Examine an exponential growth model. Using a fractal, learners calculate the perimeters of each stage. When comparing the consecutive perimeters, a pattern emerges. They use the pattern to build an equation and make conclusions.

Young scholars explore the concepts of Sierpinski's triangle, ratios, and concentrations. For this exploratory lesson, students are given three problems to solve. Young scholars learn about Sierpinski's triangle, how to calculate mpg for...

Create a personal tree. By visiting an exhibit at the National Museum of Mathematics, the resource introduces the idea of fractals. The exhibit takes an image of the person and creates a tree by repeating scaled images on the shoulders...

What effect does changing the perimeter have on the area of a figure? The five problems in the resource explore this question at various grade levels. Elementary problems focus on the perimeter of rectangles and irregular figures with...

Explore the mathematics of the paper snowflake! During the five lessons progressing in complexity from K through 12, pupils use spatial geometry to make predictions. Scholars consider a folded piece of paper with shapes cut out....

This page contains links to 4 different worksheets containing fractal problems relating to calculus.There are also 2 links to triangular and square dot paper. All items are available for download.

Use a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...

Check out the handout from a presentation that contains a collection of high school algebra projects connecting a variety of mathematics to the real world. Activities range from simple probabilities to calculus. The activities...

Guiding students through two variable (complex) functions, this worksheet helps them perform complex arithmetic on 6 expressions. They iterate several functions with given starting points, determining whether each is a prisoner, escapee,...

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]

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...

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...

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...

This is an interesting site for information on chaos and fractals. Includes links to interactive activities to learn more.

The fractal explorer shows how a very simple pattern, when repeated can produce an incredible range of images. From organic tree like structures to rigid geometric forms. Fun to use and lots of mathematical concepts involved.

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...

This web site addresses counting and adding in fractal operations, as well as the role of the Fibonacci sequence in fractal geometry.

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.

This site progresses in iterations through Mandelbrot and Julia sets to explain fractals and the mathematics behind them.

Explore the relationship between graphic patterns and their mathematical representation. This video focuses on how fractals can be a visual representation of positive exponents.

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.

This page briefly illustrates and discusses fractals, which are closely linked to the concept of iteration (repitition.) Site links to well known pictured fractals.

This site introduces the iteration of circle inversions and describes the associated properties.

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.