A cell? A bug? No, a math equation. This is a family of functions, which are expressions of relationships between sets of numbers. Jane Hawkins, professor of math, uses computers to help her understand chaotic behavior in certain functions. The family shown here is f(z) = a(z + 1/z - 1.25). Each point on the image represents the function that results when a different value of a is substituted in the equation. This map, which Hawkins has nicknamed "scarab" because its shape resembles a beetle, is somewhat mysterious so far. To learn more about the family, she uses her computer to run certain points on the map through time to see how they behave. Repeating these experiments will help her figure out what patterns on the image may denote chaotic behavior. Then she'll try to prove a mathematical theorem that proves what the picture suggests.

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