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.
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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.
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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.
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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.
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Figure 4: the digit 5 in the shape of an 11-omino |
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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.
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Figure 6: the digit 6 in the shape of a 12-omino |
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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.
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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:
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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.
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Figure 10: the digit 9 represented as a 12-omino It behaves the same as the digit 6 |
