Bigrams in SOWPODS

"Bigrams" = two-letter combinations
"SOWPODS" = a Scrabble word list

(SOWPODS is the list I keep around for playing around with word algorithms or solving puzzles, because I could get it in electronic form. Probably but not certainly downloaded from here: https://github.com/jesstess/Scrabble/blob/master/scrabble/sowpods.txt I would be happy to see other word lists available for use.)

Visualized here: the count of words which contain both the specified letters, or, if doubled, that letter twice. For example, 36,788 of the words in the list contain two A's, while 1,420 contain B and Z. The version of SOWPODS I have has 267,751 words in total.

full size

Code fragment for visualization in pyplot, taken from this heatmap tutorial and this StackOverflow answer on plotting upper or lower triangles of a matrix.

import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np

def plotBigrams():
    # an array [ bigram, count ]
    tlCounts = twoLetters()
    
    a = np.zeros( (26,26), int )    
    mask = np.tri( 26, 26, k=-1 ).transpose()
    for (bigram, count) in tlCounts:
        i = letters.index( bigram[0] )
        j = letters.index( bigram[1] )
        a[j,i] = count

    aa = np.ma.array( a, mask=mask )

    fig, ax = plt.subplots()
    c = cm.get_cmap( "viridis" )
    c.set_bad( 'w' )
    im = ax.imshow( aa, cmap = c, aspect=1.0/3.0 )
    ax.set_xticks( np.arange( 26 ) )
    ax.set_yticks( np.arange( 26 ) )
    ax.set_xticklabels( list( letters ) )
    ax.set_yticklabels( list( letters ) )

    for i in range(26):
        for j in range(26):
            text = ax.text(i, j, aa[j, i],
                           ha="center", va="center", color="w")