Talk:Garden of Eden

Theorem

The last sentence in the section contradicts everything else, unless I'm mistaken: "However, surjective cellular automata do not need to be injective." implies that {surjective} > {injective} (and {injective} is contained by {surjective}), while previously it says stuff like "the class of surjective cellular automata and those which are injective over finite configurations coincide." which implies {surjective} = {injective}, which is further supported by "In other words, a cellular automaton has a Garden of Eden if and only if it has two different finite configurations that evolve into the same configuration in one step." and stuff. Although even if that last statement is right,the theorem still proves that Life has Gardens of Eden, so I'm not really sure whether it is or not. Elithrion 18:35, 14 February 2009 (UTC)

The important distinction is between simply injective and injective over finite patterns. The theorem says that injective over finite patterns iff surjective. Thus, surjective implies injective over finite patterns, but not injective overall (that is, there may be two *infinite* patterns that are mapped to by the same infinite pattern). This could perhaps be made more clear in the article. Anyway, yes, the "picture" is {surjective} = {injective over finite patterns} > {injective}. Nathaniel 19:07, 14 February 2009 (UTC)

Ah, thanks. I guess I overlooked that distinction. Elithrion 20:42, 14 February 2009 (UTC)

I managed to find a paper documenting the Garden of Eden theorem: [[1]]. (Mutually erasable is equivalent to being finitely non-injective.) Now that I understand the situation better, I'll try to detail a proof that finitely non-injective implies non-surjective, due to a proof in Conway's Winning Ways. FractalFusion 08:23, 25 March 2009 (UTC)

Records

What do you think about insertion of following-like table? --Mtve (talk) 10:20, 7 April 2016 (UTC)

(The table has been moved to main page)--Mtve (talk) 07:26, 23 April 2016 (UTC)

Hello, Mtve. I would just insert it into the article without attempting to discuss it. From my experience, nobody bothers to discuss anything anymore on this wiki. Posting it on talk pages only increases the chance that the information will never make it to the main page.

I would avoid using things like "C2dia" and "D4" as symmetries, because those labels might be ambiguous. FractalFusion (talk) 18:22, 8 April 2016 (UTC)

Thanks for the feedback, FractalFusion! I'm going to improve links and references and then move it to the main page as you've suggested. Meanwhile, Steven Eker has made another breakthru! --Mtve (talk) 16:31, 10 April 2016 (UTC)

Well, FractalFusion, I personally don't think you give good advice to Mtve, especially having in mind your recent careless renaming of Triple pseudo still life and Quad pseudo still life without discussion. Mtve, your table is great, but if you could provide references, it would be perfect. Codeholic (talk) 06:32, 20 April 2016 (UTC)

Thanks! Links added. Please help with wording to start the paragraph about records, I really can not write anything readable. Mtve (talk) 18:38, 20 April 2016 (UTC)

Wikipedia

Would link to the Wikipedia [[2]] be appropriate here?

It discusses more then only Game of Life, but has some interesting topics covered, also in Talk page --Mtve (talk) 16:16, 12 July 2016 (UTC)

I'd say having that link would be great. Apple Bottom (talk) 18:17, 12 July 2016 (UTC)

Merging all GoE examples into this article?

User:AwesoMan3000 has proposed on every GoE page that "pretty much none of these are extremely notable on their own, and would probably be better off merged into the main article". The broken templates with multiple parameters and the long red links are quite annoying, but it's not polite to solve the problem immediately by removing them as well.

Compared with the case of pure glider generator, a completely obsolete subject, Gardens of Eden are still partly of modern interest and it is encouraged to discover record-breaking GoEs. Yet both are lack of applications to some degree, and there isn't much to write about for each individual example other than the discovery information.

What do you think? GUYTU6J (talk) 10:28, 21 July 2020 (UTC)

Looking at the issue again, I suppose a new design of the table that could possibly replace the individual articles:

Year	Author	Bounding box width × height	Orphan	Population	Density	Symmetry	Pattern	Note
1971	Roger Banks et al.	33 × 9 = 297	size = 297	226	0.7609	C1	x = 33, y = 9, rule = B3/S23 33o$2obob3ob3ob2obobobobobobobobobo$obob3ob3ob4ob3obobobobobobo$5ob3ob 3ob4ob14o$obob2ob3ob3obob3obobobobobobo$4ob3ob3ob5ob2obobobobobobo$b2o b3ob3ob3obobob13o$2ob2ob3ob3ob2ob4obobobobobobo$18ob14o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 1, which is still a Garden of Eden even after removing the five rightmost columns
1973	Jean Hardouin-Duparc	122 × 6 = 732	size = 732	576	0.7869	-	-
1973	Jean Hardouin-Duparc	117 × 6 = 702	-	-	-	-	-
1991	Achim Flammenkamp	14 × 14 = 196	size = 196	143	0.7296	C1	x = 14, y = 14, rule = B3/S23 2obobobob2obo$ob3ob3ob2obo$4ob3ob2obo$3obobobob4o$b3obob3ob2o$7ob4obo$ bobob8o$ob3ob2obobobo$6ob6o$ob2ob5obobo$3ob9o$b3obobobob3o$3obobobob2o bo$ob12o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 2
2004	Achim Flammenkamp	13 × 12 = 156	size = 136 size = 134 (alternative form from Nicolay Beluchenko, 2006)	81	0.5956	C1	x = 13, y = 12, rule = B3/S23 2bob3o$2obob5obo$obob2obobo$b4obob3o$obob2ob3obo$b3ob2obobo$2bo3b3o2b 2o$bob2obobob2o$3ob4obobo$bob4o3bo$bobob2o2bo$b2obo2b2o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 3
2004	Achim Flammenkamp	12 × 11 = 132	size = 113	72	0.6372	C1	x = 12, y = 11, rule = B3/S23 bob2ob2o2bo$2bob3ob3o$2b2ob3obobo$bob3ob3obo$5o2b4o$b2ob3obo2bo$b3obob o2bo$b2ob3o2b2o$ob3ob3obo$o2b2o2bobobo$10bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 4
2004	Achim Flammenkamp	13 × 10 = 130	-	-	-	-	-	not a GoE, one parent
2009	Nicolay Beluchenko	11 × 11 = 121	size = 109	69	0.6330	C4	x = 11, y = 11, rule = B3/S23 b3o2b2o$b2obobob3o$b3o2b5o$obobobobobo$4obobobo$4b3o$bobobob4o$obobobo bobo$5o2b3o$3obobob2o$3b2o2b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Flower of Eden, or Garden of Eden 5
2009	Nicolay Beluchenko	11 × 11 = 121	size = 113	59	0.5221	-	-
2009	Nicolay Beluchenko	11 × 11 = 121	size = 110	49	0.4455	D2_x	-
2009	Nicolay Beluchenko	13 × 11 = 143	size = 139	58	0.4173	-	-
2009	Nicolay Beluchenko	11 × 11 = 121	size = 115	47	0.4087	D2_x	-
2009	Nicolay Beluchenko	11 × 11 = 121	size = 107	51	0.4766	D4_x	-
2009	Nicolay Beluchenko	11 × 11 = 121	size = 113	45	0.3982	D4_x	x = 11, y = 11, rule = B3/S23 3b2o3bo$2bo2bobobo$bobo2bo3bo$obobo2bobo$o2bobo2bo$bo2b3o2bo$2bo2bobo 2bo$bobo2bobobo$o3bo2bobo$bobobo2bo$2bo3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here
2009	Nicolay Beluchenko	12 × 12 = 144	size = 129	50	0.3876	-	-
2011	Marijn Heule et al.	11 × 11 = 121	size = 93	65	0.6989	D8	-	almost Garden of Eden 6
2011	Marijn Heule et al.	11 × 11 = 121	size = 119	45	0.3781	D8	-	almost Garden of Eden 6
2011	Marijn Heule et al.	13 × 13 = 169	size = 153	49	0.3203	D8	-
2011	Marijn Heule et al.	10 × 10 = 100	size = 92	56	0.6087	C4	x = 10, y = 10, rule = B3/S23 bob3obo$2bobobo2bo$ob3o2b2o$bob5obo$o2bo2b4o$4o2bo2bo$ob5obo$b2o2b3obo $o2bobobo$2bob3obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 6, ranked third place in the Pattern of the Year 2011 competition on the ConwayLife.com forums, behind the lobster and the fully universal Turing machine.
2015	Steven Eker	11 × 9 = 99	size = 99	66	0.6667	-	-
2016	Steven Eker	12 × 8 = 96	size = 96	57	0.5938	C1	x = 12, y = 8, rule = B3/S23 o2b2obo2b3o$b2o2b2obobo$obobo2bobobo$b4o2b2o2bo$o3b3ob4o$2obobo2bob2o$ obo2b3obobo$b4obob4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here
2016	Steven Eker	83 × 5 = 415	size = 410	284	0.6927	C1	-
2016	Steven Eker	45 × 5 = 225	size = 223	139	0.6233	D2_+1	x = 45, y = 5, rule = B3/S23 2obobo2bob3obo2b3ob7o2b6o2bobobobo$b2obob2obobobobobob3obobobobobobob 3obobobo$2b2ob2o2b4o2b6o2b6o2b5ob5obo$b2obob2obobobobobob3obobobobobob ob3obobobo$2obobo2bob3obo2b3ob7o2b6o2bobobobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here
2016	Steven Eker	9 × 11 = 99	size = 89	55	0.6180	-	-
2017	Steven Eker	9 × 11 = 99	size = 88	50	0.5682	C1	x = 11, y = 9, rule = B3/S23 2b2ob3obo$bo2bobobo$ob3o2b3o$bobobo2bobo$b3o2b2o2bo$2o3b2o2bo$obobob3o $o2bobo2bo$b3o2b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 16 ]] (click above to open LifeViewer) RLE: here Plaintext: here	Garden of Eden 11

Any suggestions? GUYTU6J (talk) 09:12, 7 December 2020 (UTC)

Added a line to the table above. Achim's page has been updated and therefore some references are missing, but I can't get access to Wayback Machine currently. GUYTU6J (talk) 16:11, 24 December 2020 (UTC)

What references do you need access to, exactly? Ian07 (talk) 16:19, 24 December 2020 (UTC)