Activity \#1: Pretty plot - individual Create a program named pretty_plot.py that repeatedly multiplies a matrix by a point and plots the results. Start with a 2D point,
(x,y)
. This point can be represented as a vector:
v=[ x
y
]
. There is also defined a
2×2
matrix,
M=[ a
c
b
d
]
. Computing the product of
M
with
v
will give a new point
v ′
:
v ′
=Mv
. Then, multiply the matrix
M
by the new point
v ′
, to get another point, i.e.
v ′′
=Mv ′
. This can go on indefinitely, creating a long sequence of points. Your program should use numpy to create a matrix and a point. Begin with the point
(0,1)
and the matrix:
[ 1.01
−0.09
0.09
1.01
]
. Then, multiply the matrix by the point to get a new point. Repeat for a total of 200 times. Have your program plot the data points using matplotlib. Be sure to label the
x
and
y
axes, and include a title. Your title should give a brief description of the shape that the points "trace" out. Note: the purpose of this activity is to get practice with numpy, so you should use numpy for your operations, even if you find it easier to perform this computation a different way.
