“This month we consider Conway’s latest brainchild, a fantastic solitaire pastime he calls life.”

Martin Gardener, October 1970

Scientific American 

What could be more complicated than your own life? You would not believe me if I told you that it is just a game. Game of life ( simply life) is a decent simulation of real living things in such a simple way. It was invented by John Horton Conway, a professor of Finite Mathematics at Princeton University around 1970 ( during that time he was studying mathematics at Cambridge University) henceforth known as Conway Game of Life.

A game that took 18 months of thinking became a sensation when it was described in 1970 in Scientific American. The most astonishing fact is that the game was developed when there were no actual computers. He only came across a computer with a screen, the PDP(Programmed Data Processor) eighth, and the PDP seventh. Conway motivation is derived from a book called Automata Studies that consists of interesting things related to automatic machines.

Tracing the History for Conway Game of Life

Although the game was developed in 1970, its foundation was laid much before. John Von Neumann, an American Mathematician inspired Conway. John was working on the Cellular Automata or self-replicating machines. Neumann was interested in colonizing humans on a different planet. His idea was to send some machines to Mars to create an atmosphere suitable for survival and then bring in humans.

His theory included smelting of iron ore present in Mars that would provide sufficient oxygen to sustain human life although not enough. He thought to develop such machines that could replicate itself similar to DNA and RNA present in humans.

His idea deeply inspired Conway and he invented Conway Game of Life that imitated Von Neumann’s machine.

Conway told about his game to Martin Gardner, the person who used to run the Mathematical Game column in the Scientific American for 25-30 years. After his invention was published titled “Mathematical Games” he got more readers than he had ever imagined. The editors convinced Gardner to write a monthly column on it which got more reader correspondence that anything in the entire history of the magazine ever could.

About the Conway Game of Life

Conway Game of Life is an infinite two-dimensional orthogonal grid ( intersecting at right angles) of square cells, each of which is in one of the two possible states- on( live) or off (dead). Every cell interacts with its eight neighbors ( horizontally, vertically and diagonally adjacent). In a lay man’s language the game consists of some squares in a space, they are points referred to as cells. A point can either be on or off. Just like mathematics this game runs on some rules that should be strictly followed.

This game is full of surprises! In most cases, it is impossible to look at a starting point and see what will happen in the future. The only way to find out is to follow the rules of the game.

Rules governing Conway Game of Life

As we follow certain principles, certain rules in our lives that make our life unpredictable. We never know what’s coming next, we just follow the rules as we are told and things happen accordingly. In a similar way, Conway Game of Life is governed by certain rules that make the game unique in itself. Let’s have a look at some of these rules:

• If a cell has less than 2 live neighbours it would die may be due to isolation or due to lack of support
• If a cell has more than 3 live neighbours die due to overcrowding resulting in competition and lack of resources ( imitation of real life)
• A dead cell with exactly three live neighbours becomes a live cell ( by reproduction) or gets born.

These rules may look simple but they give out certain patterns that could blow up your mind. It’s time to take a glimpse at some of these patterns.

Life Patterns

Try different patterns in this interesting game and see what happens. Even random patterns could turn into real-life objects. Although Conway could draw patterns and simulate them manually one pattern the R-pentomino that defied Conway attempt of manual simulation.

The pattern became stable or predictable after 1103 steps. At that time it was a challenging problem but modern-day computers could process it within seconds. Let’s take a look at some of these predictable patterns:

Still Life objects

The most common one is called the Block. It is simply a 2×2 square of live cells.

Some other still life objects are :

• Beehive
• Boat
• Ship
• Loaf
• Snake
• Tub

Oscillators

They are the objects that change from one form to the other and eventually repeat or oscillate. The most common is the Blinker that consists of three cells:

Another common oscillator is the Toad:

Gliders

This was one of the most exciting discoveries of Conway. These common moving patterns called gliders consist of just 5 cells. An interesting thing about the pattern is that the cells don’t move, what moves is the pattern of colours of black and white. It is similar to a moving energy pattern. A glider can be assumed as a particle, more like an energy particle similar to a vortex moving through space and because of the way it’s shape repeats every 4rth cycle it has an independent existence.

Conway Challenge

In Conway Game of Life, a pattern is said to be stabilized when it stops growing similar to the R-pentomino that stabilizes at 1103 steps. It was not immediately obvious whether a given initial life pattern could grow indefinitely, or whether any pattern at all can. Conway offered a $50.00 prize to whoever could settle this dispute.

  In 1970 an MIT group headed by R.W Gosper won the prize by finding the Glider Gun that emits a new glider every 30 generations. Since the gliders are not destroyed, and the gun produces a new glider every 30 generations indefinitely, the pattern grows forever, and thus proves that there can exist initial Life patterns that grow infinitely. Here is a simplified view of how a glider gun works:

Conway Game of Life gets an upgrade

This game is a no player game. A puzzle for mathematics students, it lacked essential elements of the game: no interaction and no competition making it monotonous. Two Randolph students and a professor came with a breakthrough in 2014 that solves the about two problems.

“ What we’ve been doing this summer is taking this model and turning into a competitive game between two teams,” said Marc Ordower, a Randolph mathematics professor. The two kids, Pujan Shrestha and Tu Nguyen along with the professor redesigned the game with two teams each creating a pattern that moves across the grid. The goal is to invade the other team’s section of the board. “ It is like an untrained chess player looking at a board between two masters and not being able to see who is in the lead”, Ordower said.

       This ambitious team does not stop here. They are working with Chris Cohen, a programmer in the college’s information technology office, to create a three-dimensional game. Once they are through, they need to start with the scratch understanding the strategy players can use in the game.

Maybe it’s not just a game!

A game that conveys deeper meanings of life can’t just be a game. It may be one of those few games or the only game on which MIT has published a research paper.

It is an amalgamation of mathematics and science trying to define each other. Using Conway Game of Life as a guide and not just a game, we can unearth many secrets still lying dormant.

The behaviour of ant colonies and termites piling up wood chips can be better understood.

Traffic problems might be solved by analyzing them with mathematical tools learned from these types of simulations. The patterns and cure to computer viruses that are examples of cellular automata can be resolved using the patterns hidden somewhere in the game. Human diseases could be cured once we attain a deeper knowledge of why cells live and die.

Views and thoughts on the game by Conway

In a short movie cum documentary called Numberphile directed Brady Haran ( it is available on youtube) John Conway tells about how he invented the Game of Life and the events that led to it.

His major inspiration was Neumann’s hypothesis of the self-replication machine that led to the invention of Conway’s Game of Life. 

Although earlier Conway did not find the game so interesting and got annoyed but now that annoyance has been reduced to some extent because he realises that other people value his creation though he does not in his early days but now as he has grown old he is very much pleased that he did something great in his mathematical life.

Great people seldom value their creation and maybe that was the reason that there was a time when Conway hated the Game of Life. In Numerophile Conway tells that most of his important achievements were overshadowed by the game.

He was known only by the Game of Life although he was proud of his achievements he just didn’t want to talk about it all the time. He gave many theories like Knot theory, Number theory, Game theory and Coding theory. In Numerophile he also mentions an incident where he thought he should have changed the name of Glider to The Ant because the movement of Glider ( mentioned above in the article) is similar to an ant. According to him, some of the ideas of the game have been directly derived from real-life like if you have too many organisms of your type in a given region you die because of lack of enough food.

Rest in Peace John Conway!

English mathematician John Horton Conway,82, died of SARS COV-2. The best thing is that he is still with us in the form of all the achievements and work that he has done for the human race will be remembered forever. He will be best remembered for Conway Game of Life which continues to fascinate people even after 50 years.

Conway never thought he would achieve something in life and neither did his colleagues. After he became a mathematical prominence he became free to study anything he wished to in his life. John knew he had a few years left in his life and he wanted to spend the rest of his life studying mathematics. Conway was obsessed about the Monster Group. He wished to solve the mystery he was reborn even after 100 years.

The only thing he wanted to know before his death was why the monster group exists? According to him, there hasn’t been any explanation of the group’s existence and it’s obviously not there because of any coincidence. Maybe John was right, maybe there was no coincidence but unfortunately, he is not amongst us to find it. It is now our duty to free Conway of this burden and do something for a man who did marvels for us.

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