[meatcar]

Implementing the Conway's Game of Life on a hexagonal grid could be a fun idea. With a slow enough turn clock, you probably don't need a start/stop button, and can just mash a pattern in with one or two hands quickly and see how it evolves. Another plus is that there probably aren't too many famous hexagonal lifeforms, it would be a fun game for all ages.

This is a great reference for starting to work with hexagonal grids: https://www.redblobgames.com/grids/hexagons/

[munificent]

I thought about that too, but I think that goes against the author's goal of keeping the user in charge. With Life, the machine keeps evolving and blinking even when you don't touch it.

My goal was something fun to add to it that strictly only did anything in response to user input.

[StavrosK]

I don't think adding the time component means that the user isn't in charge any longer, especially if you add a potentiometer for controlling time all the way down to zero.

A tactile Game of Life box that you can speed up/slow down/freeze and change sounds delightful.

[sp332]

Here's an overview of hexagonal Life rules and software that already supports them: https://www.conwaylife.com/wiki/Hexagonal_neighbourhood You could step forward once or a fixed number of steps each time. Color the cells by age for more visual interest.