import random

import matplotlib.pyplot as plt

###### DO NOT change this function #####

# Function to plot the random walk for each animal

def plot$\_$walk$($animal$)$:

xs$,$ ys $=$ zip$(*$animal$[\text{'}$positions$\text{'}])$

plt$.$figure$($figsize$=(10,10))$

plt$.$scatter$($xs$,$ ys$,$ color$=$animal$[\text{'}$color$\text{'}],$ edgecolor$=\text{'}$k$\text{'},$ alpha$=0\mathrm{.}7,$ s$=100,$ marker$=$animal$[\text{'}$marker$\text{'}])$

plt$.$plot$($xs$,$ ys$,$ lw$=1\mathrm{.}5,$ ls$=\text{'}--\text{'},$ color$=$animal$[\text{'}$color$\text{'}])$

plt$.$grid$($True$)$

plt$.$title$($f$\text{'}$Path of Random Walk for $\{$animal$["$name$"]\}\text{'})$

plt$.$xlabel$(\text{'}$East$-$West'$)$

plt$.$ylabel$(\text{'}$North$-$South'$)$

# Save the plot to a file

plt$.$savefig$($f$\text{'}\{$animal$["$name$"]\}\_$random$\_$walk.png$\text{'},$ dpi$=300)$

plt$.$close$()$ # Close the figure

# You need to create the animal dictionary inside the main function where each animal has

# direction, probabilities, positions, marker and color attributes

animal $=\{\}$

def main$()$:

chuck $=\{"$name$"$: "Chuck", "directions": $["$N$","$S$","$E$","$W$"],$"probabilities":$[0\mathrm{.}25,0\mathrm{.}25,0\mathrm{.}25,0\mathrm{.}25],$"positions":$[(0,0)],$"marker":"o$",$"color":"b$"\}$

daisy $=\{"$name$"$: "Daisy","directions":$[\mathrm{.}5,\mathrm{.}167,\mathrm{.}167,\mathrm{.}167],$"positions":$[(0,0),$marker$]$:$"$s$",$"color":"r$"\}$

chester $=\{$ "name": "Chester","directions": $[\mathrm{.}5,\mathrm{.}5],$"positions":$[(0,0)],$ "marker": $"^",$ "color":"g$"\}$

for i in range$(1000)$:

walk$($Chuck$)$

walk$($Daisy$)$

walk$($Chester$)$

plot$\_$walk$($Chuck$)$

plot$\_$walk$($Daisy$)$

plot$\_$walk$($Chester$)$

def walk$($animal$)$:

direction $=$ random.choices$($animal$["$directions$"],$weight$=$animal $["$probabilities$"])[0]$

x$,$y $=$ animal$["$positions$"[-1]]$

if direction $=="$N$"$:

y $+=1$

elif direction $=="$S$"$:

y $-=1$

elif direction $=="$E$"$:

x $+=1$

else:

x $-=1$

animal$["$positions$"].$append$($x$,$y$))$

if $\_\_$name$\_\_==$'main':

main$()$

$1.$ Random Walk $-$ Description

Read the instructions carefully. Not following the instructions will result in you not getting the credit you want for the assignment.

Learning Outcomes

Use random choices to simulate random behavior in an experiment

Group data in an appropriate collection data structure such as a dictionary or list

Use Python matplotlib to put visual information on a graph and save it to a file

Separate generating numerical results from visualizing results

Use loops to avoid repeated code in your solution when working with dictionaries and lists

Structure

Files:

random$\_$walk.py

don$$t modify function plot$\_$walk that you are given

Output files:

Chuck$\_$rw$.$png

Daisy$\_$rw$.$png

Chester$\_$rw$.$png

Background

In $1827,$ the Scottish botanist Robert Brown observed that pollen particles suspended in water seemed to float around at random. He had no plausible explanation for what came to be known as Brownian motion, and made no attempt to model it mathematically. Louis Bachelier presented a clear mathematical model in his doctoral thesis, The Theory of Speculation in $1900.$ His thesis was largely ignored by respectable academics because it dealt with the then disreputable field of understanding financial markets. In $1905,$ Albert Einstein used similar stochastic thinking in physics to describe how it could be used to confirm the existence of atoms. People seemed to think that understanding physics was more important than making money, and the world started paying attention.

Brownian motion is an example of a random walk. Today, random walks are widely used to model physical processes like diffusion, biological processes like the kinetics of displacement of RNA from heteroduplexes by DNA, and social processes like movements of the stock market.

We are interested in random walks because of their wide applications to many problems, and for learning more about how to structure simulations nicely in Python.

Problem

Farmer John has three interesting pets: Chuck the chicken, Daisy the dog, and Chester the cat. Each of these animals has a different style of wandering around:

Chuck the chicken loves to wander randomly. Each second, he takes a step in a random direction: North, South, East, or West, with equal probabilities. Chuck$$s marker in a graph is a blue circle.

Daisy the dog loves to explore but she has a slight preference for the North. Each second, she takes a step with the following probabilities: North $(50\%),$ South $(16\mathrm{.}67\%),$ East $(16\mathrm{.}67\%),$ and West $(16\mathrm{.}67\%).$ Daisy$$s marker in a graph is a red square.

Chester the cat is a peculiar feline who only moves East or West, never North or South. Chester$$s marker is a green triangle.

Your task is to simulate the movement of each animal for $1000$

steps and plot their steps. Assume they always start at the barn door, which we will label $(0,0)$

$.$ We give you code for a function plot$\_$walk$($animal$)$ that you call to visualize an animal$$s path using matplotlib. Do not modify this function, just call it$.$

Key Requirements and Gradinig

While you might observe that certain rubrics are being automatically graded, please note that these scores will not be transferred to Canvas until your instructor or TA comprehensively reviews the entire project and manually assigns gra