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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Unit cell for Rule 110 in Life

Life enthusiast Jason Summers made a configuration of cells in the Life 2D CA that gets it to emulate a cell of rule 110 at a larger scale. The construction was featured on the Game of Life news page here -


Summers' Life page - with lots of other stuff about it - can be found here -


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Old Post 05-19-2006 07:45 PM
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Tony Smith
Meme Media
Melbourne, Australia

Registered: Oct 2003
Posts: 167

Thanks, but ...

The massive engineering done by affectionados of Conway's Life never ceases to bemuse me, so I am always happy to look at new examples.

However, the particular example linked seems to go a long way to failing the Principle of Computational Equivalence under the third of the four criteria that Wolfram gave (pp.726-727) for its acceptance:

But like any principle in science with real content it could in the future always be found that at least some aspect of the Principle of Computational Equivalence is not valid. For as a law of nature the principle could turn out to disagree with what is observed in our universe, while as an abstract fact it could simply represent an incorrect deduction, and even as a definition it could prove not useful or relevant.
(emphasis mine, and counting 'not (...) relevant' as a separable fourth ground for failure).

I just don't see that requiring a specific arrangement of around 1200 live cells on a 60,000 cell rectangle to emulate a single cell in a related system constitutes a useful application of theoretical equivalence. (I also suspect that much more compact emulators exist, though most likely beyond any threshold which might be penetrated by even genertic algorithms, but that would not alter my basic point.)

I should also add the disclaimer that I think the failure of PCE would be a good thing for the wider NKS project, removing an unproductive distraction.

Tony Smith
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Old Post 05-21-2006 09:00 AM
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