The “Game of Life” & Early Generative Art


by Theo Kingdom

The Game of Life is a zero-player game, which means that as the game is played, no players have input on the result. It is played on a square grid of filled-in squares or empty ones called “alive” cells and “dead” cells respectively.

The Game of Life was developed from a paper in the 1970s by John Horton Conway. John Conway (1937-2020) was a mathematician who was interested in mainly games and geometry. Although he is well known for creating GOL, his other work easily eclipsed it in the eyes of many of his peers. He has major contributions in game theory, geometry, topology, analysis and more. 

 

In the early 80s, he was involved in the discovery of the largest sporadic simple group - which is similar to discovering the largest prime number, but in terms of groups. This group can only be represented with at least 196,883 dimensions. It has 808 x 10^51 symmetries, as he had estimated. A finalized proof of this won John Conway’s doctoral student a Field’s Medal in 1998. He also worked on developing game theory in his theory of partisan games. As a model for behaviour, game theory has echoed through our economy and allowed for a new understanding of strategy. 

Funnily enough, John’s father, Cyril left school at 14 to play cards in part due to his photographic memory.

Accolades aside, many say that John Conway had a very out of the box thinking style and often poked fun at science for being too serious.

This philosophy paired with the GOL itself has pushed scientists and artists alike. It’s simple and definitive rules leading to lifelike shapes and organic progression is not something that is usually expected of computers:

A Coral and a GOL-like algorithm
 

A foundational pattern and a recently discovered pattern expanding on its function.
     
Glider - Richard Guy (1969) 
The first pattern to translate across the grid
           
                                     Bandersnatch - Entity Valkyrie (2020)

A specific “glider shifter” pattern that releases a glider with a changed path 

Winner of  Pattern of the Year 2020

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Each turn or “iteration”, the player evaluates the grid to make a new grid from the last. There is no winning or losing - the pattern develops until you decide you’ve had enough. There are three rules:

 
  • Any live cell with two or three alive neighbours survives. 
  • Any dead cell with three live neighbours becomes a live cell.
  • All other live cells die.

In this example, the first grid is evaluated cell by cell to determine the pattern on the next grid.

The cell circled in red has only one neighbor. In order for a live cell to remain alive on the new grid, it must have two or three neighbors - so this cell dies in the next grid. 

​The cell circled in green has three neighbours - so it stays alive in the next grid.​

In the output grid, the red empty cells show the number of neighbors that cell had before it died. All the alive cells here had three neighbors before (in green), but cells with two neighbors would survive too.

A cell dies because it has too many neighbors (4 > 3)  and the lowest cell in the second grid is born because dead cells with exactly three neighbours come back to life. You can try the game here: Game of Life

The inherent instability of this system birthed a community of followers that have different goals, but all are on the hunt for the next discovery of an impressive pattern.  

Notable patterns serve one of two interests - one being independent aesthetics. 

Rob’s p16 - Rob Liston (2020)
This pattern is the smallest period 16 (repeats every 16 turns) pattern in terms of population and area.

 

And the other interest being functionality within the context of other known patterns.

 

Gosper Glider Gun - Bill Gosper (1970)

The glider above was the first of a huge class of patterns called "guns. It was the first known finite pattern with unbounded growth and the core of signalling within complex modern patterns.

The Gosper Glider Gun was one of the first patterns with relevance to computing inside the Game of Life because it’s stream of gliders can serve as a 1 or a 0 if there is no stream. A sort of yes and no system - which is how all consumer computers function.

Development in this area produced patterns that could process simple interactions in these signals. These fundamental patterns serve as logic gates - which are the underpinnings of any computer. 

Gliders (AND) Gliders = Gliders  Gliders (AND) Nothing = Nothing 

This is an “AND” gate shown twice, with two different incoming streams. It stops everything, unless it has 2 incoming streams.In that case, the AND gate will produce a stream of gliders representing a 1 or yes signal. Otherwise, no stream will be produced which corresponds to a 0 or no signal.

This "AND" gate along with a few other logic gates serve as the fundamental operations for all computers. With only a couple more elements discovered, there was an opportunity to demonstrate a functional computer made entirely inside the Game of Life.

In 2000, Paul Rendell made a simple computer inside the Game of Life which qualified the game as Turing Complete, meaning it can function like any computer disregarding how inefficient it is. Rendell extended this discovery by bringing life to this simple computer. He did so by simulating an identical simple computer within the computer he had previously made.

There have been many advancements in the speed, memory, and capabilities of these computers, allowing designers to make more complicated patterns.

Digital Clock - "dim" (2017)
User “dim” on StackExchange created a digital clock in the Game of Life to fulfill a bounty request.

 

A large development in GOL was the creation of the “Metapixel” inside the game. This allowed any GOL pattern to run “on top of” a framework also made from the Game of Life - which is easier to understand with some graphics. Pictured here is one Metapixel which shades dark and light according to the logic in the Game of Life - it represents one alive cell.

 
OTCA Metapixel - Brice Due (2006)

This more illustrative animation shows the implications of the OTCA Metapixel - an infinite zoom showing that “Metapixels” can display any pattern - including themselves:

Extensions of the Game of Life along with unique computer science related ideas form the basis of generative art. 

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Here are three artists working with generative systems inspired by The Game of Life to make creative media:

Bert Chan lives in Hong Kong and is a primary contributor to the Lenia Project. His work predominantly focuses on science, but he designs typefaces as well. The Lenia Project is very similar to the Game of Life,the main exception being that the step, turn or iteration concepts are nonexistent: it is a continuous system. His work has a focus on emergent behaviour, which is the display of complex behaviour within a system involving simple rules. Chan’s work sheds light on the transition of life from chemistry to biology, what he calls “cultivating artificial life.”


“Some rudimentary developmental biology in Lenia. Complex spore develops into full form, and the full form produce simple spores.”
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Simon Alexander-Adams (@polyhop) creates generative art daily. His work sometimes includes continuous generative systems, discrete ones (like the Game of Life) and other reaction diffusion-based systems.


“Altered Pathways [ 1111 ] continued cellular automata instances.”
@polyhop (2021) Full video



“Cypher [ 1115 ] my last sketch was secretly a step towards this glyph generator 😛” 
@polyhop (2021) Full video
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Yoshi Sodeoka lives in New York and has been practising as an artist for 20 years. His works include stills, animation and audiovisual pieces among other digital mediums. Like @polyhop, his work is artistically oriented, but maybe more independent of common interest. His work sometimes incorporates audio and other signals into these systems to enhance their effect. His video accompanying “Spike” by Max Cooper includes generative techniques and possibly microscope footage of bacteria.


(Taken from the video thumbnail)

“Bugs” @yoshisodeoka (2020)
“Bugs”
@yoshisodeoka (2020)

 

Bert Chan is making discoveries in evolutionary biology that others are using to create new media or developing into new scientific discoveries. Some artists use these computer science based generative systems to enhance their practice - like polyhop. Some seem to wrap the ideology around back to the science and relish learning technicalities to achieve lightning fast reactive and beautiful designs. Although their interest could be considered removed from reality from a technical perspective or limiting from a creative perspective, John Conway always supported endeavours of this nature. For this reason, he may be mostly remembered for the GOL - one of his less prestigious discoveries in mathematics. 

“I had to sort of struggle to get the license to be interested in trivial things.” John Conway, 2015

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Frogspawn (2021) - Theo Kingdom

Theo Kingdom is an artist and photographer mainly working in a variety of digital disciplines including still image rendering, motion graphics and generative art. He also enjoys film photography and processing alongside pen-plotting and other odd ways of rendering images. Find more of Theo's work on his Instagram - @analogbandit and website.