Difference between revisions of "Self-Similarity Exploration"
From EscherMath
Jump to navigationJump to search (square limit link) |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Exploration}} | {{Exploration}} | ||
| − | {{time| | + | {{time|30}} |
{{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. 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. | ||
| + | # 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? | ||
{{clear}} | {{clear}} | ||
{{handin}} | {{handin}} | ||
[[category:Similarity and Fractals Explorations]] | [[category:Similarity and Fractals Explorations]] | ||
Latest revision as of 12:45, 15 October 2010
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. This website [1] 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).
- 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 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.
