What do spontaneous coherent excitations in the primary visual cortex look like in time and - that's what we are interested in here - in space? This is a fascinating question whose solution is, to some extent, now within reach of computational neuroscience. It is generally believed that this kind of excitation occurs in drug-induced epilepsy and, presumably, also in hallucinations.
Hallucinations (Klüver 1967, Siegel and West 1975, Siegel 1977, Cowan 1985) [8,13,14,1] are perceptions in the absence of a visual stimulus. They can occur even in subjects which have been completely blinded by a retinal disease (Zeki 1993) [16] . It was Klüver (1967) [8] who in the twenties started experiments to classify what he called ``form constants", which meanwhile have turned out to be universal characteristics of the first stage of drug-induced imagery, most notably LSD. There are at least four categories of form constant, such as grating and filigree, spiral, tunnel and funnel, and cobweb. The imagery of the second stage is much more complex and, without any doubt, involves several areas of the brain. We mention two key questions: Are the form constants generated in the primary visual cortex (areas V1 and V2) or are they due to functional feedback, i.e., feedback from other areas with different functions? Second, can we understand the form constants theoretically?
There exists a mathematically very elegant analysis of Ermentrout and Cowan (1979) [3] . Their main hypothesis, which we will adopt as well, is that the form constants can be modeled as elementary excitations in the primary visual cortex. The model uses a rate coding and takes the complex logarithm (Schwartz 1977) [12] as the retino-cortical map. The patterns follow from a bifurcation analysis in a neighborhood of the homogeneous low-activity state, a linear theory. A final result is that parallel stripes of active and quiescent neurons constitute elementary excitations of the model. Due to the retino-cortical map, some of the cortical stripe patterns should appear as spirals on the retina. One may wonder, though, what are the spontaneous excitations in a `realistic' nonlinear cortical network of spiking, noisy neurons? This is the question we will focus on. In so doing we can, and will, verify the above hypothesis. In the context of our model we conclude that several, but not all, form constants occur as spontaneous excitations. Furthermore, we do encounter spatio-temporal activity patterns as found experimentally in drug-induced epilepsy.
At the same time as us but in a network of integrate-and-fire neurons without delays, local inhibition, and noise, Milton et al. (1993) [10] found spirals as elementary excitations which evolve out of a fixed excitation center. Spirals are inconsistent with the parallel stripes referred to above. Below we will clear the situation and show that there is in fact a sequence of al least four scenarios. In so doing we will avoid any external input and exploit several neural characteristics which have been incorporated into our own spike response model.