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Most of us are taught that mathematics is clear-cut and predictable, but let's imagine that your formulas give vastly different results for only slightly different inputs. Imagine further that your formulas are completely unpredictable under certain conditions. This was the state of affairs in which Mitchell Feigenbaum, then of the Los Alamos National Laboratory, found himself while studying some very simple classes of functions in a way that no one had before. It led to the uncovering of some unexpected and universal patterns involving very simple functions. Explore the numbers and plots that underlie the Feigenbaum constant, and along the way find explanations of ideas central to chaos theory.