Subsubsection 1.1.1.2 Quadratic Julia sets
The Mandelbrot set arises in the study of the family of functions \(f_c(z)=z^2+c\text{.}\) If we iterate \(f_c\) for a fixed \(c\text{,}\) we can generate a Julia set. Here are a few examples: 
The preceding images were all generated with custom Python code. Here is an easy to use, point and click web app where you can explore the relationship between the Mandelbrot set and quadratic Julia sets: