Linear Feedback Shift Registers and Hexagram Generation

Sometimes things just click. I recently started to practise uxn again, after finally having some headspace freed up. Some exercises later I guessed I should probably start work on a small project if I want to advance. There is only so much to be learned from solving pseudocode exercises in a concatenative programming language. My choice fell on an I Ching Hexagram generator, since these already fascinated me when I worked on Ostrakinda. Basically, a hexagram is made from six lines, which are either whole or broken. Two to the power of six is sixty-four, meaning there are sixty-four different hexagrams. There is a variety of different methods for I Ching divination, and some of them involve coins, which is the reason why I got interested in this type of cleromancy in the first place.

At first I thought that it is as simple as throwing a coin and one side means a whole line while the other side would indicate a broken line. But why make it simple if you can make it esoteric? Instead, the hexagram divination method must result in a number between six and nine. The number indicates if a line is ‘young’ (not changing) or ‘old’ (changing). Most of them are ‘young’, but if you have some of the rare ‘old’ lines, you get a hexagram with variants where you have to read all the possible combinations where the ‘old’ line is broken and whole.

One of several tables taken from the explanations of the four coins aka four bits method.

Either way, I needed to implement a random number generator (RNG) in uxn. I could have used the one from Devine, but since I wanted to practise uxntal and learn a thing or two, I needed to understand the underlying logic and maths that would create a pseudo-random number. In the process of researching some easy documentation of it (random number generator for dummies), I encountered the linear-feedback shift register (LFSR), which is a type of RNG. But instead of using normal-people maths, it works with computational operations, XOR and bit shifting to be precise. And that is the moment when it clicked. Because the Wikipedia page on I Ching divination methods actually featured a version that works with four bits! So what’s better than having a four-bit divination method and an LFSR? Match made in heaven! Some moments later I had implemented the algorithm in yarromancy and I believe it is working out, although there is a lot of room for optimisation and improvement.

A 16-bit Fibonacci LFSR.

But that is part of the journey, isn’t it?