Since 1989, we have been developing curriculum materials for high school and undergraduate science education that is based on modern science research. We have developed a number of hands-on activities, laboratory experiments, and interactive visualization programs. The activities on these pages encourage students to explore how fundamentally random microscopic events can give rise to fractal macroscopic patterns in nature.

Related Pages:

• Patterns in Nature Student Activity Guides developed by participating teachers
• Java-powered Fractals in Science Simulation Activities

• Introduction
• The Fractal Coastline and Dimension
  • Coastline
    • HandsOn 1 - "Walking" Along a Coastline
    • HandsOn 2 - Measuring the Dimension of a Coastline
    • HandsOn 3 - Creating a Rope Coastline
    • HandsOn 4 - Creating a Rubber Band Coastline
    • HandsOn 5 - Covering a Coastline with Boxes
    • SimuLab 1 - "Walking" Along a Coastline
    • SimuLab 2 - Covering a Coastline
  • Dimension of "Non-Fractals"
    • HandsOn 6 - 1-, 2-, and 3-Dimensions
    • HandsOn 7 - Circle Measurement of Dimension
  • Mathematical Fractals
    • HandsOn 8- Creating Your Own Mathematical Fractal
  • Dimensions and Logarithms
  • What Do You Think?
  • Research Projects
• Measuring Randomness
  • Measuring Randomness
    • HandsOn 9 - Lottery Game
  • Observed Distributions
    • HandsOn 10 - Coin Flipping
    • SimuLab 3 - Wholesale Coin Flipping
  • Random Walks
    • HandsOn 11 - Ten-Step Random Walk
    • SimuLab 4 - One-Dimensional Random Walk
  • Pascal's Triangle
    • SimuLab 5 - Random Walk and Pascal's Triangle
    • SimuLab 6 - Width of a Distribution
    • SimuLab 7 - Average Position after N Steps
  • Measuring Average Distances
    • SimuLab 8 - Measures of Average Squared Displacement
  • Proving Average Squared Difference
  • The Wandering Ant on a Square Grid
    • HandsOn 12 - Random Walk in Two-Dimensions
    • SimuLab 9 - The Deer Program and Population Dynamics
  • Models in Science
  • What Do You Think?
  • Research Projects
• Physical and Chemical Branching Structures
  • Electrodeposition
    • HandsOn 13 - Growing a Pattern in the Laboratory
  • More on Fractal Dimension
    • SimuLab 10 - Measuring Fractal Dimension
  • Modeling Fractal Growth
    • HandsOn 14 - Building an Aggregate by Hand
    • SimuLab 11 - Building an Aggregate by Computer
    • SimuLab 12 - Changing Particle Movement
    • SimuLab 13 - Measuring the Computer-Generated Aggregation Program
  • Viscous Fingering
    • HandsOn 15 - The Hele-Shaw Experiment with Glycerin
    • HandsOn 16 - The Hele-Shaw Experiment with Carrageenan
    • SimuLab 14 - The Fractal Dimension of Hele-Shaw Patterns
  • Why Do Viscous Fingers Branch?
  • What Do You Think?
  • Research Projects
• Biological Branching Patterns
  • Bacterial Colonies
    • HandsOn 17 - Modeling a Rough Surface
    • HandsOn 18 - Bacterial Growth
  • Termite Nesting and Foraging in Two-Dimensions
    • HandsOn 19 - Termite Tunnel Patterns
  • Fractal Root Systems
    • HandsOn 20 - Building a Rhizotron and Germinating Seeds
    • HandsOn 21 - Growing Roots
  • Research Projects
• Diffusion
  • The Diffusion Chamber
    • HandsOn 22 - The Diffusing Checkers Model
    • SimuLab 15 - The Diffusion Chamber Simulation
    • HandsOn 23 - Deriving the Motion of Molecules
    • HandsOn 24 - Diffusion Chamber
    • HandsOn 25 - Location of the Precipitation Point
  • Periodic Precipitation: Liesegang Rings
    • HandsOn 26 - Liesegang Experiment
  • Research Projects
• Oozing and Growing: Percolation
  • Percolation in Nature
    • HandsOn 27 - Growing a Scattered-Seed Forest
    • SimuLab 16 - Modeling a Scattered-Seed Forest
    • SimuLab 17 - Gathering Statistics in Blaze
    • HandsOn 28 - Growing a Forest from a Single Tree
    • SimuLab 18 - Percolating Forests
    • HandsOn 29 - Jell-O Experiment
  • What Do You Think?
  • Research Projects
• Motion on a Fractal
  • Random Walk on a Fractal
    • HandsOn 30 - Random Walk on a Fractal
  • The Power Law for a Random Walker on a Sierpinski Gasket
  • Diffusion on a Sierpinski Gasket
    • HandsOn 31 - Resistance of a Fractal Network
    • HandsOn 32 - Measuring the Resistance of the Sierpinski Gasket
    • HandsOn 33 - Computing the Resistance of the Sierpinski Gasket
  • An Exact Solution for the Dimension of a Random Walk on a Sierpinski Gasket
• Software Downloads

Note: Some of these tutorials are Flash-enhanced