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The Algebra of an Infinite Grid of Resistors

The Algebra of an Infinite Grid of Resistors In a previous note we discussed the well-known problem of determining the resistance between two nodes of an “infinite” square lattice of resistors. The most common approach is to superimpose two “monopole” solutions, one representing the field for one amp of current entering a given node and flowing “to infinity”, and the other representing the field for one amp of current being withdrawn from a given node flowing in from infinity. If the two nodes

Infinite Grid of Resistors

Infinite Grid of Resistors Remain, remain thou here, While sense can keep it on. And, sweetest, fairest, As I my poor self did exchange for you, To your so infinite loss, so in our trifles I still win of you: for my sake wear this... Shakespeare There is a well-known puzzle based on the premise of an “infinite” grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below. Between every pair of adjacent nodes is a resistance R, and w

Relaxed Radix Balanced Trees (2024)

Relaxed Radix Balanced Trees I’m adding immutable vectors to my language, Ivan, and needed to pick a suitable data structure to implement them. Clojure uses Persistent Vectors (PVs) which support lookups, updates, and appends all in ‘effectively’ constant time. However, it doesn’t have efficient insert or merge operations. Relaxed Radix Balanced (RRB) Trees, introduced by Bagwell and Rompf in 2011, address this shortcoming. I had to read a few different papers to properly understand how they w