John von Neumann first presented his theory of machine self reproduction in the late 1940's in which he described a machine capable of performing the logical steps necessary to accommodate self reproduction, and provided an explanation in principle for how arbitrarily complex machines can construct other (offspring) machines of equal or even greater complexity. In this thesis, a machine having the von Neumann architecture for self reproduction is designed to operate within the computational world of Tierra. This design implements a (mutable) genotype-phenotype mapping during reproduction, and acts as an exploratory model to observe the phenomena which may arise with such a system. A substitution mapping was chosen to carry out the genotype-phenotype mapping, and two specific implementations of a substitution mapping were investigated, via the use of a look-up table and a translation table. During implementation of the look-up table, preliminary experiments showed a degeneration to self copiers where a lineage of von Neumann style self reproducers degenerated into self copiers. Further experiments showed that a particular phenomenon emerges, where "pathological constructors" quickly develop, which can ultimately lead to total ecosystem collapse. If redundancy is introduced to the genotype-phenotype mapping, certain inheritable perturbations (mutations) prove to be non-reversible via a change to the genotype, which leads to a bias in the evolution of the genotype-phenotype mapping, consistently resulting in the loss of any target symbols from the mapping which are not vital for reproduction. It demonstrated how instances of Lamarkian inheritance may occur, which allowed these genetically ``non-reversible'' perturbations to be reversed, but only when accompanied by a very specific perturbation to the phenotype. The underlying dynamics of the chosen coding system was studied in order to better understand why these phenomena occur. When implementing a translation table, the space of possible mutations to the genotype-phenotype mapping was investigated and the same phenomena observed, where non vital symbols were lost from the mapping, and an instance of Lamarkian inheritance is necessary in order to introduce symbols to the mapping.