ABOUT BOOK

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction p=pcp=p_{c}p=pc​, where pcp_{c}pc​ is the percolation threshold of random percolation. For any value of ppp in the interval pc<p≤1p_{c}< p \leq 1pc​<p≤1, our results show that the set of bridges has a fractal dimension dBB≈1.22d_{BB} \approx 1.22dBB​≈1.22 in two dimensions. In the limit p→1p \rightarrow 1p→1, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions