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I hope you know Conway's Game of Life, featuring a grid of white and black squares that change according to simple rules, but generate complicated patterns.  SmoothLife looks even more biological!  Watch this video, then learn more here:

• Stephan Rafler,  Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife,

In the original Game of Life, whether a particular square is black or white on the next move depends on its current state and how many of its 8 neighbors are black now.   In her PhD thesis, Kellie Michele Evans generalized this to Larger Than Life, where relevant neighborhood is a large disk.  In the limit where this disk becomes large, we can think of each square as a single point.   

In SmoothLife, Rafler modified the game further by using the number of black squares in a smaller disk as a substitute for whether the point itself was black or white. 

You can see lots of videos of SmoothLife and related games here:

Some of them are 3-dimensional!
Sergey Ten's profile photomichel prins's profile photoRichard Botting's profile photoJohn Baez's profile photo
In some ways it appear less visually complex than Conway's life. The basic phenomena are the "chain", the "still blob", the "anchor blob" (attached to a chain), and the "glider blob".
know life since 30 years ago on my first speccy, was intrigued by the program, nice they have updated it ;)
Some look like algae. Others very like the Original GoL. Also like some models of the spread of disease in an early cybernetics book -- either Gordon Pask or Frank George? 
But in other ways more complex, because of the continuous bendiness!
+Ashley Yakeley I suspect that the visual complexity might be similar if the map size were increased enough.  The size of a traditional slider is only 3x3 pixels.  The size of these sliders seems to consume maybe a tenth of the width of the field, so the field is only about the equivalent of a 32x32 pixel field in the original Life.  Not much room for the fancier patterns we're used to.
+Ashley Yakeley - this movie started with some sort of random configuration.  If you start Life with a large random configuration, I think the result is usually less interesting: an explosion of activity followed eventually by stagnation.  I think your impression that it gives more complicated structures comes from the fact that people work very hard to find those.  I don't know if people have tried for SmoothLife. 

The fact that gliders can turn into fixed blobs and vice versa is nice and 'biological', I think.
It seems to me  a randomized rule could be produced from that integral rule. Also disk integral could be replaced with Gaussian and ring with mexican hat (DoG) to have more natural distributions.
As far as I know, the algorithm Stephan uses is much more CPU and GPU intensive as the typical Conway GoL algorithm (given that the latter has been optimized for decades by now). It takes time to really explore what Stephan's generalized version of the game might turn up. Since he once was a student of mine, I'm naturally very excited about his discovery and implementation, which he did completely on his own.

I personally would like to see a generalization if the GoL, where the number of neighbors is randomized, as I think this might be capable of simulating biological processes from neurological networks to ant colonies, etc. 
+Sergey Ten I came up with a formulation like this in an attempt to create/invent a grid-free form of the GoL. In many biological systems you have a life/death situation but no grid. I assumed a continuous rotational symmetry in the rules and I could prove one or two results but any computer implementation involved reintroducing a grid. 
Uh-oh Michael, you're starting to sound like Stephen Wolfram.

(I kid.)
+Michael Flohr "given that [Conway GoL] has been optimized for decades by now"
Indeed. Hashlife is gives a breathtaking speedup. It basically stores a dictionary for c*n x c*n supercells after n iterations (c is the speed of light here). Feels like exponential speedup, until, of course, you run out of memory. Look for "Golly" in the GoL Wikipedia entry.
+Richard Botting  Stephan Rafler rules formulation is also grid-free. Grid-free computer implementation (particle-like) would be interesting only if rules can not be explicitly written in simple, grid-friendly form. For GPGPU (cuda, OpenCL) grid implementaion is a lot more easy then particles
yes adding a 3th dimension would be great too. :)
as would be a second and third orgamism that would prey on each other.
I think I saw an article on a 3d version in Dr. Dobb's Journal 10 years ago. Plus or minus 5 years.

Sent from R J Botting's iPod
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