The visual systems of animals provide them with information about the world they live in that is essential for their survival. An important aspect of this information is a spatial map, which allows an animal to estimate its position and orientation with respect to objects in its surroundings, such as predator or prey. An image of this environment is first formed upon the two-dimensional array of photoreceptors in the retina either by the single lens of the vertebrate eye or by the multiple lenses of the invertebrate compound eye. In response to the light stimulus, photoreceptors generate electrical signals. These signals are then relayed to other arrays of cells, which process them and generate further electrical signals, which are themselves relayed to yet other layers of the visual system. Visual information is thus transferred sequentially from layer to layer of the visual system along parallel pathways connecting these layers. These parallel pathways carry a topographically ordered set of signals, representing the visual stimulus to each layer, by projecting in a manner that preserves the spatial organization of the stimulus. Because the accuracy of the topographic map depends critically upon the accuracy of the layer-to-layer projection of parallel channels, visual systems have been of great interest to neurobiologists investigating the mechanisms underlying the formation of specific connections between neurons. The problem faced is to explain how the axon of a neuron in a particular location in one layer of the visual system manages to find and synapse onto a neuron (or neurons) at a topographically equivalent location in another layer (the target layer). One possible explanation is neuronal specificity: cells at corresponding locations in each array possess unique chemical labels that can be recognized by axons growing to each layer during development. Sperry (1963) proposed this mechanism to explain how accurate connections were reestablished during regeneration of the optic nerve (between the eye and brain) of lower vertebrates. A second possibility, axon sorting, is that axons from neighboring neurons recognize each other as they grow into the target layer and thus maintain their relative positions. This could happen if near neighbors had similar patterns of electrical activity, a mechanism that is being actively explored at present in vertebrates. Since this mechanism only explains how axons maintain their position relative to each other, some additional cues would be required to orient the whole array of axons appropriately onto the target layer. A third possibility, mechanical guidance, is that the arrangement of the axonal projection is the result of the spatiotemporal order of the growth of axons and the differentiation of target neurons. This alternative is suggested by the extreme orderliness of development. In this case an axon could be guided by other axons that grew previously and would connect to a particular target neuron because it grew to that location at a time when that neuron was ready to connect. No recognition of a specific set of other axons or targets would take place in this scenario. During the past several years my colleagues and I have carried out a series of experiments to test these various possibilities in the visual system of a small arthropod, the water flea Daphnia magna. This small crustacean is used by many aquarium enthusiasts as fish food. It has a single, cyclopic compound eye, with only 22 facets. The small size and simplicity of this visual system have permitted us to carry out an extensive analysis of the formation of the topographically ordered projection of photo-