In a context where networks grow larger and larger, their nodes become more likely to fail. Indeed, they may be subject to crashes, attacks, memory corruptions... To encompass all possible types of failure, we consider the most general model of failure: the Byzantine model, where any failing node may exhibit arbitrary (and potentially malicious) behavior. We consider an asynchronous grid -shaped network where each node has a probability A to be Byzantine. Our metric is the communication probability, that is, the probability that any two nodes communicate reliably. A number of Byzantine-resilient broadcast protocols exist, but they all share the same weakness: when the size of the grid increases, the communication probability approaches zero. In this paper, we present the first protocol that overcomes this difficulty, and ensures a communication probability of 1 - 4A on a grid that may be as large as we want (for a sufficiently small lambda, typically A lambda 10(-5)). The originality of the approach lies in the fractal definition of the protocol, which, we believe, could be used to solve several similar problems related to scalability. We also extend this scheme to a 3-dimensional grid and obtain a 1 - 2A communication probability for A < 10(-3).