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Problem Set 1 (20.4 - 4.5.08)

In this exercise we want to explore the neural field model from the lecture. Instead of calculating solutions analytically we will write a numerical simulation and visualize the solutions.

  1. The main part of the program should be a neural field simulator for a discretized rectangular 2d area (e.g. 100 times 100 "pixels"). The shape of the kernel and the sigmoidal should be changeable. Given an initial pattern one should then be able to simulate a given number of time steps. You can use wrap-around at the boundary. You can use scipy convolve.
  2. Another part of the program should visualize the 2d neural field states in some kind of animation. You can for example use the animation abilities of matplotlib or you save the individual images and present them in a slideshow.
  3. Implement the following test scenarios:
    1. Simulate a standard scenario with local excitation & global inhibition, where a random starting pattern leads to a single blob of activity.
    2. Alter the previous scenario by limiting the range of the inhibition. Demonstrate that multiple active blobs emerge.
    3. Use an asymmetric kernel to get a single moving blob.

    The code for running the three scenarios should be as decoupled from the actual simulation code as possible.