path integration.

p.s. it should be done by python matplotlib !!

la. [Spts] Suppose that an ant wandered randomly by taking steps (x,y), one per second, where at each ant step, x and y come from a normal distribution with a mean of 0 and a standard deviation of 1.0mm (assume this for all questions below). Plot a trace of the ant's path over the course of an hour lb. [10pts] Let's think about why ants need to perform path integration. Suppose that instead of path integration, when an ant found food, it just continued to wander with random steps until it got back to the nest. Using a simulation, find the probability that an ant who finds food after 1 hour will make its way back to within 10mm of the nest over the course of the next hour (note that if it comes within 10mm of a nest, it stops). Is this a good strategy? Why or why not? 1c. [10pts] If the ant searches for an hour, finds food, and then searches for the nest by continuing to walk at random, what is the average closest distance it will come to the nest over the course of the next hour? (Do not assume it stops if it comes within 10mm) Find this with a simulation