Tuesday 20 February 2024

Digits 3 to 9 in Conway's Game of Life

In my previous post, I looked at the behaviour of the digits 0, 1 and 2 under the rules of Conway's Game of Life. Today I'll look at the digits 3, 4, 5, 6, 7, 8 and 9. Let's start with the digit 3. See Figure 1.


Figure 1: 3 in the shape of an 11-omino

After about 50 steps it ends up in the form shown in Figure 2. There are two ships, two blocks, two beehives and one blinker.


Figure 2: three types of still life and one blinker

Now let's look at the digit 4 shown in Figure 3. It completely disappears after 12 steps or generations, so there's no final state that needs to shown.


Figure 3: the digit 4 in the shape of an octomino
It disappears after 12 generations

The digit 5 is shown in Figure 4 and after three steps or generations it changes into the shapes shown in Figure 5. It's really the same shape as the digit 2 and so the outcomes are basically the same, just differently orientated.


Figure 4: the digit 5 in the shape of an 11-omino


Figure 5: final state of 5 produces two boats

The digit 6 shown in Figure 6 has by far the most complicated behaviour of all the digits. After well over a thousand generations it turns into what is shown in Figure 7.


Figure 6: the digit 6 in the shape of a 12-omino


Figure 7: the complicated final state of the digit 6.
There are additional gliders not shown

Figure 8 shows the digit 7 that, after six generations, turns into a blinker.


Figure 8: the digit 7 as an heptomino
After six generations it becomes a blinker

The digit 8, shown in Figure 9, disappears after 21 generations:


Figure 9: the digit 8 as a 13-omino
It disappears after 21 generations

The digit 9, shown in Figure 10, will behave exactly the same way as for the digit 6, only the orientation will be different.


Figure 10: the digit 9 represented as a 12-omino
It behaves the same as the digit 6

No comments:

Post a Comment