The usual "running bond" brick pattern (if 2:1 rectangular 2D bricks) forces any vertical crack in the wall to (if it only cracks mortar, not bricks) have length at least 3 times the straight line length. However, a horizontal crack can go straight, and a diagonal staircase crack will have length magnification factor sqrt(2). Here the factor 3 seems max possible and is a sense in which this brick pattern provides optimum resistance to vertical cracking. Not only that, the running bond pattern with L:1 bricks seems optimal for any L>1 in this sense (distance amplification factor=L/2+1), and also not only over rectangular bricks, but indeed I suspect over ALL convex tesselator shapes with unit area and given perimeter, the optimum brick shape is a rectangle and the optimal brick laying pattern is running bond, for the purpose of resisting vertical cracking. (Can you prove or disprove?) It is pointless to make L too large, though, since beyond some threshold it becomes energetically easier to crack the bricks, not the mortar. But running bond sucks as far as its crack resistance in certain other (non-vertical) directions is concerned. The "herringbone" bricklaying pattern with 2:1 bricks (pictures: http://oregonbrick.com/brick%20patterns.html) forces crack length amplification factor>=1.5 for both vertical and horizontal crack directions, albeit again sqrt(2) for 45-degree diagonal cracks. It is also possible to lay herringbone with L:1 bricks for any L>1, including non-integer L: http://www.mytinyworld.co.uk/images/superpic/brick-12th-0001.jpg Apparently this bricklaying pattern was invented by Filippo Brunelleschi (1377-1446) the architect behind the dome of the great cathedral in Florence (and it was employed in the dome). I believe this still is the largest masonry dome ever built. Quite possibly it will never be exceeded because nobody today would be interested in using masonry anymore. The crack-length amplification factor for this pattern for integer L and either horizontal or vertical direction of cracking, is (2L-1)/L, but it seems to me this can be increased a bit if we use non-integer L. Still, though, for 45-degree diagonal direction of cracking, the amplification factor remains only sqrt(2). QUESTION: Using L:1 rectangular bricks, does there exist any pattern such that the crack length amplification factor always is >=C, for some C>sqrt(2), no matter what direction? What is the greatest achievable C? If nonconvex tesselators are allowed, then Gosper's fractal "snowflake" shaped "bricks" would assure crack-length amplification factor of INFINITY... but only in the limit where the mortar thickness tends to 0.