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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 %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Random walk with memory.}
Some animals perform a random walk when searching for food. In some
cases this random walk is not completely random. In fact, sometimes
there is some memory involved. Whenever there is a positive gradient
in food gain between successive steps the animal will continue in the
very same direction as before. When the next step leads to a decrease
in food gain the animal switches back to a random walk.
The movement pattern of some animals can be described as a random walk when
searching for food. In some cases this random walk is not completely
random. In fact, sometimes there is some memory involved. Whenever
there is a positive gradient in food gain between successive steps the
animal will continue in the very same direction as in the step before. When the
next step leads to a decrease in food gain the animal switches back to
a random walk and changes directions randomly.
\begin{questions}
@ -28,8 +29,8 @@ in food gain the animal switches back to a random walk.
food sources (Gaussian blotches of food).
\begin{parts}
\part{} Create a plot of the world.\\[0.5ex]
\part{} Create a model animal that performs a pure random walk. The
\part{} Create a plot of the world using \code{imshow}.\\[0.5ex]
\part{} Create a model animal (agent) that performs a pure random walk. The
agent can walk in eight different directions (the cardinal and
diagonal directions) with a stepsize of 10\,cm
(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
borders of the world choose a different direction.\\[0.5ex]
\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,
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]
@ -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
run the simulations several times to get a good estimate of the
neumbers.
\part{} Can you think about better search strategies?
\end{parts}
\end{questions}