Statistics of hidden stop codons

First, I calculate the probability of getting hidden stop codons in each frame, for each pair of aminoacids (the following assumes uniform probability for all codons, including stops):

>> [probstop_fr1,probstop_fr2]=paresaa2probs(codigo);
>> subplot(1,2,1)
>> imagesc(probstop_fr1)
>> subplot(1,2,2)
>> imagesc(probstop_fr2)

I build a program that finds these probabilities in genes, and I check it with random genes with uniform probabilities for the bases:

>> gen=randgen(30000000,1,codigo);
>> [probstop_fr1_gen,probstop_fr2_gen]=gen2probstop(gen,codigo);
>> close all
>> subplot(1,2,1)
>> imagesc(probstop_fr1_gen)
>> subplot(1,2,2)
>> imagesc(probstop_fr2_gen)

I check that when the number of bases in the random gene increases, the probabilities tend to be more similar: