Chaos and Fractals

Subsection 2.2.1 Computing orbits

Suppose \(f(x) = \frac{1}{5}x^2 - 2x + 6\text{.}\) Here's how to compute the first five iterates of \(x_0=1\) under \(f\) using Sage:

Note that the computation is exact. That is, we get rational numbers like \(21/5\text{,}\) rather than decimal approximations like \(4.2\text{.}\) Often we would prefer decimal approximations. Let's set xi = 1.0 in the code block above and compute 100 iterates.