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Complex Analysis: an Open Source Textbook

Chapter 4 Sequences, Series, and Fractals

In 1980 Benoit Mandelbrot led a team of mathematicians in producing some stunning computer graphics from very simple rules for manipulating complex numbers. This event marked the beginning of a new branch of mathematics known as fractal geometry. Many of the tools needed to appreciate Mandelbrot’s work are contained in this chapter. We look at extensions to the complex domain of sequences and series, ideas that are part of a standard calculus course.