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[project random walk] improve text, some hints for plotting

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Jan Grewe 2019-01-13 11:58:33 +01:00
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projects/project_random_walk/random_walk.tex
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@ -13,12 +13,13 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Random walk with memory.} \section*{Random walk with memory.}
Some animals perform a random walk when searching for food. In some The movement pattern of some animals can be described as a random walk when
cases this random walk is not completely random. In fact, sometimes searching for food. In some cases this random walk is not completely
there is some memory involved. Whenever there is a positive gradient random. In fact, sometimes there is some memory involved. Whenever
in food gain between successive steps the animal will continue in the there is a positive gradient in food gain between successive steps the
very same direction as before. When the next step leads to a decrease animal will continue in the very same direction as in the step before. When the
in food gain the animal switches back to a random walk. next step leads to a decrease in food gain the animal switches back to
a random walk and changes directions randomly.
\begin{questions} \begin{questions}
@ -28,8 +29,8 @@ in food gain the animal switches back to a random walk.
food sources (Gaussian blotches of food). food sources (Gaussian blotches of food).
\begin{parts} \begin{parts}
\part{} Create a plot of the world.\\[0.5ex] \part{} Create a plot of the world using \code{imshow}.\\[0.5ex]
\part{} Create a model animal that performs a pure random walk. The \part{} Create a model animal (agent) that performs a pure random walk. The
agent can walk in eight different directions (the cardinal and agent can walk in eight different directions (the cardinal and
diagonal directions) with a stepsize of 10\,cm diagonal directions) with a stepsize of 10\,cm
(approximately). Let the agent start at a random location in the (approximately). Let the agent start at a random location in the
@ -37,7 +38,7 @@ in food gain the animal switches back to a random walk.
disappears from the world, of course). If the agent bumps into the disappears from the world, of course). If the agent bumps into the
borders of the world choose a different direction.\\[0.5ex] borders of the world choose a different direction.\\[0.5ex]
\part{} Plot a typical example walk. (You can also make an animation \part{} Plot a typical example walk. (You can also make an animation
with MATLAB)\\[0.5ex] with MATLAB, see plotting chapter in the script).\\[0.5ex]
\part{} Same as above, but create a model animal that has some memory, \part{} Same as above, but create a model animal that has some memory,
i.e. the direction is kept constant as long as there is a positive i.e. the direction is kept constant as long as there is a positive
gradient in the food gain. Otherwise, a random walk is performed.\\[0.5ex] gradient in the food gain. Otherwise, a random walk is performed.\\[0.5ex]
@ -46,6 +47,7 @@ in food gain the animal switches back to a random walk.
appropriate plots and apply statistical methods. You will need to appropriate plots and apply statistical methods. You will need to
run the simulations several times to get a good estimate of the run the simulations several times to get a good estimate of the
neumbers. neumbers.
\part{} Can you think about better search strategies?
\end{parts} \end{parts}
\end{questions} \end{questions}