The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a sparse neural network. More recent work has demonstrated the remarkable result that certain sparse DNNs can train to the same precision as dense DNNs at lower runtime and storage cost. An intriguing class of these sparse DNNs is the X-Nets, which are initialized and trained upon a sparse topology with neither reference to a parent dense DNN nor subsequent pruning. We present an algorithm that deterministically generates sparse DNN topologies that, as a whole, are much more diverse than X-Net topologies, while preserving X-Nets' desired characteristics.