Here you can zoom around the Mandelbrot Set, which is a fun thing to do if you cannot sleep at night. The set is a good example of how a simple mathematical equation can produce complex behaviour. The black region represents points that are in the set. An iterative algorithm is used to determine whether points are in the set or not. For those points not in the set, the colour intensity indicates how many iterations of the algorithm were required to determine that the point was not in the set. With brighter colours

The backend server for the calculation runs as a serverless AWS Lambda function.