Difference between revisions of "Self-Similarity Exploration"

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{{Exploration}}
 
{{Exploration}}
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{{objective|Learn how Escher and Dali used self-similarity in their artwork.}}
 
{{objective|Learn how Escher and Dali used self-similarity in their artwork.}}
# Look at [[Square Limit]] ({{Magic}} pg. 182), and the geometric scaffolding on page 183.  Figure out how the scaffolding corresponds to the printed image.
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# Look at [[Square Limit]] ({{Magic}} pg. 182), and the geometric scaffolding on page 183.  Figure out how the scaffolding corresponds to the printed image.  This website [http://www.tess-elation.co.uk/self-similar-tessellations] may help.
 
# How many woodblocks would Escher have carved to make [[Square Limit]]?  How many times would he have pressed the block to make one print?  (Hint:  Look for his initials in the print).
 
# How many woodblocks would Escher have carved to make [[Square Limit]]?  How many times would he have pressed the block to make one print?  (Hint:  Look for his initials in the print).
 
# [[Image:face-of-war.jpg|thumb|<cite>The Face of War</cite>.  Salvador Dali, 1940.]] Describe the (three) transformations which are iterated in Dali’s [[wikipedia:The Face of War|The Face of War]].
 
# [[Image:face-of-war.jpg|thumb|<cite>The Face of War</cite>.  Salvador Dali, 1940.]] Describe the (three) transformations which are iterated in Dali’s [[wikipedia:The Face of War|The Face of War]].
 
#Look at [[Print Gallery]] and also look at Escher’s preparatory sketches for [[Print Gallery]] in {{Magic}}, pages 130-133.  What’s going on in this picture?  Is it self-similar?
 
#Look at [[Print Gallery]] and also look at Escher’s preparatory sketches for [[Print Gallery]] in {{Magic}}, pages 130-133.  What’s going on in this picture?  Is it self-similar?
 
# Explore the [http://escherdroste.math.leidenuniv.nl/ Escher and the Droste Effect] website.  How did they fill in the hole in the middle of [[Print Gallery]]? Describe the self-similarity of the filled-in picture.
 
# Explore the [http://escherdroste.math.leidenuniv.nl/ Escher and the Droste Effect] website.  How did they fill in the hole in the middle of [[Print Gallery]]? Describe the self-similarity of the filled-in picture.
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# Use a fractal generation program (such as this [http://www.cs.princeton.edu/~wayne/mandel/mandel.html Mandelbrot Set Applet]) to explore the Mandelbrot Set.  The Mandelbrot set is self-similar.  Can you find smaller copies of the original picture inside itself?
 
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[[category:Similarity and Fractals Explorations]]
 
[[category:Similarity and Fractals Explorations]]

Latest revision as of 12:45, 15 October 2010


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Objective: Learn how Escher and Dali used self-similarity in their artwork.

  1. Look at Square Limit (Magic of M.C. Escher pg. 182), and the geometric scaffolding on page 183. Figure out how the scaffolding corresponds to the printed image. This website [1] may help.
  2. How many woodblocks would Escher have carved to make Square Limit? How many times would he have pressed the block to make one print? (Hint: Look for his initials in the print).
  3. The Face of War. Salvador Dali, 1940.
    Describe the (three) transformations which are iterated in Dali’s The Face of War.
  4. Look at Print Gallery and also look at Escher’s preparatory sketches for Print Gallery in Magic of M.C. Escher, pages 130-133. What’s going on in this picture? Is it self-similar?
  5. Explore the Escher and the Droste Effect website. How did they fill in the hole in the middle of Print Gallery? Describe the self-similarity of the filled-in picture.
  6. Use a fractal generation program (such as this Mandelbrot Set Applet) to explore the Mandelbrot Set. The Mandelbrot set is self-similar. Can you find smaller copies of the original picture inside itself?

Handin: A sheet with answers to all questions.