Using Python

3D Plot (Gabor Function)

The following function z = f(x,y) is used to describe the visual response properties of a vertically oriented simple cell receptive field in primary visual cortex. In short, positive regions of this function represent the areas of the animals visual field that would activate the neuron if the image was brighter there, while negative regions represent areas of the visual field that would activate the neuron if the image was darker there. Basically, when you overlay this function on an image, it can tell you how the associated neuron would respond if the animal was looking at that image.

In Python format (using the numpy library as np):

Z = np.exp(-0.5 * (X**2/4 + Y**2/4)) * np.sin(2 * np.pi * 0.2 * X)

In R format:

Z = exp(-0.5 * (X^2/4 + Y^2/4)) * sin(2 * pi * 0.2 * X)

For today, lets observe what this function looks like using any kind of 3D plots (contour plot, surface plot, or mesh plot). The x and y axes are distances in centimeters from the center. The z response is the optimal brightness of the image to make the visual neuron respond.

Be sure to label your axes and give the plot an appropriate title. Also, be sure to pick appropriate limits of your x and y axes to display enough of the image to understand what it represents. (hint: it approaches the value of 0 as you move away from the centers)