For general discussion about Conway's Game of Life.
Sokwe
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I read sections 3.1 through 3.4. Here are my some corrections (some may have already been mentioned and corrected earlier in this thread). Line numbers do not include section headings, figure captions, or footnotes. Negative line numbers mean they are counted from the bottom of the page.

Corrections:
• Page 51 Figure 3.1 (a): Barberpoles (and thus bipole) were found by the M.I.T. group, according to Martin Gardner's Feb 1971 Mathematical Games column dvgrn 10/4: fixed
• Page 53 Line 13: "combinations and known objects" is possibly intended to be "combinations of known objects". Check the wording carefully, as I'm not entirely sure. dvgrn 10/4: yup, pretty sure that's just a typo -- fixed
• Page 54 Figure 3.7 (b): Roteightor RLE does not match image (wrong phase)
• Page 57 Line -1: Remove 96 from and add 93 to the list of oscillators that use caterer dvgrn 10/4: already fixed
• Page 58 Figure 3.15: The caterer on rattlesnake is not a combination of a finger and dot spark. In fact, finger sparks cannot typically interact with dot sparks as claimed. dvgrn 10/4: not sure I've fixed this completely -- here's what I tried: Finger sparks can be combined with either dot spark predecessors (as in (b)) or standard domino sparks (as in (c)), but thumb sparks are best paired with domino sparks (as in (a))
• Page 59 Line 17: "arrangements of small still lifes" -> "arrangements of still lifes and sparkers" dvgrn 10/4: fixed
• Page 59 Line -11: "as this twin" -> "as the twin" dvgrn 10/4: already fixed
• Page 61 Line 1: "dot sparker known whose spark" -> "dot sparker whose spark" dvgrn 10/4: fixed
• Page 61 Figure 3.23 (b): p24 T-tetromino hassler RLE does not match image (wrong phase) dvgrn 10/4: fixed
• Page 61 Line 14: The p4 sparker used in the p24 shuttle was not seen earlier, as claimed. dvgrn 10/4: added clarifying footnote
• Page 62 Figure 3.26: The tub-stabilized form of Eureka was not the first known pre-pulsar shuttle (see Lifeline vol. 11 pgs. 16-17) dvgrn 10/4: fixed
• Page 234 Line 1: "high period-guns" -> "high-period guns" dvgrn 10/4: fixed
• various locations: There are a few cases where "period-[n]" is written (where [n] is some specific number), when the standard in the text appears to be "period [n]". just search "period-" to find them. dvgrn 10/4: fixed in chapters 3, 5, 6, 7, 8
The following are comments and recommendations that don't necessarily require any changes:
• Page 53 Figure 3.5: Maybe add note about discoverer (Bill Gosper, Sep 1971) dvgrn 10/4: added
• Page 54 Line -2: Remove "simply", as it's redundant dvgrn 10/4: fixed
• Page 59 Figure 3.18: Remove "(with improvements to decrease their size by Matthias Merzenich)", as it's unnecessary detail and the improvements were essentially trivial dvgrn 10/4: removed
• Page 60-61 Figures 3.21, 3.22: The reactions described as pushing a T-tetromino "left by 2 cells and mirroring it", but this reaction is typically considered a "left by 3 cells" push. This could maybe be reworded, although it's not essential. dvgrn 10/4: added another clause
The following are RLEs that don't precisely match their respective images (typically due to, e.g., rotation or reflection), but correction isn't strictly necessary:
• Page 54 Figure 3.7 (e) Dinner table RLE does not match image (rotated 90 degrees) dvgrn 10/4: fixed
• Page 54 Figure 3.7 (e) Honey thieves RLE does not match image (flipped across diagonal axis) dvgrn 10/4: fixed
• Page 54 Figure 3.7 (i) No-name p36 RLE does not match image (flipped across diagonal axis) dvgrn 10/4: fixed
• Page 54 Figure 3.8 (a) No-name p6 RLE does not match image (flipped across horizontal axis) dvgrn 10/4: fixed
• Page 57 Figure 3.13 (h) Rattlesnake RLE does not match image (rotated 90 degrees) dvgrn 10/4: fixed
• Page 58 Figure 3.14 (a) Caterer RLE does not match image (rotated 90 degrees) dvgrn 10/4: fixed
• Page 58 Figure 3.14 (b) T-nosed p4 RLE does not match image (rotated 90 degrees) dvgrn 10/4: fixed
• Page 58 Figure 3.15 (a) p4 thumb on fumarole RLE does not match image (rotated 90 degrees) dvgrn 10/4: fixed
• Page 58 Figure 3.15 (a) p4 thumb on fumarole RLE does not match image (rotated 90 degrees) dvgrn 10/4: duplicate
• Page 58 Figure 3.17 The order of reflection reactions in RLE does not match image (duoplet should be on the left and banana on the right) dvgrn 10/4: fixed
• Page 59 Figure 3.18 Honey farm hassler collection RLE is out-of-date (see https://conwaylife.com/wiki/Honey_farm_hassler) [NJ Oct. 8: Fixed.]
• Page 60 Figure 3.19 (a) Gourmet RLE does not match image (rotated 180 degrees) dvgrn 10/4: fixed
• Page 61 Figure 3.26 Pre-pulsar shuttle collection RLE is out-of-date (see https://conwaylife.com/wiki/Pre-pulsar_shuttle) [NJ Oct. 8: Fixed.]
Also, some of the wiki links on the pattern files pages need to have "index.php?title=" removed. For example, the wiki link for the quad pseudo still life on this page. [NJ Oct. 7: Fixed.]

10/8 All reports in this post have been addressed.
-Matthias Merzenich

pew
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Joined: May 8th, 2020, 7:58 pm

As a casual hobbyist who is interested but not invested, how comprehensive is this? I would love to learn more about constructions, macropatterns, etc.

The book looks amazing btw.

Rocknlol
Posts: 119
Joined: April 15th, 2012, 9:06 am

Overall this has been a really enjoyable read! A few nits/questions so far:
• Page 5: Not sure how accurate using "isotropic rules" is here since Life-like rules are isotropic as well—maybe specify that these sorts of rules are "nontotalistic" here? dvgrn 10/4: added indexed reference to "INT rules"
• Page 14: I might add a caveat here about the Pufferfish, since it's a non-switch-engine-based puffer found in a symmetric soup dvgrn 10/4: leaving this on the grounds that symmetric soups are not "randomly filling some portion of the Life plane"
• Page 16: The mention of the longest-lasting 10-cell mesuthelah being found in 2019 feels a bit disconnected from the rest of the sentence since there's no immediate connection between "what is the longest lasting 10-cell pattern is an open question" and "the longest lasting known 10-cell pattern was found in 2019"—wondering if it'd be clearer to explicitly say something along the lines of "people are still pushing the bounds of how long >9-cell mesuthelahs can last"? dvgrn 10/4: added a clause to clarify relevance.
• Page 22: Is there a reason why Figure 1.36(b) is referred to as an "orphan" while the other two patterns in the section are referred to as Gardens of Eden? dvgrn 10/4: see definition of "orphan" on previous page
• Page 37: Has the proof for no 2/3-cell width Gardens of Eden ever been published? I can't seem to find it myself dvgrn 10/4: answered below
• Overall question on 2.1 (since I don't actually know the answer here); do pseudo-still lives require overpopulation for any reason? If pseudo-still lives were redefined to include quasi-still lives, what would that impact besides pseudo-still life enumeration? dvgrn 10/4: "pseudo" does require overpopulation, just by the definition of "pseudo": " Furthermore, there must be at least one dead cell that has more than three alive neighbours in the overall pattern but has less than three alive neighbours in the subpatterns." Dropping the distinction between "pseudo" and "quasi" would -- specifically in the case of B3/S23 -- remove a useful distinction, since quasi still lifes are in general much easier to make glider constructions for than pseudo still lifes -- so much so that the quasi still lifes are not nearly as interesting to work on syntheses for, so they mostly get ignored on the assumption that they're trivial to solve. That isn't necessarily true for all sizes of still lifes making up a quasi constellation -- just the ones for which "edgy" syntheses are known. It might be tricky to build some of the many pairs of shuriken in quasi position, for example.
• Page 79: This may be a bit too pedantic, but I'm wondering if a better way to define the speed of light would be the velocity that information itself can travel on the Life grid, rather than the speed limit of objects, considering that spaceships (in a vacuum, anyway) have a sub-c limit dvgrn 10/4: read through this, but didn't see an easy change that seemed like an improvement. It's definitely true that the speed of light is really more relevant to the speed of information transfer, and is not closely related to the speed of "objects", since the top speed of moving objects in a vacuum (in this particular B3/S23 rule) are much slower.
10/3 All reports in this post have been addressed.

Sokwe
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Rocknlol wrote:
September 27th, 2021, 2:22 am
Has the proof for no 2/3-cell width Gardens of Eden ever been published? I can't seem to find it myself
Not to my knowledge. All I know about it is what's written on Achim Flammenkamp's Garden of Eden page
Achim wrote:In 2016 Steven Eker pointed out, that Jean Hardouin-Duparc only proved that height 1 is impossible and unsuccessfully searched for Garden of Eden pattern up to height 5. All these early found objects were constructed from strips of fixed width which were extended until the new object has no predecessor. In April 2016 Steven Eker, working at SRI International, California, USA, communicated me in a private email that he has extended Jean's automaton/grammar based proof and was able to prove with more sophisticated techniques the non-existence of Garden of Eden pattern of height 2 and height 3. With up-to-date hardware he was still unable to decide the case of height 4 due to the enormous state space of this tree-search.
You would likely need to contact Steven Eker for the details.
-Matthias Merzenich

MathAndCode
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Page 43 has the sentence, "To see why this claim is true, notice that the middle-right live cell in the red configuration already has 3 live neighbors, so the 3 cells to its immediate right must be dead so as to avoid a birth—in other words, this cell is the central cell in the yellow configuration." It seems to me that this refers to the central cell in the yellow square, so instead of avoid a birth, the sentence should say something like avoid death from overpopulation. dvgrn 27 Sep: fixed.

10/3 All reports in this post have been addressed.

Hdjensofjfnen
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Location: r cis θ

Some corrections:

p171 ex 6.32 - typo: “pseudo-random” instead of “pseuro-random” dvgrn 30 Sep: fixed.
p177 fig 7.4 - typo: “its” instead of “it” dvgrn 30 Sep: fixed.
p205 ex 7.35 lacks a solution [NJ Oct. 8: Fixed.]
p205 ex 7.37 - never heard the oscillator called “Wainwright’s p72”, nor is there a redirect for that name on LifeWiki dvgrn 30 Sep: there is now!

p437 soln 7.14c dangles [NJ Oct. 8: I believe that this fixed itself as the book's layout changed as a result of other changes. Please bring this issue up again if it is not yet fixed.]
p437 soln 7.18c 3 - 3 is not congruent to 3 (mod8) dvgrn 30 Sep: fixed.
p438 soln 7.25 is incomplete. Should say, “As the conduit name suggests that the Herschel is turned 180 degrees in 60 generations, a closed loop should have a period of 120 generations.” dvgrn 30 Sep: fixed.

10/8 All reports in this post have been addressed.

Code: Select all

x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo! Code: Select all x = 7, y = 5, rule = B3/S2-i3-y4i 4b3o$6bo$o3b3o$2o$bo!  Chris857 Posts: 13 Joined: June 10th, 2020, 11:26 pm ### Re: Beta Reader Thread for Game of Life Textbook "We can thus encode a a huge variety of unsolved mathematical and computational problem into Life patterns..." - There is a repeated "a a", and "problem" should be "problems". dvgrn 9/30/2021: checked in fix. "and the fact that it has the same period (46) as this twin bees shuttle." - Should "this" be "the"? dvgrn 9/30/2021: checked in fix. "In particular, the period 24 oscillator in Figure 3.23(b) uses a figure eights and..." - "eights" should "eight" (there's only 1 figure eight in the oscillator) dvgrn 9/30/2021: checked in fix. "simply by placing multiple gliders in loop at whatever spacing we like." - should "in loop" be "in a loop" or "in the loop"? dvgrn 9/30/2021: checked in fix. Edit: 2nd, 3rd, 4th suggestion "No object, whether in a vacuum or not, cannot possibly..." - This reduces to "No object cannot possibly", which seems to have too many negatives. Maybe change "cannot" to "can", or "No" to "Any"? dvgrn 10/3/2021: checked in fix. Section 4.6.1 Spaceship Speeds "Figure 4.47 provides a collection of the smallest known orthogonal spaceships (in terms of number of alive cells)" (emphasis mine) - However, Figure 4.47 shows Spaghetti Monster for 3c/7, when the smallest 3c/7 is Soba. (as a note, spaghetti monster is also referenced in table 4.1 and in the index at the end) dvgrn 10/3/2021: checked in fix. "...it can be quite difficult to coordinate them so that they all arise at the desired time." - should "arise" be "arrive"? dvgrn 10/3/2021: checked in fix. "Rich’s p16 (plus a lot of extra debris) is forms when..." - either remove "is" or change "forms" to "formed" dvgrn 10/3/2021: checked in fix. Edit: 5th, 6th, 7th, 8th suggestion 10/3 All reports in this post have been addressed. AlephAlpha Posts: 52 Joined: October 6th, 2017, 1:50 am ### Re: Beta Reader Thread for Game of Life Textbook It seems that the proof of Theorem 1.2 (No Thin Gardens of Eden) on page 22 is incomplete. The last sentence of the proof says that: moving the alive cell from A to Y does not affect the evolution of any of the other 3×3 blocks to its right (which can be done via a simple case analysis). But there is one case that such move will affect the evolution of the block to its right: when the middle cell of the 3×3 block is followed by a domino, i.e. when there is bob2ob. For example, if we try to construct a parent for the following pattern: Code: Select all x = 7, y = 1, rule = B3/S23 ob2ob2o!  The construction in the proof gives: Code: Select all x = 15, y = 9, rule = B3/S23 ob2ob2ob2ob2obo$b13o$15o$4obo2bo2b4o$b2obob2ob2ob2o$4o2bobo2b4o$15o$b
13o$ob2ob2ob2ob2obo!  But the child of this "parent" is actually: Code: Select all x = 7, y = 1, rule = B3/S23 obo2b2o!  The problem is caused by the alive cell to the bottom right of the domino. To fix the problem, we need to move this cell to its right. If the domino is followed by another domino, we also need to move the bottom right cell of that domino. Like this: Code: Select all x = 15, y = 9, rule = B3/S23 ob2ob2ob2ob2obo$b13o$15o$4obo2bo2b4o$b2obob2ob2ob2o$4o2bo2bo2b3o$15o$b
13o$ob2ob2ob2ob2obo!  I'm not sure if there are other problems. [NJ Oct. 6: Great catch! I have patched up the proof.] 10/8 All reports in this post have been addressed. dvgrn Moderator Posts: 8275 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: ### Re: Beta Reader Thread for Game of Life Textbook A new build of the textbook PDF is available. Nathaniel is aiming to do a rebuild every Friday. Typo reports in the forum thread that are marked (by colored edit, with a date before 10/1) as being fixed, could now be reviewed. We're still working on the rest of the reported items. Chris857 Posts: 13 Joined: June 10th, 2020, 11:26 pm ### Re: Beta Reader Thread for Game of Life Textbook Some more: ISSUE 1 "For example, the conduit in Figure 7.5(a) is called NE5T-4 (to be clear, the dash in this name is a minus sign, not a separator—the timing of the output glider is −4) and the ones in Figures 7.5(b) and 7.5(c) are both called NW31T120.7 The first and second natural gliders (i.e., the southwest and northwest gliders in Figure 7.5(c)) are not included in the name of a Herschel-to-glider conduit unless they are its only output." - This section confused me. In particular, figure 7.5(c) is said to be NW31T120, i.e. it emits a NW glider. But the sentence right after says that the NW (and SW) gliders are not included in the name unless they are the only output, but this conduit has a SE output glider, so it seems like the NW glider shouldn't be in the name? https://conwaylife.com/ref/lexicon/lex_n.htm agrees that this conduit is NW31T120, but it seems like the name should be SE..something.. based on the description, unless I'm misunderstanding something. dvgrn 10/3: added some clarification about SE7T14 output ISSUE 2 Figure 7.8(a) - The position of the input glider in the image and the RLE are slightly different (RLE is 4 gen further out). Figure 7.8(b) has matching image and RLE. dvgrn 10/3: changed pattern to match image ISSUE 3 "we can create conduits **[THAT]** take a single glider as input" - The word "that" is missing. dvgrn 10/3: fixed ISSUE 4 Figure 7.23 does it matter that the RLE has different orientation than image? dvgrn 10/3: changed RLE to match image ISSUE 5 "if the output block is already present, it is temporary destroyed" - Change "temporary" to "temporarily" dvgrn 10/3: fixed ISSUE 6 "By combining these two period-multiplying reactions together, we can multiply a gun’s period by any number whose prime factorization contains only 2 or 3, with at least one factor of 2. We can thus use this technique to thin out a glider stream by a factor of 4, 6, 8, or 9, for example." - But 9 doesn't have a factor of 2? Why is "at least one factor of 2" mentioned, if 9 is listed? dvgrn 10/3: technical reasons: the tripling reaction contains a p2 blinker, so it only works to double even-period streams. Added a sentence to (hopefully) clarify this. ISSUE 7 "The reason that these conduits are useful is that they can act as logic circuits that test whether or not a a signal" - repeated "a a" dvgrn 10/3: already fixed 10/3 All reports in this post have been addressed. Nathaniel Site Admin Posts: 770 Joined: December 10th, 2008, 3:48 pm Location: New Brunswick, Canada Contact: ### Re: Beta Reader Thread for Game of Life Textbook Thanks for the corrections, everyone! A newly-compiled version of the book is now up. It contains all fixed that are dated October 8 or earlier. Macbi Posts: 818 Joined: March 29th, 2009, 4:58 am ### Re: Beta Reader Thread for Game of Life Textbook p37: making it the fastest-recovering known glider eater This is known to be the fastest possible. dvgrn 10/15: adjusted wording to mention the computer-search proofs. p121: In fact, syntheses are known for all 78 297 strict still lifes with 19 or fewer live cells. Yes, but you probably want to update this to the 20 cell figure. dvgrn 10/15: Done. Quick, somebody finish the last 408 21-cell still lifes so we have to change this again! p239: In this section, we are discussing the growth rate of the population of a pattern, which can be made arbitrarily slow. I'm being pedantic, but this isn't quite true since you can't grow uncomputably slowly. dvgrn 10/15: responded below, haven't changed anything yet p361: Shouldn't the minute hand on the clock be at (2^36)%60, which is 16? NJ 10/15: yep, I've changed this. However, there are probably a boatload of these that are wrong in the book, and I doubt that I'll correct them all. When the number of generations is a small, explicit number (like in most figures early in the book), the clock arrows are automatically computed. However, for large times like "2^36", the macro isn't smart enough to figure out what that means, so I just told it to point there arrows anywhere, thinking that no one would notice/care. Looks like you noticed p361: t travels in much the same way as a glider, but 2^36 times as slowly. If it goes 2^18 cells every 2^36 generations, doesn't it actually go only 2^18 times as slowly? dvgrn 10/15: depends on your definition of "slowly", but you're basically right so I've added a clause about the step size increasing. p371: Weird indentation. dvgrn 10/15: This is vaguely tolerable -- the indentation is the continuation of a bullet point in a paragraph on the previous page. 10/15: All reports in this post have been addressed. Sokwe Moderator Posts: 2034 Joined: July 9th, 2009, 2:44 pm ### Re: Beta Reader Thread for Game of Life Textbook • The pdf bookmark for Appendix A.3 does not include the$\Theta$. It should be solvable by replacing line 78 of appendix_math.tex with the following: Code: Select all \section{Big-\texorpdfstring{$\Theta$}{\unichar{"0398}} Notation}\label{sec:bigO} While there are other Unicode thetas, U+0398 is the earliest, so it should work with the widest range of PDF viewers. dvgrn 10/15: checked in for today's compile NJ 10/15: I ran into some encoding issues when trying to compile, so I changed it so that it displays the Theta symbol in the section title, but the word "Theta" (not the symbol) in the bookmark. • Do you prefer "Pi" or "$\pi$" in the name of Appendix B.8? It's currently "Pi". I'm not recommending a change, but just mentioning it as a possibility. I think it's generally preferable to avoid math in section titles, but using "$\pi\$" might be helpful in differentiating the numerical constant from the pi-heptomino. If you were to change it, you should use the same trick as in Appendix A.3 to get a Unicode pi (U+03C0) in the bookmarks. NJ 10/15: I did this, since we do indeed refer to the mathematical constant via the Greek symbol, not "pi" throughout the rest of the book.
• Not essential, but in the comment on line 18 of main.tex I think you should replace "real names" with "preferred names". It may be the case that someone's preferred name for credits doesn't match their forum handle or their "real" name. NJ 10/15: Changed this. dvgrn 10/15: Hang on, I thought _I_ did this. Anyway, it's changed.
10/15: All items in this post have been addressed.
-Matthias Merzenich

dvgrn
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Macbi wrote:
October 11th, 2021, 6:52 am
p239:
In this section, we are discussing the growth rate of the population of a pattern, which can be made arbitrarily slow.
I'm being pedantic, but this isn't quite true since you can't grow uncomputably slowly.
Pedantic-ish-ness is perfectly welcome, but I'm not going to change this unless I can think of something to change it to. Is "grow uncomputably slowly" really a phrase that means anything that's relevant here?

I think of "arbitrarily slow" as being relatively clear -- meaning, "if it's not slow enough for you, you can make it slower", or "Name any specific speed, and you can make a pattern whose population grows slower than that speed."

Macbi
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Joined: March 29th, 2009, 4:58 am

dvgrn wrote:
October 15th, 2021, 10:34 am
Pedantic-ish-ness is perfectly welcome, but I'm not going to change this unless I can think of something to change it to. Is "grow uncomputably slowly" really a phrase that means anything that's relevant here?
Yeah, I couldn't think of a better wording either. Don't worry about it.
"Name any specific speed, and you can make a pattern whose population grows slower than that speed."
That's what's not true. For example let f(n) be the least m such that BusyBeaver(m) > n. Then there's no pattern and C > 0 such that the pattern's population gets arbitrarily large but is always less than Cf(n).

dvgrn
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Macbi wrote:
October 15th, 2021, 11:03 am
"Name any specific speed, and you can make a pattern whose population grows slower than that speed."
That's what's not true. For example let f(n) be the least m such that BusyBeaver(m) > n. Then there's no pattern and C > 0 such that the pattern's population gets arbitrarily large but is always less than Cf(n).
See, I tried adding the word "specific" so you wouldn't go defining Busy Beaver functions on me. In my simple-minded world, you haven't named a specific speed unless you've chosen a value of n.

Nathaniel
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