标题： 电阻电路中的分形：斐波那契电阻网络 显示英文标题

标题： Fractality in resistive circuits: The Fibonacci resistor networks

摘要： 我们提出两种基于斐波那契序列的新类型的无限电阻网络：一种是电阻组的串联连接并联（类型1），另一种是电阻组的并联连接串联（类型2）。 我们证明了网络等效电阻的序列在参数$\alpha=\frac{r_2}{r_1} \in [0,+\infty)$上一致收敛，其中$r_1$和$r_2$是网络中的第一个和第二个电阻。 我们还证明了这些网络表现出自相似性和尺度不变性，这模仿了自相似分形。 我们还提供了一些推广，包括基于高阶斐波那契序列和其他递归组合序列的电阻网络。 显示英文摘要

摘要： We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network's equivalent resistance converges uniformly in the parameter $\alpha=\frac{r_2}{r_1} \in [0,+\infty)$, where $r_1$ and $r_2$ are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.