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. | # 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 [[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. | ||
| + | # Use a fractal generation program (such as [http://mac.softpedia.com/progDownload/FractalWorks-Download-29328.html FractalWorks for Mac]) to explore the Mandelbröt Set. The Mandelbröt set is self-similar. Can you find smaller copies of the original picture inside itself? | ||
{{clear}} | {{clear}} | ||
{{handin}} | {{handin}} | ||
[[category:Similarity and Fractals Explorations]] | [[category:Similarity and Fractals Explorations]] | ||
Revision as of 11:31, 6 March 2009
Objective: Learn how Escher and Dali used self-similarity in their artwork.
- 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.
- 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).
- Describe the (three) transformations which are iterated in Dali’s The Face of War.
- 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?
- 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.
- Use a fractal generation program (such as FractalWorks for Mac) to explore the Mandelbröt Set. The Mandelbröt set is self-similar. Can you find smaller copies of the original picture inside itself?
Handin: A sheet with answers to all questions.
