Complexity Explorer Santa Few Institute

Fractals and Scaling (Fall, 2015)

Lead instructor:

This course is no longer in session.

2.7 Programs and Resources » Other resources

Brainfilling Curves: A Fractal Bestiary, by Jeffery Ventrella.  An attractively illustrated book with many surprising variations on the Koch curve.  Available at: https://archive.org/details/BrainfillingCurves-AFractalBestiary.

Philip Ball's Nature's Patterns trilogy is fantastic. A well-grounded, accessible introduction to an enormous range of pattern-forming systems. Of the three, Branches is the most relevant to the material from this unit.

  • Ball, Philip. Branches: Nature's patterns: a tapestry in three parts. Oxford University Press, 2009.
  • Ball, Philip. Shapes: Nature's patterns: a tapestry in three parts.  Oxford University Press, 2009.

  • Ball, Philip. Flow: Nature's patterns: a tapestry in three parts.  Oxford University Press, 2009.

Classic Iterated Function Systems, a set of web pages by Larry Riddle.  Available at: http://ecademy.agnesscott.edu/~lriddle/ifs/ifs.htm.  A clear and accessible introduction to IFSs and L-systems.

Falconer, Kenneth. Fractal geometry: mathematical foundations and applications. John Wiley & Sons, 2004. This is the definitive mathematical text on fractals.  Includes extensive treatment of iterated function systems.  Written at a level appropriate for junior-level mathematics majors.

Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. Chaos and fractals: new frontiers of science. Springer Science & Business Media, 2006.  Has an excellent discussion of a wide variety of ways of making and thinking about fractals.  Highly recommended.  Don't be intimidated by its immense size; this is a friendly and accessible book.

The wikipedia articles on l-systems and iterated function systems are good places to start if you want to dig deeper into these topics.

The wikipedia article on fractal landscapes is good, as is this description by Paul Martz of some of landscape-generating algorithms.