'''
Making plots pretty

Matplotlib provides some possibilities of personalising your plots. In this 
exercise, we will explore some of these options.

We will work with a function f(x) = sqrt{4*D*t} for the root mean squared 
distance (in micrometers) of a random walk, and two averaged measurements of 
particles, which will have deviations from the ideal mathematical function. 
We will create the data using the `np.random.normal()` command, which 
will introduce noise into our perfect function. `np.random.normal()` 
creates a random number, where the probability of a number being chosen is 
determined by a normal distribution.
'''

import matplotlib.pyplot as plt
import numpy as np

time = np.linspace(0, 50, 50)
calculated_rmsd = np.sqrt(4 * 15 * time)
measured_1 = calculated_rmsd + np.random.normal(0, 2, len(time))
measured_2 = calculated_rmsd + np.random.normal(0, 2, len(time))

'''
First, create a regular plot of the three trajectories. Don't forget to label 
the axes and create a legend.
'''

# Your code here

'''
There are several ways to enhance this plot.
1. Plot size: You can specify plot size using the command 
`plt.figure(figsize=(a,b))` before plotting, where (a,b) gives the size of 
each edge. Experiment with the size of your plot and choose an appropriate 
sizing for your plot.

2. Alter colour by adding `color = "colour name"` to the `plt.plot()` command. 
List of named colours in matplotlib: 
https://matplotlib.org/stable/gallery/color/named_colors.html 

3. Alter linewidth by adding `linewidth = a` to the `plt.plot()` command, where
`a` gives the width of the line in points.

4. Change the linestyle using `linestyle = "style"` to the `plt.plot()` command. 
List of linestyles: 
https://matplotlib.org/stable/gallery/lines_bars_and_markers/linestyles.html 

Advanced: Introducing special characters in axis labels: In this example, the 
`y`-axis has been labelled using `plt.ylabel("distance [um]")` to indicate that
the axis measures distance, in micrometers. However, we can also make the label 
show the character for micro (or almost any other character). 
For that, we use `plt.ylabel(r"distance $[\mu m]$")`. Here, we put the special 
characters between dollar signs ($), and then use \mu to get the greek letter 
mu. Similarly, we can get any other greek letter. For those familiar with Latex, 
we can also put equations into labels using LateX formalism.
'''

# Your code for pretty matplotlib plot