Part 5. - Hallucinations
Perhaps you have wondered where the wonderful shapes of hallucinations come from. They arise in the primary level of the visual cortex known as the V1 layer. Along its path the V1 area is divided into hypercolumns of neurons and each hypercolumn corresponds to a small field of the retina. Each hypercolumn contains columns of neurons that respond not only to dark and bright but also to edges of all angular orientations. So its the lay-out of the hypercolumns and orienation preferences that enables us to detect contours, surfaces and textures.
Inside the hypercolumn neurons interact with most other neurons. But when it comes to neurons from other hypercolumns, the nerve cells are quite selective. They will interact only with neurons in the same angular preference and this allows the V1 area to detect continous contours.
 Fig.10 Connections in V1. Neurons will interact with neurons from other hypercolumns, only if the latter lie in the direction of their orientation and if the neurons have the same angular preference.
Lets present the V1 layer as a mathematical plane. Each hypercolumn is defined as a point, in this plane, with a set of coordinates (x and y). In turn each point of the plain corresponds to a hypercolum and each neuron is defined by the coordinates of its own hypercolumn along with an angular preference coordinate θ (where θ is between 0o and π). So to sum up the V1 area can be defined as a plane with a set of three bits of information - x, y and θ.
So a neuron with an angular preference of θ0 that lies in a hypercolumn defined by coordinates x0 and y0 will have the following coordinates x0; y0; θ0. This neuron will interact with most other neurons in the x0; y0 hypercolumn. However it will interact with neurons from other hypercolumns only if the hypercolumn lies in a straight line at an angle θ0(the line must go through both hypercolumns) and if those neurons have an angular preference θ0.
This interaction pattern is highly symmetric. If two elements (x0, y0, θ0) and (s0, t0, φ0) interact with each other, then the elements you get by shifting along, that is (x0+a, y0+b, θ0) and (s0+a, t0+b, φ0) for given a and b will interact in the same way. The pattern is also invariant upon rotations and reflection of the plane (fig.11).
 Fig.11 Interactions between V1 elements as a function of rectangular coordinates and angular preference. Look at the text for a detailed explanation.
Computer rendering shows that this model is sensitive to symmetries and mathematics illustrate that its the symmetries that are responsible for the emergence of periodic patterns of neural activity. The model suggests that its the lay-out of hypercolumns and angular preferences (responsible for pattern and contour detection) that generate hallucinations. When you plug in an activator in this circuitry (say LSD) the neural activity increases, and this is translated into the emergence of visual hallucinations.
 Fig12. Computer generated repressentations of form constants that can arise as increased neural activity in V1.
If you find this interesting and you like hallucinations I have the following experiment you can do. Probably many of you are already familiar with this. We are going to perform a thorough visual stimulation of cortical cells responsive to bars at 45o angle. The outcome should be short-term visual distortion as a result of too much neurotransmitters released between cortical cells of different hypercolumns at 45o angle.
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