An advanced level description of the nature of Brownian motion. Brownian motion, a model formulated to predict matters involving uncertain elements, is related to medical imaging, fractals, robotics, aerosol particles, and stock market...

In this lesson, students will participate in discussions and activities that will have them explore the number patterns and fractal properties of Pascal's Triangle.

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 worksheet provides exercises in working with number patterns. Included are questions related to fractals, patterns in exponents, and perimeter and area.

Students consider the patterns that emerge from agent models and geometric fractals.

A great resource for beginners. The site begins with a definition of iteration of functions, and proceeds from there to discuss fractal dimension.

Students can use this interactive tool to explore a Mandelbrot set of fractals. As they increase magnification up to 250,000,000 times, they keep returning to an image similar to the one they started with.

Based off of the hit television show NUMB3RS, this lesson introduces students to the notion of Brownian motion and has students graph a sample Brownian particle. In Brownian motion, each "step" depends on the "steps" taken previously,...

See a good example of a mathematical construct that is a fractal known as a Sierpinski gasket.

Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, and also learn about properties of fractal objects.

Play the Chaos Game by experimenting with probabilities. Learn about an apparently random process with a not-so-random, geometric fractal result.

A clipart illustration by Phillip Martin titled "Fractals."

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

Explore fractions, ratios, area, and perimeter through guided practice lessons.

Students learn about the characteristics of fractals. The resource consists of a lesson plan, video, and interactive resource that explores fractals.

Step through the generation of Sierpinski's Carpet, a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

Create your own fractals by drawing a "line deformation rule" and stepping through the generation of a geometric fractal.

Step through the generation of the Koch Snowflake, a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.

With the included programs students can design paths and have the calculator increase the complexity of the path to simulate the generation of a fractal.

This is 4-problem quiz/practice. What of the following weights could be used for the subdivision algorithm to give us a fractal?

Enter a complex value for "c" in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.

Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.

Generate complicated geometric fractals by specifying starting polygon and scale factor.

A collection of interactive visualizations that were produced through analysis of economic, political, and market research data. Topics are diverse, e.g., military spending and trade, immigration, consumer spending, crime, unemployment,...