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If we filter away this background pattern, there are clearly some particle-like patterns left, which we can see in the below picture. These patterns move and collide according to consistent rules. | If we filter away this background pattern, there are clearly some particle-like patterns left, which we can see in the below picture. These patterns move and collide according to consistent rules. | ||
[[File:Rule 110 filter.png|900px]] | [[File:Rule 110 filter.png|900px|left|thumb|110 space-time diagram (left) filtered by the transducer Filter({sub[(00010011011111)∗]}) (right) (C.S. McTague, J.P. Crutch field, 2006)]] | ||
Three localized patterns are of particular importance in the Rule 110 universal machine. They are shown in the image below, surrounded by the repeating background pattern. | Three localized patterns are of particular importance in the Rule 110 universal machine. They are shown in the image below, surrounded by the repeating background pattern. | ||
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The leftmost structure shifts to the right two cells and repeats every three generations. It comprises the sequence 0001110111 surrounded by the background pattern given above, as well as two different evolutions of this sequence. In the figures, time elapses from top to bottom: the top line represents the initial state, and each following line the state at the next time. | "The leftmost structure shifts to the right two cells and repeats every three generations. It comprises the sequence 0001110111 surrounded by the background pattern given above, as well as two different evolutions of this sequence. In the figures, time elapses from top to bottom: the top line represents the initial state, and each following line the state at the next time. | ||
The center structure shifts left eight cells and repeats every thirty generations. It comprises the sequence 1001111 surrounded by the background pattern given above, as well as twenty-nine different evolutions of this sequence. | The center structure shifts left eight cells and repeats every thirty generations. It comprises the sequence 1001111 surrounded by the background pattern given above, as well as twenty-nine different evolutions of this sequence. | ||
The rightmost structure remains stationary and repeats every seven generations. It comprises the sequence 111 surrounded by the background pattern given above, as well as five different evolutions of this sequence. | The rightmost structure remains stationary and repeats every seven generations. It comprises the sequence 111 surrounded by the background pattern given above, as well as five different evolutions of this sequence." (Wikipedia, Rule 110) | ||
===Reference=== | ===Reference=== |
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