Diurnal Age Meets Conway's Game Of Life

 I've written about Conway's Game of Life in two recent posts:

• The Game of Life on Saturday, the 16th of December 2023 and

• 108 Meets Conway's Game Of Life on Friday, the 9th February 2024

I've been playing around with an app called "Life" on my iPhone that allows the game to be run but I prefer on browser-based app that I can access from my laptop. To that end, I've been playing around with one of three websites recommended by Gemini:

• Conway's Game of Life (Golly edition): https://conwaylife.com/

This website utilizes the popular "Golly" simulation software, offering advanced features like pattern libraries, scripting, and different grid geometries. You can save and export your simulations in various formats.

• Game of Life Online: https://playgameoflife.com/

This website allows you to draw patterns directly on the grid with an intuitive interface. While it lacks advanced features, it's great for quick visualizations and sharing creations.

So in this post, I'm looking at the first of the recommendations and playing around with a new idea. I want to investigate how the number associated with my diurnal age behaves under the Game of Life rules. The number for today, 27346, is shown in Figure 1. All the digits from 0 to 9 can be created using a 3 x 5 pixel grid, the smallest possible size.

Figure 1

The rules lead, after 125 steps, to the image shown in Figure 2:

Figure 2

What would be interesting to keep track of are the number of steps required to reach a stable state. It's clear that the stable states arising from numbers are not unique. For example 16161 will end up the same as 19191 if we don't regard mirror images, rotations and reflections as different. However, most numbers should result in stable states that are different from one another. I can attach images of these stable states to my Airtable database. 

I'll explore the other two Gemini recommendations later. Any particularly interesting stable states or record number of steps arising from these diurnal age investigations can be the subject of future posts. In the case of 27346, we can say that the stable state consists of five blocks (the simplest still life) and one hive or beehive (the second most common still life).

 

This ongoing, daily exercise is a great way to deepen ones understanding of a topic. It was only through my adherence to the investigation of the number associated with my diurnal age that I widened and deepened my understanding of number theory. It's a great maxim: once a day but everyday and can be and should be applied to more aspects of my daily life.