An important computational model studied in Formal Languages and Automata Theory is the Turing machine and its extensions like the multitape Turing machine. Designing such machines is challenging because of the low level of abstraction they provide making it difficult to understand why words in an unrestricted language are accepted or rejected or why the value of a function is correctly computed. Furthermore, many students may struggle to understand how to design such machines using nondeterminism or mutation. To address these problems, this article presents two new dynamic visualization tools for machine execution: one for Turing machines and one for multitape Turing machines, both of which are integrated into the domain-specific language FSM. These tools visually trace all computations that may be performed in a stepwise manner and aid students in the validation and verification process of their machines. In addition to tracing an arbitrary machine designed by the programmer, the tools display when state invariant predicates hold or fail hold. The results of a formative empirical study exploring student perceptions suggest that the tools are well-received and help students understand, debug, and validate their designs. In addition, the results also suggest that students feel that the tools help them understand nondeterminism.