  The busy beaver problem is a well-known example of a non-computable function.
In order to determine a particular value of this function, it is necessary to
generate and classify a large number of Turing machines. Previous work on this
problem has described the processes used for the generation and classification
of these machines, but unfortunately has generally not provided details of the
machines considered. While there is no reason to doubt the veracity of the
results known so far, it is difficult to accept such results as scientifically
proven without being able to inspect the appropriate evidence. In addition, a
list of machines and their classifications can be used for other results, such
as variations on the busy beaver problem and related problems such as the
placid platypus problem. In this paper we investigate how to generate classes
of machines to be considered for the busy beaver problem. We discuss the
relationship between quadruple and quintuple variants of Turing machines, and
show that the latter are more general than the former. We give some formal
results to justify our strategy for minimising the number of machines
generated, and define a process reflecting this strategy for generating
machines. We describe our implementation, and the results of generating various
classes of machines with up to 5 states or up to 5 symbols, all of which
(together with our code) are available on the author's website.
