# Four elements repetition in a texture [closed]

I have to create a texture using 4 different elements (call them A,B,C,D or whatever you want) on a 6x7 grid. The goal is to obtain a pattern with the least repetitions of the same element in horizontal, vertical and diagonal directions, especially, if possible, should be avoided to repeat the same element in adjacent blocks. I think there should be different solution to this, just answer with what you came up with.

• I'm not clear on what you're counting as a repetition. – xnor Mar 6 '15 at 21:45
• I know this question sounds simple but is varies alot based on priority. Is A and A being diagonally adjacent worse than horizontally adjacent? Is A and A being diagonally adjacent worse than it having three As separate but in the same row? – kaine Mar 6 '15 at 22:22

Starting from the nucleus

$$a b a\\ b c b\\ a b a\\$$

add "layers" of two characters alternating onto the nucleus. For example, the next iteration will be

$$c d c d c\\ d a b a d\\ c b c b c\\ d a b a d\\ c d c d c\\$$

This array can be extended infinitely, and all elements of this infinite array will have neighbours in all 8 directions that are different from itself, except at the corners.

$$c d c d c d\\ a b a b a b\\ c d c d c d\\ a b a b a b\\ c d c d c d\\ a b a b a b\\ c d c d c d\\$$

Simply take a 6x7 subset of this infinite array at any position where no corner exists to produce an answer.

Here is one:

$$a b c d a b\\ b c d a b c\\ c d a b c d\\ d a b c d a\\ a b c d a b\\ b c d a b c\\ c d a b a d\\$$

In the row you must have 2 repetitions and in the column 3.

• If you look in diagonal, there is the same letter in each oblique line (going from lower left to upper right) – Lorenzo Mar 6 '15 at 21:14
• You are right! I missed diagonally. – Moti Mar 7 '15 at 2:14