<p>Apparently, Game of Life has been implemented in Game of Life.  For example:
<a href="https://www.youtube.com/watch?v=xP5-iIeKXE8" rel="nofollow">https://www.youtube.com/watch?v=xP5-iIeKXE8</a></p>

<p>The device used here is called the "<a href="http://www.conwaylife.com/wiki/OTCA_metapixel" rel="nofollow">OTCA Metapixel</a>", and supports all life-like cellular automata.  It is 2058 cells on a side (of which 10 overlap when paired next to another) leading to a 2048 square pattern.</p>

<p>What I'd like to know is the size of lower bounds on the size of such devices.  The metapixel is programmable, but restricting solely to game of life, perhaps it could be made significantly smaller.</p>

<p>Something on the order of 16x16 would be excellent for (for example) simulating Game of Life in Game of Life in Game of Life.  Even 64x64 would be an improvement.</p>

<p>I have looked a bit at how the metapixel works, and there's a lot of stock pieces that have just been tacked together.  This suggests that smaller devices could be produced with less-flexible structure.</p>

CC BY-SA 3.0
2014-05-01T21:42:21.920Z
You can look at the previous (smaller and more rigid) 500x500 [P5760 Unit life Cell](http://www.conwaylife.com/wiki/P5760_unit_Life_cell). I think that there are not too many people in the world trying to build small Life Cell "Metapixels" ... so if you are a Game of Life fan you can try to improve the record yourself! You  can also try to send an email to Brice Due and ask him if he knows what is the current smallest size and/or if someone is working on it.
Marzio De Biasi
CC BY-SA 3.0
2014-05-01T22:02:55.147Z
See also the [Deep Cell](http://www.conwaylife.com/wiki/Deep_cell). However, while googling around I just found that there is also a [256x256 unit cell that simulates Rule-110](http://gameoflife-news.blogspot.it/2005/12/unit-cell.html) (which is Turing complete) ... :-) ... "CA-mania" I'll say ...
Marzio De Biasi
CC BY-SA 3.0
2014-05-02T16:55:36.243Z
What rules out the trivial $1 \times 1$ simulation?
Geoffrey Irving
CC BY-SA 3.0
2014-05-03T17:20:01.100Z
@GeoffreyIrving, 1x1 trivially is impossible, it's life in life not just one life, that means one cell should simulate a life and whole system should simulate a pattern of one cell (live pattern). 1x1 cell dies in a next move which is not useful. But there is e.g a 4x4 sample which runs forever, but aggregation of many of that pattern cannot simulate same thing as one ordinary pattern. And here OP asks for more general versions. e.g Life in Life in Life.
Saeed
CC BY-SA 3.0
2014-05-03T19:39:33.690Z
What is the definition of simulating life in life?  The existing expensive simulations seem to be a homomorphism from life instances to life instances with a left inverse.  If that's the definition, the identity map works.
Geoffrey Irving
CC BY-SA 3.0
2014-05-04T02:35:22.940Z
@GeoffreyIrving, I don't know exact definition, but as you mentioned homomorphism is close. But the problem of identity map is, does not lead to infinite sequence. After a first iteration stops. It's not life at all, as otherwise you are right. Here I think the problem is finding a pattern which always contains both zero and one elements ...
Saeed
<cellular-automata>
Meta Game of Life
geometrian
# Meta Game of Life

(Asked by: username_0 on 2014-05-01)

Apparently, Game of Life has been implemented in Game of Life. For example:
<https://www.youtube.com/watch?v=xP5-iIeKXE8>

The device used here is called the "[OTCA Metapixel](http://www.conwaylife.com/wiki/OTCA_metapixel)", and supports all life-like cellular automata. It is 2058 cells on a side (of which 10 overlap when paired next to another) leading to a 2048 square pattern.

What I'd like to know is the size of lower bounds on the size of such devices. The metapixel is programmable, but restricting solely to game of life, perhaps it could be made significantly smaller.

Something on the order of 16x16 would be excellent for (for example) simulating Game of Life in Game of Life in Game of Life. Even 64x64 would be an improvement.

I have looked a bit at how the metapixel works, and there's a lot of stock pieces that have just been tacked together. This suggests that smaller devices could be produced with less-flexible structure.

**Tags:** cellular-automata
> **Comments:**
> **username_1**: You can look at the previous (smaller and more rigid) 500x500 [P5760 Unit life Cell](http://www.conwaylife.com/wiki/P5760_unit_Life_cell). I think that there are not too many people in the world trying to build small Life Cell "Metapixels" ... so if you are a Game of Life fan you can try to improve the record yourself! You  can also try to send an email to Brice Due and ask him if he knows what is the current smallest size and/or if someone is working on it.  
> **username_1**: See also the [Deep Cell](http://www.conwaylife.com/wiki/Deep_cell). However, while googling around I just found that there is also a [256x256 unit cell that simulates Rule-110](http://gameoflife-news.blogspot.it/2005/12/unit-cell.html) (which is Turing complete) ... :-) ... "CA-mania" I'll say ...  
> **username_2**: What rules out the trivial $1 \times 1$ simulation?  
> **username_3**: @GeoffreyIrving, 1x1 trivially is impossible, it's life in life not just one life, that means one cell should simulate a life and whole system should simulate a pattern of one cell (live pattern). 1x1 cell dies in a next move which is not useful. But there is e.g a 4x4 sample which runs forever, but aggregation of many of that pattern cannot simulate same thing as one ordinary pattern. And here OP asks for more general versions. e.g Life in Life in Life.  
> **username_2**: What is the definition of simulating life in life?  The existing expensive simulations seem to be a homomorphism from life instances to life instances with a left inverse.  If that's the definition, the identity map works.  
> **username_3**: @GeoffreyIrving, I don't know exact definition, but as you mentioned homomorphism is close. But the problem of identity map is, does not lead to infinite sequence. After a first iteration stops. It's not life at all, as otherwise you are right. Here I think the problem is finding a pattern which always contains both zero and one elements ...  

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## 0 answers

