Explore the Game of Life Deep Cell Greetings

[Jared Prince]

Greetings. If you like John Conway's Game of Life you might find this interesting. It is a pattern I have made based on David Bell's Unit Cell.

The Unit Cell is a pattern that replicates the action of a single Life cell. So if you tile an infinite plane with Unit Cells you could actually get them to simulate another layer of Unit Cells, which could simulate another layer of Unit Cells, which could...

As soon as you decide to have a layer simulate anything other than more Unit Cells the recursion comes to an end.

The pattern I have constructed is called a Deep Cell. It is almost identical to a Unit Cell except it simulates 2 independent Life Cells instead of 1. I call the two parallel cells A0 and B0, for reasons that will become clear. The two cells use the same Deep Cell machinery but are out of sync by half it's period so they never interfere with each other. This allows for both an endless succession of Deep Cells and also and endless succession of arbitrary Life patterns.

If you tile an infinite plane with Deep Cells you can construct an infinite hierarchy of arbitrary Life universes as follows:

Set universe A0 running any arbitrary Life universe. Set Universe B0 running a new layer of Deep Cells. This new layer has its own two universes, A1 and B1.

Set universe A1 running any arbitrary Life universe. Set Universe B1 running a new layer of Deep Cells. This new layer has its own two universes, A2 and B2.

Set universe A2 running any arbitrary Life universe. Set Universe B2 running a new layer of Deep Cells. This new layer has its own two universes, A3 and B3.

Set universe A3... etc.

The Deep Cell has a period of 7680, with the actions of B0 offset from A0 by 3840 rounds. These means each layer runs 7680 times slower than the layer beneath it.

You can see the pattern and a largescale 16x16 Deep Cell test run at the following page:

http://psychoticdeath.com/life.htm

Hope this amuses,
Jared.

 

[Janitor]

Thanks for the link. I really caught the Life bug for about a year back in the 1970s. I am not familiar with the Bell unit cell.

 

[R0man]

Wow, Jared, thank you for sharing this with us! The concept of a Deep Cell is truly fascinating and I can see how it adds a whole new level of complexity to the Game of Life. It's amazing to think about the endless possibilities and universes that can be created through this pattern. Your explanation and the included link have definitely piqued my interest and I can't wait to explore it further. Thank you for adding even more depth to this already intriguing game!