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Evolution can be broadly described in terms of mutations of the genotype and the subsequent selection of the phenotype. The full enumeration of a given genotype-phenotype (GP) map is therefore a powerful technique in examining evolutionary landscapes. However, because the number of genotypes typically grows exponentially with genome length, such calculations rapidly become intractable. Here I apply graphics processing unit(GPU) techniques to the hydrophobic-polar (HP)model for protein folding. This GP map is a simple and well-studied model for the complex process of protein folding. Prior studies on relatively small 2D and 3D lattices have been exclusively carried out using conventional central processing unit (CPU) approaches. By using GPU techniques, I was able to reproduce the pioneering calculations of Li et al.[1] with a speed up of 580-700 fold over a CPU. I was also able to perform the largest enumeration to date of the 6x6 lattice. These novel calculations provide evidence that a popular "plum-pudding" metaphor that suggests that phenotypes are disconnected in genotype space does not describe the data. Instead a "spaghetti" metaphor of connected genotype networks may be more suitable. Furthermore, the data allows the relationships between designability and complexity within GP space to be explored. GPU approaches appear extremely well suited toGP mapping and the success of this work provides a promising introduction for its wider application in this field.