Abstract
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 = p(o), where p(c) is the percolation threshold of random percolation. For any value of p in the interval p(c) < p <= 1,
our results show that the set of bridges has a fractal dimension d(BB)
approximate to 1.22 in two dimensions. In the limit p -> 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.
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