Small-angle x-ray scattering, nitrogen adsorption, and scanning tunneling microscopy show that a series of activated carbons host an extended fractal network of channels with dimension D(p) = 2.8-3.0 (pore fractal), channel width 15-20 A (lower end of scaling), network diameter 3000-3400 A (upper end of scaling), and porosity of 0.3-0.6. We interpret the network as a stack of quasiplanar invasion percolation clusters, formed by oxidative removal of walls between closed voids of diameter of approximately 10 A and held in registry by fibrils of the biological precursor, and point out unique applications.