Fractals%20for%20Kids

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Fractals for Kids

• Clint Sprott
• Department of Physics
• University of Wisconsin - Madison
• Presented at the
• Chaos and Complex Systems Seminar
• in Madison, Wisconsin
• on January 28, 2014

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November 6, 2013

• Dear Professor Sprott
• We are book publishers based in the UK. Among our
  many titles is a series of colouring books we
  have produced these in a range of subjects,
  ranging from flowers and impossible figures to
  stained glass, fairies and mandalas. My
  colleagues in Sales have suggested that it might
  be interesting to produce a fractals colouring
  book. For most of our colouring books we
  commission professional illustrators to provide
  mono pictures or patterns with outlines so that
  the purchaser has well defined areas to colour.
  Obviously, fractals are very different from the
  usual types of illustration we use for our
  colouring books. If the idea is to work, we are
  in need of expert input. Would you be interested
  in helping us to produce fractal images that
  could be used for our colouring book? 
• I look forward to hearing from you.
• Best wishes
• Tessa Rose

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Fractals

• According to Benoit B. Mandelbrot (1924-2010), in
  Fractals and Chaos, Springer, 2004
• Roughly speaking, fractals are shapes that look
  the same from close by and far away.
• - - -
• A self-explanatory term for looking the same
  from close by and far away is self-similar.
• - - -
• I named them, tamed them into primary models of
  roughness, and helped them multiply.
• - - -
• As for the word fractal, I coined it on some
  precisely datable evening in the winter of 1975,
  from a very concrete Latin adjective, fractus,
  which denoted a stones shape after it was hit
  very hard. Lacking time to evolve, fractal rarely
  strayed far from the notion of roughness.

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Iterated Function Systems
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Lindenmayer Systems

• Turtle Graphics
• F Move forward one step while drawing a line
• f Move forward one step without drawing a line
• Turn left through a specified angle
• - Turn right through a specified angle
• Typical axiom FFFF (draw a square)
• Typical rule F ? FF-F-FFFF-F
• ?
• Apply rule recursively with decreasing step size
• Result is a very long string of commands
• ? This rule makes a Koch Island (snowflake)

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Cellular Automata
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References

• http//sprott.physics.wisc.edu/
  lectures/coloring.ppt (this talk)
• http//sprott.physics.wisc.edu/chaostsa/ (my
  chaos textbook)
• sprott_at_physics.wisc.edu (contact me)