中点三角形和相似缩小正三角形的无限叠代，形成三角形电阻分形网络.自相似性要求节点上电流分配和比例系数不变.利用基尔霍夫定律，得到了这些系数的值.利用电阻电路的线性关系，得到了分形网络节点之间的等效电阻.

A fractal resistor network is constructed by infinite iterations of midpoint triangle or titled regular triangles whose sides are replaced by resistance wire. The distribution and scale coefficients of currents on some nodes are invariant by the self-similarity conditions. These coefficients are calculated from the Kirchhoff law. Also，the equivalent resistance between two nodes are derived by the line relationship of resistor network.