TED Talks
Ted: Ted Ed: Fractals and the Art of Roughness
Mathematics legend Benoit Mandelbrot develops a theme he first discussed in 1984- the extreme complexity of roughness and the way that fractal math can find order within patterns that seem unknowably complicated. [17:10]
University of Massachusetts
Fractal Project: Exploring Fractals
A good beginner's site for fractals - the language is straightforward and requires only minimal experience to be able to understand the topic. (Note: When clicking on links on archived site, they may pause and appear not to be found...
Fundación Cientec
Fractales en Su Aula
Lesson plans and activities available in Spanish dealing with fractals. Some are also available in English. Activities are step by step and easy to understand. Included topics are the Koch Snowflake, Sierpinski's triangle, and Pascal's...
Rice University
Rice University: Cynthia Lanius: Fractals Unit
This site from the Rice University provides a Fractals Unit for Elementary and Middle School Students. Find out what a fractal is and what it looks like. You can value fractals for their visual delight or mathmatical properties. This is...
![University of Waterloo: Cemc: Math Circles: Patterns [Pdf] Unknown Type](https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/FPO-knovation.png "University of Waterloo: Cemc: Math Circles: Patterns [Pdf] Unknown Type")
University of Waterloo (Canada)
University of Waterloo: Cemc: Math Circles: Patterns [Pdf]
This worksheet provides exercises in working with number patterns. Included are questions related to fractals, patterns in exponents, and perimeter and area.
Boston University
Boston University: Chaos, Fractals and Arcadia
This is an interesting site for information on chaos and fractals. Includes links to interactive activities to learn more.
Incredible Art Department
The Incredible Art Department: Art Tessellations
Looks at tessellation artists, including M.C. Escher, Robert Fathauer, and Roger Penrose. This is followed by a discussion of fractals and their similarities and differences to tessellations, and links to lessons and resources on...
Boston University
Fractal Geometry of the Mandelbrot Set Ii
This web site addresses counting and adding in fractal operations, as well as the role of the Fibonacci sequence in fractal geometry.
National Council of Teachers of Mathematics
The Math Forum: Fractals
This site contains many links to Fractal information where students go to the given links to discover interesting facts about fractals and many mathematical equations that represent a fractal.
Boston University
Bu: Fractal Geometry of the Mandelbrot Set
This site progresses in iterations through Mandelbrot and Julia sets to explain fractals and the mathematics behind them.
Shodor Education Foundation
Shodor Interactivate: Lesson: Finding Patterns in Fractals
Young scholars will find patterns in fractals through this lesson and describe them mathematically. Students will use their prior knowledge of arithmetic with rational numbers in this lesson.
Shodor Education Foundation
Shodor Interactivate: Lesson: Fractals
This site provides some links to activities and lesson plans dealing with fractals and chaos.
PBS
Pbs: Positive Exponents as Fractals
Explore the relationship between graphic patterns and their mathematical representation. This video focuses on how fractals can be a visual representation of positive exponents.
PBS
Pbs: Negative Exponents as Fractals
Determine the relationship between graphic patterns and what they represent mathematically. This video focuses on how fractals can be a visual representation of negative exponents, which are a way to express repeated division.
Wolfram Research
Wolfram Math World: Fractals
This page briefly illustrates and discusses fractals, which are closely linked to the concept of iteration (repitition.) Site links to well known pictured fractals.
Other
Research Pages: Circle Inversion Fractals
This site introduces the iteration of circle inversions and describes the associated properties.
Illustrative Mathematics
Illustrative Mathematics: 6.ee,g Sierpinski's Carpet
In this task, 6th graders are presented with a large square divided into 9 squares and the center square is then removed. They are asked to find the area of the 8 remaining squares. Each smaller square is divided in the same way and the...
National Council of Teachers of Mathematics
Nctm: Figure This: Fractals
Can you figure out what pattern comes next? Explore patterns and perimeter in this math challenge on fractals. A one page activity from the NCTM Math Challenges for Families collection.
PBS
Pbs: Human Tree: Ratios
Watch as the National Museum of Mathematics creates an interesting series of images using ratios. This video focuses on the proportional relationship observed in fractals and challenges you to do some critical thinking using ratios and...
Curated OER
Research Pages: Circle Inversion Fractals
This site introduces the iteration of circle inversions and describes the associated properties.
Curated OER
Research Pages: Circle Inversion Fractals
This site introduces the iteration of circle inversions and describes the associated properties.
Other
Eal: Fract Ed
A great resource for beginners. The site begins with a definition of iteration of functions, and proceeds from there to discuss fractal dimension.
Other
Academic Info: Mathematics Gateway
This site provides a comprehensive index and general directory to math sites that will help students in the study of circles.
Interactive Mathematics
Interactive Mathematics: Complex Numbers
The world of complex numbers is explored through mini lessons, interactive examples, applications and demonstrations. Topics covered include definitions, basic operations, graphing, different forms of complex numbers, products,...