import math
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.ticker import StrMethodFormatter as SMF
import pandas as pd
import seaborn as sns

#Create Data
data = pd.DataFrame(columns = ['Units',
                               'Tens',
                               'Freq'])

for t in range(0,10) :
    for u in range(0,10) :
        data = data.append({'Units' : u,
                            'Tens' : t,
                            'Freq' : 0},
                           ignore_index = True)
        
for i in range(0,100) :
    v = ((i**2 + i) / 2) % 100
    data.at[v, 'Freq'] += 1
    
data

	Units	Tens	Freq
0	0	0	2
1	1	0	2
2	2	0	0
3	3	0	5
4	4	0	0
...	...	...	...
95	5	9	2
96	6	9	2
97	7	9	0
98	8	9	0
99	9	9	0

100 rows × 3 columns

sns.set()
fig = plt.figure(figsize = (12.15, 10))
ax = fig.add_subplot(xlim = (-0.5, 9.5),
                     ylim = (-0.5, 9.5))

heatmap = plt.scatter(x = data['Units'],
                      y = data['Tens'],
                      c = data['Freq'],
                      cmap = 'YlGn',
                      marker = "s",
                      s = 2850)

#Title setup.
ax.set_title('Distribution of Last Two Digits of Triangular Numbers', fontsize = 24)

#X-axis setup.
ax.set_xlabel('Units Digit', fontsize = 22)
ax.set_xticks(range(0,10))
#Y-axis setup.
ax.set_ylabel('Tens Digit', fontsize = 22)
ax.set_yticks(range(0,10))
ax.tick_params(axis = 'both', which = 'major', labelsize = 18)


common = [('03', 3, 0),
          ('28', 8, 2),
          ('53', 3, 5),
          ('78', 8, 7)]

for c in common:
    plt.annotate(c[0],
                 (c[1], c[2]),
                  c = "w",
                  fontsize = 28,
                  ha = "center",
                  va = "center")


#Colorbar.
plt.colorbar(heatmap).set_label('# of Occurences \n Every 100', fontsize = 22);

fig.savefig("2023.03.03 Express.png",
            bbox_inches = 'tight')

Rohan Lewis

2023.03.06