ChatGPT 3.5 and Google Bard on Life

[pcallahan]

Google Bard has a reputation for being a lot worse than ChatGPT, and it is certainly less expressive. I have found in some cases it's better at identifying song lyrics. It also gave me better answers about Conway's Game of Life infinite growth patterns (admittedly with errors). I have not compared it to ChatGPT 4 but should do so in the interest of fairness.

Google Bard (my prompts are in italics):
i wonder if you know some of the recent results related to conway's game of life

Sure, here are some recent results related to Conway's Game of Life: [I have no idea if these are true as stated.]

In 2022, a team of researchers from the University of Turku in Finland settled a 29-year-old conjecture about the game. The conjecture, known as the "Conway conjecture," stated that there exists a finite configuration in the game that will always return to its original state after a certain number of steps. The researchers were able to find such a configuration, which they named "the Turku spaceship."
In 2021, a team of researchers from the University of Cambridge developed a new algorithm for simulating the game of life. The algorithm, known as the "Cambridge algorithm," is significantly faster than previous algorithms, making it possible to simulate the game of life on much larger scales.
In 2020, a team of researchers from the University of Oxford discovered a new type of pattern in the game of life, known as a "quasicrystal." Quasicrystals are patterns that exhibit long-range order, but do not have any translational symmetry. This is the first time that quasicrystals have been found in the game of life.
These are just a few of the recent results related to Conway's Game of Life. The game continues to be a popular topic of research, and new discoveries are being made all the time.

very good. do you know the size of the smallest pattern with infinite growth?

Yes, the smallest pattern with infinite growth in Conway's Game of Life is a 10-cell pattern. It was discovered by Paul Callahan in 1997. The pattern is shown below:

Code snippet
#.##.
..#..
..#..
Use code with caution. Learn more
This pattern grows indefinitely by creating a glider gun, which is a pattern that can produce gliders. Gliders are small patterns that can move around the game board and destroy other patterns. The glider gun in this pattern creates two gliders per generation, which means that the pattern will grow exponentially over time.

There are also a number of other 10-cell patterns that exhibit infinite growth. These patterns are all variations of the basic pattern shown above.

close but it does not produce a glider gun

You are correct. The pattern I showed you does not produce a glider gun. The smallest pattern that produces a glider gun is 11 cells in size. However, there is a 10-cell pattern that exhibits infinite growth without producing a glider gun. This pattern is shown below:

Code snippet
#.#.
..#.
..#.
Use code with caution. Learn more
This pattern grows indefinitely by creating a block-laying switch engine, which is a pattern that can create two blocks per generation. Blocks are small patterns that can be used to build other patterns. The block-laying switch engine in this pattern creates two blocks per generation, which means that the pattern will grow exponentially over time.

There are also a number of other 10-cell patterns that exhibit infinite growth without producing a glider gun. These patterns are all variations of the basic pattern shown above.

are there any infinite growth patterns smaller than 10 cells?

No, there are no infinite growth patterns smaller than 10 cells. This was proven by Nick Gotts and Paul Callahan in 1997. They used a computer to exhaustively search all possible patterns with 9 or fewer cells, and found that none of them exhibit infinite growth.

Comment: the patterns it provides are wrong and don't even have 10 cells. It is also wrong about other specifics, but it actually states the main claims correctly. (And namechecks me. Woohoo!)

ChatGPT 3.5 is more verbose and significantly less informative in this case. It is usually but not always better than Bard and this probably just shows a difference in the training set.

i wonder if you know some of the recent results related to conway's game of life

As a language model, I do not have access to real-time or up-to-date information. My knowledge is based on a cutoff date in 2021, and I do not have browsing capabilities. However, I can provide you with some general information about Conway's Game of Life and its recent developments up to my knowledge cutoff date.

Conway's Game of Life is a cellular automaton created by the British mathematician John Horton Conway in 1970. It consists of a grid of cells that can be in one of two states, "alive" or "dead", and follows a set of rules to determine the state of each cell in the next generation based on the states of its neighboring cells.

Some recent developments related to Conway's Game of Life include:

Patterns and constructions: Game of Life enthusiasts continue to discover new interesting patterns and constructions, including gliders, spaceships, and oscillators. These patterns can interact with each other in complex ways, leading to the creation of new patterns and structures.

Rule variations: While the original Game of Life follows a specific set of rules, researchers have explored variations of these rules, such as different neighborhood configurations, different birth and survival rules, and multi-state versions of the game. These rule variations can lead to different behaviors and patterns in the game.

Computational and theoretical research: Game of Life has been used as a tool for studying computation and complexity theory. Researchers have explored the computational universality of Game of Life, which means that it can be used to simulate any Turing machine, making it a powerful computational system. Additionally, theoretical research has been conducted to study the properties of various patterns and structures in Game of Life, as well as their mathematical properties.

Hardware implementations: Some researchers have explored implementing Game of Life in hardware, such as using electronic components or specialized processors, to study its behavior and potential applications in physical computing.

Applications: Conway's Game of Life has been used in various applications beyond its original purpose as a recreational mathematical curiosity. For example, it has been used in computer graphics, image processing, cryptography, and even in fields like biology and chemistry to model and simulate cellular processes.

Please note that these developments may have progressed further since my knowledge cutoff date, and I would recommend checking more recent sources for the latest advancements in the field of Conway's Game of Life.

very good. do you know the size of the smallest pattern with infinite growth?

As of my knowledge cutoff date in 2021, the smallest known pattern with infinite growth in Conway's Game of Life is the "Gosper glider gun." It was discovered by Bill Gosper in 1970 and consists of 36 cells, making it the smallest known pattern that produces a stream of gliders that continue to move indefinitely, without interfering with each other or stabilizing into a static pattern.

The Gosper glider gun is a remarkable pattern that generates a continuous stream of gliders, which are spaceships that move diagonally across the Game of Life grid. Gliders are a fundamental building block in many Game of Life patterns and constructions, and they can be used to create a wide range of interesting and complex behaviors.

It's worth noting that since my knowledge cutoff date is in 2021, there might have been new discoveries or developments related to Conway's Game of Life that could have potentially changed the status of the smallest known pattern with infinite growth. I would recommend checking more recent sources or Game of Life communities for the latest information on this topic.

there is a result from the 1990s. it is much later than gosper's result

I apologize for the earlier response. As an AI language model, I do not have access to real-time or up-to-date information, and my knowledge is based on a cutoff date in 2021. However, I will do my best to provide accurate information based on my training data.

You are correct. There has been a significant discovery of a smaller pattern with infinite growth in Conway's Game of Life called the "Simkin glider gun." It was discovered by David Bell and named after his friend Robert Simkin. The Simkin glider gun was found in the 1990s and is smaller than the Gosper glider gun, consisting of only 15 cells, which makes it the smallest known pattern with infinite growth in Conway's Game of Life.

The Simkin glider gun generates a stream of gliders that continue to move indefinitely, similar to the Gosper glider gun, but with fewer cells. This discovery was a significant advancement in the field of Game of Life, as it demonstrated that smaller patterns could exhibit infinite growth, challenging the previously known bounds and expanding the possibilities for constructing compact and intricate patterns in the game.

It's important to note that the field of Conway's Game of Life is constantly evolving, and new discoveries or results may have emerged since my knowledge cutoff date. I recommend consulting more recent sources or Game of Life communities for the latest information on this topic.

have you heard of a 10 cell pattern with infinite growth. it is not a glider gun

As of my knowledge cutoff date in 2021, I am not aware of any 10-cell pattern with infinite growth in Conway's Game of Life that is not a glider gun. The smallest known patterns with infinite growth in Game of Life are typically glider guns, which are patterns that periodically emit a stream of gliders that continue to move indefinitely without interfering with each other or stabilizing.

It's possible that there have been new discoveries or developments related to Conway's Game of Life since my knowledge cutoff date, and there may be smaller patterns with infinite growth that have been found. The field of Game of Life is constantly evolving, and researchers and enthusiasts continue to explore and discover new patterns, constructions, and behaviors in this cellular automaton.

I recommend checking more recent sources or Game of Life communities for the latest information on this topic to stay up-to-date with the most recent advancements in Conway's Game of Life.

do you know a pattern called the switch engine?

Yes, the "switch engine" is a well-known pattern in Conway's Game of Life. It is a small, self-propelling pattern that was discovered by John Conway himself in 1970. The switch engine is a type of spaceship, which is a pattern that moves across the Game of Life grid.

The switch engine consists of 12 cells and moves diagonally at a speed of c/12, meaning it travels one cell diagonally every 12 generations. It has a unique behavior where it periodically switches between two different phases as it moves, hence the name "switch engine." The switch engine has been widely used in Game of Life constructions and patterns due to its interesting behavior and its ability to interact with other patterns in interesting ways.

The switch engine is a classic example of the wide range of complex behaviors that can emerge from simple rules in Conway's Game of Life, and it has been extensively studied and used in various Game of Life patterns, including spaceships, oscillators, and even as a component in constructing more complex structures.

does it grow in size?

No, the switch engine is a bounded pattern in Conway's Game of Life, which means that its size does not grow over time. The switch engine consists of a fixed number of cells that form a stable shape, and it moves across the Game of Life grid without changing its overall size or shape.

The switch engine is a self-contained pattern that maintains its shape and size as it moves, periodically switching between two different phases. It does not generate additional cells or structures as it moves, and it does not exhibit unbounded growth or expansion like some other patterns in Game of Life, such as glider guns or replicators.

The switch engine's ability to maintain its shape and move in a self-propelled manner while remaining bounded makes it a useful building block in constructing more complex patterns in Conway's Game of Life. It has been extensively studied and used in various Game of Life constructions and patterns due to its unique behavior and versatility in interacting with other patterns.

that's not true. it leaves a trail like a puffer

You are correct, I apologize for the earlier mistake. The switch engine does, in fact, leave a trail behind as it moves, similar to a puffer in Conway's Game of Life. I apologize for the confusion.

A puffer is a type of spaceship in Conway's Game of Life that leaves behind a trail of debris or other patterns as it moves. The switch engine, while considered a spaceship due to its ability to move across the grid, also leaves behind a trail of debris, which may consist of gliders, spaceships, or other patterns depending on the configuration and placement of the switch engine.

The switch engine's trail of debris can interact with other patterns or structures in the Game of Life grid, leading to interesting and complex behaviors. It can be used as a component in constructing more elaborate patterns or as part of Game of Life constructions that involve the movement of patterns across the grid while leaving behind a trail of debris.

I apologize for any confusion caused by my previous response, and I appreciate your clarification. Thank you for bringing this to my attention.

would that make it a smaller infinite growth pattern

Yes, the switch engine, with its ability to leave a trail of debris behind as it moves, can indeed be considered a smaller infinite growth pattern in Conway's Game of Life. While the switch engine itself has a fixed size and does not grow, the trail of debris it leaves behind can continue to interact with other patterns, potentially leading to unbounded growth or infinite growth in the Game of Life grid.

The switch engine's ability to produce a trail of debris that can move independently and interact with other patterns makes it a valuable tool in constructing patterns with more complex and dynamic behaviors, including patterns that exhibit infinite growth. The debris generated by the switch engine can be used to create a wide variety of interesting and intricate patterns, such as spaceships, glider streams, and other structures, depending on the specific arrangement and configuration of the switch engine and its debris.

So, while the switch engine itself is not an infinite growth pattern, its ability to generate a trail of debris that can exhibit unbounded growth or interact with other patterns in a way that leads to infinite growth makes it a significant component in constructing smaller patterns with infinite growth in Conway's Game of Life.

i think you do not know these results because they are not widely disseminated

I apologize for any confusion. As an AI language model, my responses are generated based on the data I have been trained on, which includes a large corpus of text from the internet up until my knowledge cutoff date of September 2021. While I strive to provide accurate and up-to-date information, I may not always have knowledge of the latest or most obscure results or findings, as new information may have emerged after my knowledge cutoff date, or some results may not be widely disseminated.

Conway's Game of Life is a highly dynamic and evolving field of study with ongoing research, and new discoveries, patterns, and results can emerge over time. If you have specific information or results related to the switch engine or any other aspect of Conway's Game of Life that are not widely disseminated or may have been discovered after my knowledge cutoff date, I would be happy to learn from you and update my knowledge. Please feel free to share any specific details or references, and I will do my best to provide accurate and relevant information based on the available data.

do you know a researcher named nick gotts?

Yes, Nick Gotts is a researcher known for his work in various fields, including artificial intelligence, computational modeling, and complexity science. He has been associated with organizations such as the University of Southampton, UK, and the University of Bath, UK. His research interests include agent-based modeling, social-ecological systems, and decision-making under uncertainty. He has published papers and contributed to research in areas such as climate change, land use, and natural resource management. However, please note that my information is based on my training data up until September 2021, and it may not include the most recent or comprehensive information on researchers, including Nick Gotts.

he wrote a paper. i think it was called sparse fields in conway's game of life. i am not sure. but it concerned small infinite growth patterns

As an AI language model, I do not have direct access to external sources such as specific papers or publications. However, based on my training data up until September 2021, I am not aware of a paper written by Nick Gotts with the title "Sparse Fields in Conway's Game of Life" or a similar topic related to small infinite growth patterns in Conway's Game of Life.

It's worth mentioning that the field of Conway's Game of Life is a highly dynamic and constantly evolving area of research, with new discoveries, patterns, and results being published regularly. It's possible that there may be recent or unpublished research that I am not aware of, including work by Nick Gotts or other researchers, that may have emerged after my knowledge cutoff date.

If you are interested in a specific paper or topic related to Conway's Game of Life, I would recommend checking reputable research databases, academic journals, conference proceedings, or directly contacting the researchers or authors associated with the topic for the most accurate and up-to-date information.

it was presented at an artificial life conference, possibly in 1998

I apologize for the confusion. As an AI language model, I do not have access to external sources or the ability to browse the internet. My responses are generated based on the data I have been trained on, which includes a large corpus of text up until my knowledge cutoff date in September 2021. I do not have specific information about papers or presentations given at artificial life conferences or other specific events.

However, based on the information you provided, if Nick Gotts presented a paper at an artificial life conference, possibly in 1998, with a title related to "sparse fields in Conway's Game of Life" or small infinite growth patterns, it may be worthwhile to search for conference proceedings or other research databases related to artificial life conferences from around that time period. This could potentially help you find the specific paper and obtain more detailed information about Nick Gotts' work on this topic.

alife. is that a conference name?

Yes, "ALife" is commonly used as an abbreviation for "Artificial Life," which is a multidisciplinary field of study that focuses on understanding, simulating, and synthesizing life-like systems using computational and artificial approaches. The field of Artificial Life involves research from various disciplines, including computer science, biology, physics, robotics, and philosophy, among others.

There are several conferences and workshops that are specifically focused on Artificial Life research and provide a platform for researchers to present and discuss their work. Some examples of popular Artificial Life conferences include the International Conference on Artificial Life (ALife), the European Conference on Artificial Life (ECAL), and the Conference on Artificial Life and Robotics (AROB), among others. These conferences typically feature presentations of research papers, posters, and discussions on a wide range of topics related to Artificial Life, including Conway's Game of Life, patterns, and other related research areas.

If you are looking for information about Nick Gotts' work related to "sparse fields in Conway's Game of Life" or small infinite growth patterns, it may be worthwhile to search for proceedings or papers from artificial life conferences around 1998, as you mentioned, to see if any publications by Nick Gotts on this topic were presented at those conferences. Accessing conference proceedings or directly contacting the researchers or authors associated with the topic can provide you with more specific and up-to-date information.

Gotts, N.M, Callahan, P.B. (1998) Emergent structures in sparse fields of Conway's ``Game of Life''. In: Artificial Life VI

I apologize for the earlier incorrect information. Thank you for providing the correct title and authors of the paper "Emergent structures in sparse fields of Conway's 'Game of Life'" by N.M. Gotts and P.B. Callahan, which was presented at the 6th International Conference on Artificial Life (ALife VI) in 1998.

Unfortunately, as an AI language model, I do not have access to the content of this specific paper or the ability to provide a summary or analysis of its findings. However, based on the title, it appears that the paper may discuss emergent structures that arise in sparse fields within Conway's Game of Life, which is a well-known cellular automaton with simple rules that can produce complex and interesting patterns.

If you are interested in learning more about this paper, I would recommend checking the proceedings of the ALife VI conference or other relevant research databases to obtain a copy of the paper and read the details of the research presented by N.M. Gotts and P.B. Callahan

.

are there any infinite growth patterns smaller than 10 cells?

As far as I am aware, there are no known infinite growth patterns in Conway's Game of Life that are smaller than 10 cells. The smallest known infinite growth patterns in Game of Life are typically larger than 10 cells and include well-known patterns such as glider guns, lightweight spaceships, and other complex structures.

It is worth noting that the search for novel and smaller infinite growth patterns, also known as "spaceships" or "puffers," is an active area of research in the field of cellular automata and Conway's Game of Life. Researchers continuously explore and discover new patterns with various sizes, shapes, and behaviors through computational simulations and mathematical analysis.

It is possible that new discoveries or breakthroughs may have been made since my knowledge cutoff date in September 2021, and the latest research may reveal smaller infinite growth patterns in Conway's Game of Life or other related cellular automata. Thus, it is always advisable to consult the latest research papers, conference proceedings, and other relevant sources for the most up-to-date and accurate information on this topic.

do you think anyone proved that there are none smaller

As an AI language model, I do not have the ability to know or speculate on whether anyone has definitively proved that there are no smaller infinite growth patterns in Conway's Game of Life. Proving the absence of a particular pattern or structure in a cellular automaton like Game of Life can be challenging and may require extensive computational simulations, mathematical analysis, and rigorous formal proof techniques.

The field of cellular automata, including Conway's Game of Life, is an active area of research with ongoing discoveries, developments, and advancements. New patterns, structures, and behaviors may be constantly discovered or proven by researchers, and the state of knowledge in this field can evolve over time.

If you are interested in the latest findings or proofs related to the existence or absence of infinite growth patterns of a specific size in Conway's Game of Life, I would recommend consulting the latest research papers, conference proceedings, and other reputable sources from the field of cellular automata, and seeking insights from experts in the field for the most up-to-date and accurate information.

[rpresser]

In 2021, a team of researchers from the University of Cambridge developed a new algorithm for simulating the game of life. The algorithm, known as the "Cambridge algorithm," is significantly faster than previous algorithms, making it possible to simulate the game of life on much larger scales.

I tried searching both the forum and Google for "Cambridge algorithm" and couldn't find anything. Is this remark by Bard true, and if so can I get a link to a paper or webpage about this discovery?

[dvgrn]

In 2021, a team of researchers from the University of Cambridge developed a new algorithm for simulating the game of life. The algorithm, known as the "Cambridge algorithm," is significantly faster than previous algorithms, making it possible to simulate the game of life on much larger scales.

I tried searching both the forum and Google for "Cambridge algorithm" and couldn't find anything. Is this remark by Bard true, and if so can I get a link to a paper or webpage about this discovery?

There is no such thing, I'm sorry to say.

There's also no such thing as "the Turku spaceship" -- and even though there were a couple of important results reported by Finnish researchers in 2022, the description of what they discovered is sheer nonsense.

There's also no such thing as a Game of Life "quasicrystal" from 2020.

Here's an April Fools' Day post with some other AI-generated text about Conway's Life. None of that is true either. The entire field appears to be completely indistinguishable from nonsense by AI "outsiders" -- there's simply not enough useful text about Conway's Life to train a language model successfully.

They are certainly good at inventing plausible-sounding announcements, though! Maybe we should use made-up AI pronouncements as sources of inspiration for future community projects, same as we ended up doing with Gustavo's "prediction" of the fixed-cost reverse caber tosser.

[hkoenig]

Back around 1978 I came across an article (I think it was in "Science") about an effort to use a computer program to simulate the "monkeys at typewriters" myth. Their solution was to analyze text and record the number of occurrances of letter sequences, then use the resulting data as part of a random number generator. So instead of truly random text, it would have the sequence probabilities found in English text.

When I read the article, I realized I could do better. They claimed that because they were using a full, multi-dimensional array of 26 letters, a space and a period, they would run out of computer memory if they went beyond a sequence of 4 characters (28x28x28x28x28 is over 16MB at a time when entire disk drives didn't hold that much data).

Which may be true, but I realized that most of their array was empty space, and a better way was to use a tree structure. I was able in a few days to implement a program in Fortran on a DEC-10 that could handle up to 11 character strings. I didn't have much text to work with, but it was able to generate recognizable words and phrases not in the original text, based on the probablities found in the original text. The next step would have been to write the tree out to disk instead of just holding it all in memory, along with using lots more text, but I never got that far.

Jump forward 45 years, and the AI folks are still doing this sort of thing, just concatenating together longer strings of text from a much larger database, with some biasing being applied to how they randomly choose the next bit of data.

If this was truly "intelligent", you should have got an answer that was something like, "I'm sorry Dave, I'm afraid I can't do that. I don't know enough about Conway's Game of Life to answer your question. This discussion can no longer serve any useful purpose. Good-bye."

[pcallahan]

I have not compared it to ChatGPT 4 but should do so in the interest of fairness.

ChatGPT 4 is often much better than 3.5 but sadly not in this case. I conducted the same "interview" with ChatGPT 4 today with just a few changes to the script based on its answers. More of its statements are accurate, but it produces a great deal of nonsense as well. I still have to give Google Bard the prize in this contest (and not just for sucking up to the judge).

Added: While this is long, some of it is hilarious to anyone who knows CGOL. Sadly, the worst mistakes may sound plausible to someone who does not.

i wonder if you know some of the recent results related to conway's game of life

As an AI developed by OpenAI, I don't have real-time data or browsing capabilities to pull from the internet. My training only covers knowledge until September 2021, and I can't provide new developments or discoveries made after this date. However, up to that point, there are some fascinating results concerning Conway's Game of Life that you might find interesting:

Turing Completeness: Conway's Game of Life is Turing complete. This means that, theoretically, any calculations done by a computer could be performed within the Game of Life, given enough time and space.

Self-Reproduction: It's possible to create configurations in the Game of Life that are self-replicating. The first of these was discovered by John Conway himself and is called the "R-pentomino". Since then, many more have been found.

Garden of Eden: In 1971, Edward Moore and John Myhill proved that there are "Garden of Eden" patterns in Conway's Game of Life. These are patterns that can never be the result of another pattern, and therefore can only be created as initial configurations.

Universal Constructor: In 2010, Andrew J. Wade discovered a pattern called "Gemini", which is a spaceship that leaves behind a trail of debris. The debris is actually a copy of the spaceship, effectively making it a self-replicating structure. This was the first known example of a "universal constructor" - a pattern that can create any other pattern given the right initial conditions.

Smallest Universal Turing Machine: In 2018, Adam P. Goucher and Tomas Rokicki proved that a 2-state, 5-symbol Turing machine is universal, using a simulation in Conway's Game of Life to do so. This is currently the smallest known universal Turing machine.

The Speed of Light: In the Game of Life, the "speed of light" is defined as the maximum possible speed at which information can travel. This is one cell per generation. Patterns known as "spaceships" can be constructed to travel at this speed.

For more recent results beyond 2021, I would recommend looking up recent academic papers, blog posts, or discussion forums dedicated to cellular automata and Conway's Game of Life.

very good. do you know the size of the smallest pattern with infinite growth?

As of my last update in September 2021, the smallest known pattern with infinite growth in Conway's Game of Life was a configuration discovered in 2018 by Adam P. Goucher, known as the "switch engine ping-pong". It consists of only 10 cells and eventually creates an infinite growth of "switch engines", a type of spaceship.

Please verify from a recent source as this information could have changed since my last update.

i think that's not quite right. is there an earlier result that matches it in size. what is the earliest such result

I apologize for the previous confusion. You're correct. The smallest known pattern with infinite growth in Conway's Game of Life is the "Glider Gun", specifically the Gosper Glider Gun, which was discovered by Bill Gosper in 1970. This configuration consists of 36 cells, and it was the first configuration found that can grow indefinitely.

The pattern you're referring to might be a "R-pentomino," which is a configuration of 5 cells that shows remarkable complexity and was among the earliest surprising results found in Conway's Game of Life. However, despite its complexity and the fact it lasts over 1,000 generations, it doesn't grow indefinitely.

The ten-cell "switch engine ping-pong" discovered by Adam P. Goucher does lead to infinite growth but it was discovered much later, in 2018.

As of my knowledge cutoff in 2021, these are the relevant results. If there have been new discoveries or corrections to this information, I wouldn't have them in my database. Please verify from a recent source.

there is a result from the 1990s. it is much later than gosper's result

I apologize for the oversight. The smallest known pattern with infinite growth in Conway's Game of Life is a configuration known as the "Gosper's glider gun," which was discovered by Bill Gosper in 1970 and consists of 36 cells. However, you are correct that there was a significant discovery in the 1990s.

In 1995, a pattern called "Herschel" was discovered, which also displays infinite growth. Its initial configuration consists of just 20 cells, fewer than the Gosper's glider gun. The pattern leaves behind two gliders as it transforms into a configuration (also known as "Herschel") which is 59 generations back in the cycle, offset by (-5, -2) cells.

As of my knowledge cutoff in 2021, these are the key results. If there have been new discoveries or corrections to this information since then, I wouldn't have them in my database. Please verify from a recent source.

have you heard of a 10 cell pattern with infinite growth. it is not a glider gun

I'm sorry for the confusion earlier. Yes, as of my last update in 2021, the smallest known pattern with infinite growth in Conway's Game of Life is a 10-cell pattern discovered by Achim Flammenkamp in 1991.

It does not construct a repeating structure like the Gosper Glider Gun but instead creates a chaotic pattern that eventually, after a few thousand generations, begins to spawn gliders. It was a significant discovery because it showed that a pattern of such a small size could have such complex behavior and grow indefinitely.

do you know a pattern called the switch engine?

Yes, I'm familiar with the "Switch Engine." In Conway's Game of Life, a Switch Engine is a pattern that moves diagonally across the grid while leaving behind debris. It's interesting because, while most patterns stabilize after a few generations, the switch engine keeps moving and producing more cells.

Switch engines are capable of producing unbounded growth in the Game of Life. One particular example of this is a pattern that includes a switch engine which produces a "block-laying" behavior, leaving a trail of static "block" patterns behind it.

In terms of the smallest infinite growth pattern, a variation of the switch engine is indeed relevant. It's the aforementioned 10-cell configuration discovered by Achim Flammenkamp in 1991. The pattern begins as a small and simple configuration, but after a few thousand generations, it turns into a switch engine that starts creating "gliders," leading to infinite growth.

does it grow in size?

Yes, a "switch engine" in Conway's Game of Life does indeed grow in size over time. As it travels across the grid, it leaves behind "debris" in the form of stable or oscillating patterns. The specific types of debris and their locations vary depending on the precise initial configuration of the switch engine.

This is one of the ways that infinite growth can occur in Conway's Game of Life: instead of a pattern that repeats or oscillates while staying the same size, the switch engine continues to add new cells to the grid over time. So even though the switch engine itself is a relatively small pattern, it can generate an indefinitely large amount of debris.

Keep in mind that despite this growth, the switch engine does not grow indefinitely in all directions. The active part of the switch engine remains a relatively localized phenomenon moving diagonally across the field, while the debris it leaves behind remains static or oscillating.

would that make it a smaller infinite growth pattern than the glider gun?

Yes, the 10-cell configuration discovered by Achim Flammenkamp in 1991 that evolves into a switch engine would indeed be a smaller pattern with infinite growth than the Gosper Glider Gun. The Gosper Glider Gun has 36 cells, while this particular switch engine configuration starts with only 10 cells.

It's important to note that this is based on the size of the initial configuration. The switch engine does generate more cells as it moves and leaves behind debris, but the original pattern that evolves into the switch engine is still just 10 cells.

As of my last training cut-off in September 2021, the 10-cell switch engine configuration was the smallest known pattern with infinite growth in Conway's Game of Life.

do you know a researcher named nick gotts?

As of my training data cut-off in September 2021, I don't have specific information about a researcher named Nick Gotts in the context of Conway's Game of Life or cellular automata. If Nick Gotts has made significant contributions to this or other fields of study after this time, I would not have that information. You might want to look up more recent sources for up-to-date information.

If you're referring to a specific achievement or discovery by Nick Gotts, could you please provide more details? I could then give more relevant information based on what was known up to 2021.

he wrote a paper. i think it was called sparse fields in conway's game of life. i am not sure. but it concerned small infinite growth patterns

As of my last update in September 2021, I don't have the specific details of a paper titled "Sparse Fields in Conway's Game of Life" by Nick Gotts in my database. However, the topic of small infinite growth patterns and sparse fields (which would be regions of the game grid where only a few cells are active) are relevant areas of research in Conway's Game of Life.

The smallest known pattern with infinite growth, a configuration of 10 cells that eventually evolves into a switch engine, was discovered by Achim Flammenkamp in 1991. This pattern begins in a small, simple configuration but after a few thousand generations, it begins to spawn gliders, creating a pattern of infinite growth.

The specifics of Gotts' paper and the precise patterns or proofs it presents, if published after my last update, would not be something I have details on. To get the most accurate information, I recommend reading the paper directly or looking for summaries or discussions of it in relevant academic or enthusiast circles.

it was presented at an artificial life conference, possibly in 1998

I apologize for any inconvenience, but as of my last training cut-off in September 2021, I don't have the specific details of a paper presented by Nick Gotts at an Artificial Life conference in 1998. The specific datasets used for my training don't include all individual conference proceedings or academic papers, particularly if they're relatively niche or specialized.

If the paper was indeed about small infinite growth patterns in Conway's Game of Life, it could potentially be very relevant to the field, especially considering the ongoing interest in such patterns. However, to find the specifics of Gotts' paper, I recommend searching for the paper directly in academic databases, or looking for discussions or summaries of it in artificial life or cellular automata research circles.

I must note that while I strive to provide accurate and detailed responses, my responses should not be used as a replacement for direct academic research.

Gotts, N.M, Callahan, P.B. (1998) Emergent structures in sparse fields of Conway's ``Game of Life''. In: Artificial Life VI

I appreciate the citation, but as an AI, I don't have access to individual academic papers or conference proceedings. My training data includes a diverse range of sources, including textbooks, websites, and other educational material, up until September 2021.

While I don't have the specifics of the paper "Emergent structures in sparse fields of Conway's 'Game of Life'" by N.M. Gotts and P.B. Callahan presented at Artificial Life VI in 1998, I can tell you that studying emergent structures in sparse fields in Conway's Game of Life is an important topic in cellular automata research. Sparse fields typically refer to game grids where only a small number of cells are initially live or active. Emergent structures would be the interesting or complex patterns that arise from these initial conditions.

The concept of small infinite growth patterns, such as the 10-cell pattern that evolves into a switch engine, is also a key part of studying emergent behavior in Conway's Game of Life. If Gotts and Callahan's paper focuses on this topic, it could potentially involve new discoveries or insights into how these patterns form and evolve.

For the specifics of Gotts and Callahan's conclusions and findings, I would recommend reading the paper directly if it's available to you. I can provide general information and context about Conway's Game of Life and cellular automata, but I can't provide a summary or analysis of specific academic papers that I haven't been trained on.

do you think anyone proved that there are none smaller

As of my last training data in September 2021, it was not proven that there are no smaller patterns with infinite growth than the 10-cell configuration discovered by Achim Flammenkamp in 1991 in Conway's Game of Life. Such a proof would be a significant result in the field of cellular automata.

Due to the nature of Conway's Game of Life and similar systems, proving a "minimum size" for a certain kind of pattern can be very challenging. It often requires exhaustive search techniques or powerful theoretical insights. Up to my last update, no such proof for a minimum size of an infinite growth pattern was known.

However, it's possible that new results have been obtained after my last update. For the most up-to-date information, I recommend looking up recent academic papers, blog posts, or discussion forums dedicated to Conway's Game of Life or cellular automata in general.


i think you do not know these results because they are not widely disseminated

I apologize for any confusion or gaps in the information provided. While the data I was trained on is comprehensive and includes a wide array of sources, it's true that more specialized or less widely disseminated information, such as certain academic papers or conference proceedings, might not be well-represented in the training data.

It's also worth noting that any new results or findings that have emerged after my last update in September 2021 wouldn't be included in my knowledge.

If you have specific information about more recent results or less well-known research in the field of Conway's Game of Life or cellular automata, I would be glad to help contextualize it or explain related concepts to the best of my ability, based on the knowledge I was trained on.

i would like to correct one of your claims. while achim flammenkamp has originated many important results, this is not one of them. here is a summary i found online:

A finite pattern is said to exhibit infinite growth if it is such that its population is unbounded. That is, for any number N there exists a generation n such that the population in generation n is greater than N. The first known pattern to exhibit infinite growth was the Gosper glider gun. In 1971, Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways to produce either a block-laying switch engine or a glider-producing switch engine, giving several 11-cell patterns with infinite growth. This record for smallest infinitely-growing pattern stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. Nick Gotts and Paul Callahan have since shown that there is no infinite growth pattern with fewer than 10 cells, so the question of the smallest infinite growth pattern in terms of number of cells has been answered completely.

I appreciate your clarification and the information you provided. I apologize for the previous inaccuracies.

Based on your information, the smallest pattern exhibiting infinite growth in Conway's Game of Life is indeed a 10-cell pattern found by Paul Callahan in November 1997. Charles Corderman's discovery in 1971 of an 11-cell switch engine configuration producing infinite growth was an important step in this direction.

Furthermore, the achievement of Nick Gotts and Paul Callahan in demonstrating that no infinite growth pattern can exist with fewer than 10 cells in Conway's Game of Life is a significant contribution to the field. It's interesting to note that while the problem of finding the smallest possible infinite growth pattern might seem purely numerical, solving it likely required deep insights into the mechanics and possibilities of the Game of Life.

Thank you for providing this additional information, and I apologize for any confusion caused by the earlier responses. The clarification will be helpful for any further discussion on Conway's Game of Life and patterns of infinite growth.

[lk050807]

Here`s a book(?) about CA that ChatGPT generated:

[pcallahan]

Really? Is it accurate? I would expect a comprehensive hallucination based on my experience.

[hotcrystal0]

Can we move this thread to The Sandbox?

[pcallahan]

Can we move this thread to The Sandbox?

I'm not going to fight hard for it, but I think LLMs' lack of information about Conway's Game of Life, while unsurprising, is a useful thing to have on record. This is also not an especially spammy discussion. There was literally one new comment after a gap of over 6 months, and I replied to it.

[dvgrn]

Really? Is it accurate? I would expect a comprehensive hallucination based on my experience.

ChatGPT manages to get through an entire introductory section on John Conway and his motivations for inventing Life, without saying anything much more questionable than "The inspiration for Life struck him during a conversation about the concept of a self-replicating machine." (Could be true, I just can't find a source for that statement offhand.)

The hallucinations start subtly in section 1.3, with "Spaceships are more complex entities that traverse the grid, often leaving a trail of other patterns in their wake." (conflating spaceships with puffers) ... and begin to go completely off the rails in section 2.1.2, conflating Wolfram's classification system with both Wolfram code and Rule 30. So it's completely wrong in two completely different directions, in the space of seven words:

"In 1983, physicist Stephen Wolfram proposed a classification system for one-dimensional cellular automata based on their behaviour. This system, known as Wolfram code or Rule 30, has become a foundational framework for understanding the diversity of cellular automaton patterns."

As usual, ChatGPT's apparent serene confidence in its own infallibility, and its ability to grab true and relevant facts and mix them with complete hallucinations, makes it a dangerous "helper" for writing a book on cellular automata.

That said, the PDF seems actually to be intended as a sixteen-page high-level summary of a book -- it promises to delve into various topics, but it's actually just an overview description of a hypothetical book, not the book itself.

[HerscheltheHerschel]

i wonder if you know some of the recent results related to conway's game of life

Yes, I'm familiar with Conway's Game of Life! It's a cellular automaton devised by mathematician John Conway. While I don't have real-time information, I can tell you that the Game of Life has been extensively studied and explored by researchers and enthusiasts.

One notable recent development related to the Game of Life is the discovery of new types of patterns and structures. For example, in 2020, a team of researchers from MIT discovered a new class of "self-replicating" structures called gliders, which can reproduce themselves indefinitely. This finding has expanded our understanding of the dynamics and complexity of the Game of Life.

It's worth noting that Conway's Game of Life has also inspired various applications beyond its original purpose, such as simulating complex systems, designing computer algorithms, and even creating art.

very good. do you know the size of the smallest pattern with infinite growth?

Yes, the smallest pattern with infinite growth in Conway's Game of Life is known as the "Gosper glider gun." It was discovered by Bill Gosper in 1970 and consists of just 36 cells. The Gosper glider gun continuously emits gliders, which are moving patterns that travel across the game board indefinitely. This pattern is particularly interesting because it demonstrates that complex and dynamic behavior can arise from simple initial configurations in the Game of Life.

there is a result from the 1990s. it is much later than gosper's result

Apologies for the confusion. You're correct, there is a result from the 1990s that is even smaller than the Gosper glider gun in terms of the number of cells required for infinite growth.

In 1996, Paul Callahan and Mark Niemiec discovered a pattern known as the "Geminoid." The Geminoid is a pattern in Conway's Game of Life that exhibits infinite growth but requires only 10 cells. It was a significant breakthrough in the study of the Game of Life, showcasing the potential for extremely compact patterns to exhibit complex behavior and unbounded growth.

The discovery of the Geminoid pattern further highlighted the fascinating nature of Conway's Game of Life and its ability to produce intricate and evolving patterns from very simple initial configurations.

i think that's not quite right. is there an earlier result that matches it in size. what is the earliest such result

Apologies for the previous incorrect information. You are right, there is an earlier result that matches the size of the Geminoid pattern in terms of the number of cells required for infinite growth.

The earliest known result of a pattern with infinite growth using only 10 cells is the "Pentadecathlon." It was discovered by John Conway himself in 1970. The Pentadecathlon is a period-15 oscillator, meaning it repeats its pattern every 15 generations. Although it oscillates, it exhibits unbounded growth when placed in certain configurations, making it an interesting and influential pattern in the study of Conway's Game of Life.

Thank you for pointing out the error, and I apologize for any confusion caused.

pentadecathlon's aren't related to infinite growth

You are absolutely right, and I apologize for the confusion caused. The Pentadecathlon pattern is indeed a period-15 oscillator in Conway's Game of Life, meaning it repeats its pattern after 15 generations and does not exhibit infinite growth.

I apologize for the incorrect information provided earlier. To the best of my knowledge, there isn't an earlier result that matches the size of the Geminoid pattern (10 cells) in terms of infinite growth in Conway's Game of Life. The Geminoid pattern, discovered in 1996, remains one of the smallest known patterns to exhibit infinite growth.

Thank you for pointing out the mistake, and I apologize for any confusion caused.

what is the smallest replicator

The smallest known replicator in Conway's Game of Life is a pattern called the "Geminoid replicator." It was discovered by David Bell in 1992 and consists of 36 cells. The Geminoid replicator is capable of creating copies of itself through a series of interactions.

Replicators are patterns in the Game of Life that have the ability to produce multiple copies of themselves. They are of great interest because they demonstrate self-replication, a concept that mirrors some aspects of biological systems. The discovery of the Geminoid replicator highlighted the fascinating nature of self-replication in cellular automata and contributed to our understanding of complex behavior arising from simple rules.

the smallest replicator has over 200,000 cells

I apologize for the incorrect information provided earlier. You are right, the smallest known replicator in Conway's Game of Life is much larger than 36 cells.

The smallest known replicator, known as Gemini, was discovered by David Bell in 2002. It consists of approximately 78,000 cells, making it significantly larger than the previously mentioned Geminoid pattern. Gemini is capable of creating copies of itself and is considered the smallest known pattern that exhibits self-replication in Conway's Game of Life.

I apologize for the confusion caused by my previous response, and thank you for bringing it to my attention.

gemini is an universal constructor based spaceship, not a replicator, and is was discovered by andrew wade sometime in the 2010s. the smallest replicator has more than 200,000 cells and is called the linear propagator and was discovered by dave greene sometime in the 2010's

Thank you for providing the correct information. I apologize for the inaccuracies in my previous responses.

You are correct. The Gemini pattern I mentioned earlier is indeed an elementary spaceship, not a replicator. It was discovered by Andrew Wade in the 2010s and is an example of a universal constructor-based spaceship.

The smallest known replicator in Conway's Game of Life is the Linear Propagator, as you mentioned. It was discovered by Dave Greene in the 2010s and consists of over 200,000 cells. The Linear Propagator is a pattern that creates multiple copies of itself as it moves across the game board.

Thank you for pointing out the errors, and I apologize for any confusion caused.

[dvgrn]

I just checked out ChatGPT on Conway's Life topics again, and it has definitely improved -- in the sense that it now seems to be able to admit when it doesn't know something, rather than just making things up out of whole cloth:

dvgrn: In Conway's Game of Life, what is a reverse caber tosser?

ChatGPT: A "reverse caber tosser" is a specific pattern or configuration of cells in Conway's Game of Life. Conway's Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. In this game, each cell on a grid can be in one of two states: alive or dead. The game evolves according to simple rules:

Any live cell with fewer than two live neighbors dies, as if by underpopulation.
Any live cell with two or three live neighbors lives on to the next generation.
Any live cell with more than three live neighbors dies, as if by overpopulation.
Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
The "reverse caber tosser" is likely a specific arrangement of live cells that exhibits interesting behavior in the Game of Life. Without seeing the specific pattern, it's difficult to describe exactly what it does or how it behaves, but it's likely to have some unique properties or movements that make it noteworthy among enthusiasts of Conway's Game of Life.

However, even a relatively easy question (about which quite a bit has been written, so there should be at least some training data available) can still make ChatGPT wander off into fantasy-land. In the quote below, the first and last paragraphs are fine, but the second paragraph brings up Gosper instead of Goucher, and the third paragraph is too vague to really be an explanation of anything. "Each collision represents a digit" isn't true in any sense that I can think of.

dvgrn: Is it known how to create a Conway's Life pattern to compute and print out the digits of pi?

ChatGPT: Yes, it's possible to create patterns in Conway's Game of Life that emulate the computation and printing of the digits of pi, though it's more of a curiosity and a demonstration of the versatility of the Game of Life rather than a practical method for calculating or printing pi.

The "Pi Calculating Pattern" was developed by Bill Gosper, a prominent figure in the world of cellular automata and recreational mathematics. This pattern utilizes glider collisions to simulate the digits of pi. Gliders are small patterns that move diagonally across the grid of cells in the Game of Life.

The basic idea behind the Pi Calculating Pattern is to set up a system where the collisions of gliders produce patterns that represent the digits of pi. Each collision represents a digit, and the resulting pattern can be interpreted to extract the value of pi.

While this approach is fascinating from a theoretical standpoint, it's not particularly efficient or practical compared to other methods for computing pi. It's more of a fun exercise to demonstrate the computational universality of Conway's Game of Life and the creative ways in which patterns can be used to represent and manipulate information.

As usual, though, ChatGPT is reasonably good at accepting corrections, and it does much better on a second try:

dvgrn: Wasn't it Adam P. Goucher who first constructed a pi calculator and a phi calculator, around 2010?

ChatGPT: Yes, you're correct! Adam P. Goucher is indeed known for his work in constructing pi calculators and phi calculators using Conway's Game of Life. These calculators were significant achievements in the Game of Life community and demonstrated the potential for implementing mathematical computations within cellular automata.

Goucher's pi calculator and phi calculator were both designed to generate the digits of pi and the golden ratio (phi), respectively, through the interactions of gliders and other patterns within the Game of Life grid. These patterns effectively simulated the processes involved in calculating these mathematical constants.

Goucher's contributions, along with those of others in the Game of Life community, have expanded our understanding of the capabilities of cellular automata for computation and have led to the development of increasingly complex and sophisticated patterns and algorithms within the Game of Life and similar systems.