We propose that Z-Cracks arise from a ( G ) as a function of propagation angle ( \theta ). In standard materials, ( G(\theta) ) has a single sharp maximum. In Z-Crack materials, the anisotropy creates two local maxima within 15° of each other (Figure 2). The crack tip thus "dithers" between these modes.

: Zachary observed a real-world social network of a university karate club for two years [1, 2]. A conflict between the club’s administrator ("John A.") and the instructor ("Mr. Hi") led to the club splitting in two [2]. The "Crack" : Using a mathematical model based on maximum flow-minimum cut