Exploration 2: Substitution Fractals

  1. Find or draw a picture you like, with prominent parts inside its outline. The object can contain the parts, such as an owl’s head with two big eyes, or an open book with large illustrations. Or it can be made of the parts, for example, a word out of letters, or a window out of panels. You can also start with an abstract shape, like a triangle split into triangles. Replace each part with a miniature copy of the whole shape. Repeat several times. You just drew several levels of a substitution fractal! (see image below for an example)
  2. Substitution fractals show parts of parts of parts, such as one-tenth of one-tenth of one-tenth of a meter making a millimeter. Substitution fractals focus inward: you zoom in, almost like a microscope. What else can you find that pulls you inward through nested pictures — art, abstract designs, nested dolls, symbolic pieces, such as Bruegel’s “Big fish eat small fish.” Nested structures also appear in traditional architecture, rhymes, and stories, such as “This is the house that Jack built.” What can you find?
  3. One of the most famous ways to make this kind of fractal is called the “Droste Effect” — you can find many examples online. Consider looking at the online tool http://www.photospiralysis.com/ to make Droste Effect images. There are also droste effect plug ins and effects in many visual software, like photoshop. What Droste effect images did you find?

This exploration is due in class next Monday — bring the image you drew and any thoughts you have about nexted structures or the Droste effect. If you have a cool image that you found or created, leave it in a comment below!



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