Introduction to Fractal Geometry and Chaos Theory

Welcome! Here you will find a variety of links to online resources used as a part of this workshop series.

  • Copies of fractal sketching templates – including Sierpinski Triangle and “Iterating a Curve” sheets (also includes Koch Snowflake and Sierpinski Carpet templates)
  • Richardson Plot results – for recording the data gathered to calculate the dimension of the coast of Great Britain
  • The Chaos Game – demonstrating the constrained randomness of chaos, and the patterns that can emerge. Developed by former F&C student Istvan Burbank
  • Iterating Linear Functions – examples used in the exploration of iterations of linear functions in the real number system
  • Cobweb Diagram Geogebra Apps – for visualizing iterations of functions in the real number system
  • Logistic Function Catalog of Behavior – for recording the destination of orbits of the function ax(1-x) for different values of a
  • Logistic Function Cobweb Diagram – a Desmos graph for exploring the logistic function specifically (note that this graph only uses 40 steps of iteration; some orbits may take longer to reach their “destination”)
  • Logistic Orbit Generator – a Google sheet that shows the first 500 iterations of two adjacent seeds for a given value of a.
  • Feigenbaum Plot Viewer – a highly detailed version of the Feigenbaum Plot. Click and drag a rectangle to zoom in on that portion. Right click to show the orbit of that value of a. Developed by former F&C student Paul Fisher-York
  • Iterating Complex Numbers Worksheets – including polar/rectangular conversions, iterating linear functions, and iterating quadratic functions.
  • Complex Paint – a tool for iterating linear and non-linear functions in the complex number system. Must be downloaded to use. Apple and Windows versions available.
  • Fractal Zoomer – a tool for exploring the Mandelbrot Set. Must be downloaded to use. Apple and Windows versions available

Here are some supplemental resources that we did not use as a group, but you may want to investigate on your own.

  • FractaSketch – simple fractal sketching software. Program must be downloaded to use, Windows and Apple versions available. Software still in beta, so susceptible to crashes. Developed by former F&C students Devon Loehr and Connor Simpson
    • Draw the template for your fractal using iterating and non-iterating segments. Right click (Windows) or Ctrl-Click (or Two-Finger click, Mac) to end your template. The dotted line that appears will be the reference segment that each iterating segment you included in your template will use. Read the README file contained for more instructions.
    • Online version here
  • IFS Construction Kit – a more mathematically robust fractal designing software. Must be downloaded to use, Windows version only.

Assignments and Mathematical Musings from Mr. Kirk

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