order to view the virtual manipulatives.
http://nlvm.usu.edu/en/nav/frames_asid_151_g_3_t_3.html

Iterative. Generate six different fractals. Java software needed to view.
http://nlvm.usu.edu/en/nav/frames_asid_135_g_3_t_3.html

Koch & Sierpinski virtual manipulative. Change colors and pause the fractal simulation at any point.
http://nlvm.usu.edu/en/nav/frames_asid_137_g_3_t_3.html

Fractal Explorer
The fractal explorer shows how a very simple pattern, when repeated can produce an incredible range of images

In ScienceDaily Researchers End Debate Over Fractal Analysis Of Authentication Of Jackson Pollock’s Art

Fractal Paper Toys
http://www.ss42.com/pt/fractle/fractle-fidgets.html

Fractal Cutout Card Cut out a 3-dimensional fractal and turn it into a pop-up card.

Constructing The Dragon: Step by step process of constructing the first few levels of the Dragon fractal from an 11 inch strip of paper. From the Fractal Grower.

The Fractal Foundation offers Fractivities which are hands-on projects that teach fractal concepts in a fun, artistic way. Choose from the Koch Curve, Nature Walk Bingo, tetrahedrons, and more.

Sierpinski’s triangle is an example of a fractal, or a never-ending pattern that is similar at different sizes. It also resembles a geometric evergreen tree! In this activity, you will learn how to cut and fold your own fractal tree into a holiday card. https://www.youtube.com/watch?v=Xq25Ofm8UZU

Fractal Geometry of Nature from Euler’s Academy YouTube channel https://www.youtube.com/watch?v=iAjxA5_pNnk

An article from Scientific American How Fractals Can Explain What’s Wrong with Wall Street

Fractals Unit: Iterative Formation written by Cynthia Lanius This page explains what fractals are and how to create one using simple means. There are several applets to watch the formation of basic fractal patterns as well as activities to draw or cut fractals out of paper.

Draw a Fractal Dragon using colored pencils.

Smithsonian Magazine article Fractal Patterns in Nature and Art Are Aesthetically Pleasing and Stress-Reducing

Fractal Diversions by Robert Fathauer has been playing around with fractals for over 25 years, both as recreational math and as mathematical art. View his gateway to his explorations. Everything from Fractal Tiling to Polyhedra, Iterated Knots and more. Papers Related to Fractals, Knots, and Tiling.

Fractals – The Hidden Dimension NOVA
What do movie special effects, the stock market, and heart attacks have in common? They are connected by a revolutionary new branch of math called fractals, which changed the way we see the world and opened up a vast new territory to scientific analysis and understanding. Meet the mathematicians who developed fractals from a mere curiosity to an approach that touches nearly every branch of understanding, including the fate of our universe.
https://www.youtube.com/watch?v=d0Exnv8Ym7s

Explore the Mandelbrot set, the most famous of fractals, to a magnification of 250,000,000x. Discover what is meant by self-similarity and understand how the iconic Mandelbrot-set shape keeps turning up at smaller scales.

Interactive Mathematics Miscellany and Puzzles Fractals and Chaos

Mathigon Fractals Course online course for fractals

Youcubed Fractals Line Fractal, Hilbert 3D Space Filler, Snowflake, and Advanced Fractals.

Wolfram Demonstrations Project: Wolfram offers interactive demonstrations on a variety of topics, including fractals. These demonstrations allow students to visualize and interact with different types of fractals, which can help deepen their understanding. Wolfram Demonstrations Project – Fractals

Fractals and Chaos | Introduction To MATLAB Programming MIT offers course materials, including lecture notes and assignments, on fractals and chaos theory. These materials are suitable for older students who want a more in-depth study.