Fig. 4: Honeycomb circuit lattice and its impedance results.
From: Anomalous fractal scaling in two-dimensional electric networks
a Illustrative honeycomb lattice with a zigzag edge design when N = 5. A unit cell consists of nodes belonging to two sublattices A (black circles) and B (black-framed white circles). The blue and red lines represent the node links with the different admittances of za and zb, respectively. The faded cells indicate the extension of the circuit when N = 6, as an example. b The impedance response of the circuit in (a). The circuit is a resonant medium when za = 1(iωL) and zb = iωC and presents sharp impedance resonances as a function of the circuit size. The parameters used are ωC = 1 for the uniform circuit made of only capacitors and ωC = 1, ωL = 2.21 for the LC honeycomb circuit. c Fractal scaling of the 2D honeycomb lattice in the circuit size and driving frequency domain when C = L = 1. The brightest and darkest branches represent the strong anomalous impedance resonances, which depend on the circuit size N. The legend located above the density plot indicates the logarithm of the absolute impedance.
