PSYCHOTIC DEATH





JOHN CONWAY'S GAME OF LIFE!

Every bodies favorite cellular automaton. (Rule 110: "Like Hell it is!") If you don't know what John Conway's Game of Life is, google it. The universe may at bottom be a cellular automaton, so if you're a budding cosmological engineer you'd better get to work with those gliders and eaters.




 
David Bell's Unit Cell

Like most healthy people I'm obsessed with copies of copies and simulations of simulations and infinite levels of nested recursion. In that regard this particular Life pattern is pretty fascinating. Its an arrangement of cells that, on the large scale, mimics the action of a single life cell. So fractal like, the entire pattern is acting like a single element of the pattern, or vice versa, a single element of the pattern is acting like the entire pattern. If you tiled an infinite plane with these you could generated a Life universe on top of a Life universe. Or you could generate another layer of Unit Cells, which generates another layer of Unit Cells, which generates another layer of Unit Cells...

David Bell's Unit Cell




 
The Deep Cell

The Unit Cell is damn cool. It occurred to me that even better than generating an infinite hierarchy of Unit Cells would be to generate an infinite hierarchy of any Life universes at all. So in 1998 I created the following slight variation on the Unit Cell called the Deep Cell (because it allows infinitely "Deep" nesting of Life universes.). Of course, all the tricky stuff was already done by David Bell, I just modified a few components.

The basic idea with the Deep Cell is that instead of simulating one Life cell it simulates two at a time, independent of each other and out of sync by half the cell's period. It is simulating two interleaved Life Universes, which I call A0 and B0. Here is the description from the .LIF file:

Deep Cell by Jared James Prince. A slight modification of David
Bell's Unit Cell, see Unit Cell for background. Runs 2 Life universes
instead of 1(referred to as A0 and B0). The 2 universes do not
interact. Period 7680. The ON/OFF state of A0 is found every 7680
rounds and is indicated by the presence/absence of a glider
between the 6 boats in the upper left quadrant. The state of B0 is
indicated the same way but offset by 3840 rounds. So every n*7680
for A0 and n*7680+3840 for B0. This version is set with A0 initially
ON (indicated by glider in boats) and B0 in a pre-start ON state
(indicated by 3 blocks in the vertical chamber in the lower left
quadrant) so B0 will be officially ON in 3840 rounds. To start A0 OFF,
delete the glider. To start B0 OFF, delete the 3 blocks. An infinite
tiling of Deep Cells allows for an infinite hierarchy as follows: Set
universe A0 to generate an arbitrary Life pattern. Set universe B0 to
generate another layer of Deep Cells. This new layer has two
universes, called A1 and B1. Set universe A1 to generate an arbitrary
Life pattern. Set universe B1 to generate another layer of Deep
Cells. This new layer has two universes, called A2 and B2. Set
universe A2 to generate an arbitrary Life pattern. Set universe B2 to
generate another layer of Deep Cells. This new layer has two
universes, called A3 and B3...
Written in 1998 but couldn't be tested properly, forgotten, then
remembered and tested 2004.

Here's what the Deep Cell looks like. It is almost identical to a Unit Cell.

I couldn't test it back in 1998 because the computer was too slow and the software could only handle a 3x3 array of Deep Cells which wasn't enough to be sure it was working. Recently I stumbled over Nick Bostrom's Simulation Argument (that if humanity doesn't kill itself then we are probably in a computer simulation, www.simulation-argument.com). That got me thinking about recursively simulated universes (again) which reminded me of the Deep Cell. Using the new freeware Life32 I was able to run a 16x16 array of Deep Cells and they did what they were supposed too. So I figured it was time to stick it on the net. If you want to play with a Deep Cell you can either download the gif above or the zipped .LIF format file below.

I have also included a test of the Deep Cell, a large Life pattern of 16 by 16 Deep Cells. Universes A0 and B0 have been set to generate different patterns.

Universe A0 starts in the following 16x16 configuration.
A central p3 Cross with 4 p2 Blinkers in the corners.

Universe B0 starts in the following 16x16 configuration.
A p14 Tumbler over two p1 Table Pairs.

Here's what is says in the .LIF file about the test:

Test of the Deep Cell by Jared James Prince. 16x16 Deep Cells.
Universe A is a p3 Cross with 4 p2 Blinkers in the corners. Universe
B (in its pre-start state) is a p14 Tumbler over two p1 Table Pairs.
Ran for 153600 rounds for A and 157440 rounds for B, equivalent to
20 rounds for each pattern, output was as expected. See Deep Cell
for more info.

The test pattern is very large so it can take a while to load, in Life32 a bitmap version of the pattern takes about 2 minutes to load on a 1GHz computer, during which time it looks as if Life32 has locked up (it hasn't). It also runs very slow, it takes a couple of hours on a 1Ghz cpu to do the 157440 rounds.

DeepCell.LIF (Zipped)
DeepCellTest16x16.LIF (Zipped)

Well, that's it for the moment. If you have any comments, feel free to email me, jared(at)psychoticdeath.com.
Keep those glider guns pumping!




 
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