I wonder why the authors took the time to generate an image of their pattern but refrained from giving the actual DEFINITION. This does not foster constructive discussion of any possible ideas present. As can be seen in dozens of well-meaning comments here, people waste time reversing and guestimating parameters etc.

Looking at the layman letters that my institute gets on a regular basis, I can say, that this is unfortunately a recurring theme with amateur mathematicians: They fail to state their basic definitions and assumptions and seem all to eager to dive right into applications, be it computer graphics, cryptography or finance.

More to the point: This picture seems from a cursory inspection to plot T(k,n) with n=row, k=column from the top left. But why is this interesting?