Kitchen Science Fractals

This book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.
Contents:

• IFS Labs:

  • Finding IFS for Fractal Images
  • Spiral Fractals from IFS
  • Finding IFS Rules from Images of Points
  • A Fractal Leaf by IFS
  • Fractal Wallpaper
  • Cumulative Gasket Pictures
  • IFS and Addresses
  • Decimals as Addresses
  • IFS with Memory
  • IFS with More Memory
  • Data Analysis by Driven IFS

• Dimension and Measurement Labs:

  • Dimension by Box-Counting
  • Paper Ball and Bean Bag Dimensions
  • Calculating Similarity Dimension
  • Sierpinski Tetrahedron
  • Koch Tetrahedron
  • Sierpinski Hypertetrahedron
  • Basic multifractals: ?(?) Curves

• Iteration Labs:

  • Visualizing Iteration Patterns
  • Synchronized Chaos
  • Domains of Compositions
  • Fractals and Pascal's Triangles
  • Fractals and Pascal's Triangle Relatives
  • Mandelbrot Sets and Julia Sets
  • Circle Inversion Fractals
  • Fractal Tiles

• Labs in the Studio and in the Kitchen:

  • Fractal Painting: Decalcomania 1
  • Fractal Painting: Decalcomania 2
  • Fractal Painting: Bleeds
  • Fractal Painting: Mixing
  • Fractal Painting: Dripping
  • Fractal Paper Folds
  • A Closer Look at Leaves
  • Structures of Vegetables
  • Cooking Fractals

• Labs in the Lab:

  • Magnetic Pendulum
  • Optical Gasket
  • Video Feedback Fractals
  • Electrodeposition
  • Viscous Fingering
  • Crumpled Paper Patterns
  • Fractal Networks of Resistors
  • Fractal Networks of Magnets
  • Synchronization in Fractal Networks of Oscillators

• What Else?:

  • Building Block Fractals
  • Non-Euclidean Tilings
  • Fractal Perimeters
  • Multifractal Finance
  • Fractal Music
  • Other Ideas

• Why Labs Matter

Readership: Advanced high school and beginning college students, including those in the humanities, with an interest in how fractal mathematics can reveal patterns in the natural world. Teachers and researchers interested in broadening their understanding of fractal modeling will also find this book of interest.
Key Features:

• This book provides simple experiments that range from computer programs through painting and cooking, to fluid mechanics, electronics, and chemistry. With this background, the reader will be well-prepared to perform their own experiments, and possibly uncover new ways fractals occur in our world
• Working with Benoit Mandelbrot we field-tested these labs with groups of high school and college teachers. The computer experiments can be run with Mathematica and Python code provided, and almost all of the physical experiments can be performed with readily-available equipment and supplies