Dimension of Sierpi skis Square Problem: Figure 11-6g shows the pre-image and the first iteration of Sierpi skis square. The original pre-image is divided into four self-similar squares, each of which has side lengths that are 40% of the side lengths in the pre-image. a. The complete Sierpi skis square is formed by iterating infinitely many times. What, then, is the dimension of the final Sierpi skis square? Sierpi skis square. How does the result correspond to the dimension of the square? Sierpi skis square. How does the result correspond to the dimension of the square? d. Suppose that the self-similar squares at each iteration had side lengths that were 50% of the side lengths of the preceding image. How would this change the dimension of the square? Why is it not correct to call Sierpi`nskis square a fractal in this case? e. Suppose that the self-similar squares at each iteration had side lengths that were 60% of the side lengths of the preceding image. How would this change the dimension of the square? How would it affect the total area of the square?

Ento 2010 Week 12 Notes April 4, 2016 o Mantids can “hear” the sonar of bats Mantids dive to avoid the bats o Importance of “behavior” in mimicry: Caterpillars avoid birds Birds see leaf damage and find caterpillars Cryptic caterpillars look like leaf or twig ...