Registered: Oct 2003
Posts: 17

Last edited by Evangelos Georgiadis on 09-13-2005 at 01:56 AM

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Registered: Aug 2003
Posts: 712

Um, those are the left-right, white-black, and both left-right and white-black transforms of 110. Not exactly an earth-shaking result.

ArrayPlot[CellularAutomaton[#, {{1}, 0}, 30]] & /@ {110, 124, 137, 193}

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Registered: Aug 2003
Posts: 712

It is useful to dot i's and cross t's in formal mathematical dialect. Everyone is aware of symmetries in ECAs from things like switching black and white and right and left. Since 110 is not symmetric, it being universal means its "family" of 4 ECAs is universal since they are basically the same rule. That part is not a significant extension, it is true but it is also obvious once one knows 110 is universal. That is all I meant.

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