ConwayLife.com

dvgrn wrote:That "minimum bounding box" might start some arguments. Maybe "bounding box with smallest long diameter" or something along those lines?

Exactly, thanks for better wording! Could also be "smallest square bounding box".

Just discovered that http://www.conwaylife.com/wiki/70P2H1V0.1 has the minimum bounding box (21 is the minimum of bigger sides, and 12 is the minimum other side for all of width 21) or period 2 spaceships, it's also the only one in 12x21 box.

A bit offtopic because not exactly about GoL, but while trying to understand why GoL is so special from other CAs, I've made a search for random GoEs for Life-likes whose Born and Stay rules are sequential, and there are the tables of minimal and maximal bounds of side sizes of squares where GoEs ca...

They share the record (it doesn't matter which was found first). It's perfect then! If no 3x3 tile can become a GoE, no matter how many times it's repeated, it almost seems like in the limit there would have to be a 3x3 agar predecessor of every 3x3-tiled infinite agar. I remember I've drawn graphs...

Okay, I've made a start -- added the 89-cell GoE to the records table. Almost perfect! The only thing is second line from bottom is a honorable mention but not a record (red), since the third line from bottom had height 5 before that. The table on the bottom of Achim's pages notes the minimal densi...

I don't think he has made any of his work public. The best way to get that information is probably to email him directly. You might be able to contact him through his work email at SRI International. His information can be found here . Thanks, I saw his page, I don't get enough courage to bother hi...

Some questions: -How do you find these? I've found Eker's new patterns by routine checking of Achim Flammenkamp's page. I'm not aware of any other sources, if you know Eker's blog or some other place where his results get published - it would be really great. I have no idea on how he finds his patt...

There are new Gardens of Eden found by Steven Eker, now only with 89 cells! Information is here http://wwwhomes.uni-bielefeld.de/achim/orphan_10th.html And also I've found GoE-4G (no grand-grand-grand-parent pattern), http://frox25.no-ip.org/~mtve/wiki/GardenOfEden4G.html Unfortunately I can't put i...

Hmm! I don't have much to say, but these are interesting and great work :) Thank you very much, really nice to hear this! Are you working on these with that algorithm you came out with a while before? Basically I just run a SAT solver (cryptominisat is great) to search a parent for random pattern, ...

Notes on periodic GoEs. 3x3 : It seems no 3x3 tile can become a GoE. 3x4 : Indeed possible, as shown by Gamedziner. Non-squares to be investigated: 2x4, 2x5, 2x6, 3x4, 2x7 and 3x5. 4x4 : There are 805 possible 4x4 tiles (sequence https://oeis.org/A255016, see also http://arxiv.org/abs/1502.03792v1)....

Gamedziner wrote:

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..X.$
.X.X$
XXX.!

Assuming you've repeated this 6 times horizontally and 7 times vertically, yes, it's also periodic GoE. Nice catch!

Hello everybody! There are some interesting things found while searching for more Gardens of Eden, so new thread is started to welcome your opinions and ideas. First, random GoEs. Surprising fact: random pattern of size 20x20 with 50% on-cells is GoE with probability around 1/4. But 72% on-cells wil...

Garden Of Eden - 3G, or "no-grand-grand-parent" pattern, bounding box is 29x29, not optimized yet: XXX.X.XXXX.X.X....X..X..X...X XXX.X.XX.XX.XX.....XXX.X.X.X. ..X......XX.X..XX..XXX....XXX ....XXX..X.X..X..XXXX..X.XXX. .X..XXX...........X.X.XXX.XXX XXXXX..XX.XXX.....X...X.XX.X. ..X.X.X.XXXX..X.X...X...

GoE2g#1 bounding box size was 23x24, GoE2g#2 was 24x25 and GoE2g#3 is 22x22: ?XXX...........X.X.XXX ?X..XX.XXX.....X...X.X ?X.X.XXXX..X.X...XXX.X ?.X.XXXX.XXX...X.XX.X. ?.XX.XX....X.XXXXXXXXX ?.XXX..XXXX.XXXXXXXX.X ?X.XXX.XXXX..X.XXX.XX. ?XX..XXX.X.X.X.X.XX.XX ?X.XXX....X..X..X.X..X ?.X..X.X.XXX.X.....

muzik wrote:I was thinking "Mountain of Eden".

Very nice, thank you!

No, it still has parents. You're right, my mistake. Do you want to name your original grandparentless pattern? I've been referring to it as "mtve's pattern" or "grandparentless pattern" which are awkward. Sticking with the biblical theme set by "Garden of Eden", a fitting name might be "Cain". Seco...

I also cut off some cells on the left side of mtve's pattern and found that this pattern (not including red border cells) also has on grandparents : x = 26, y = 25, rule = LifeHistory .24D$.D7AB5AB4AB3A2D$.DBA2B2A2B3A2B4AB2A2BAD$.DABAB4AB4AB2ABA2B3AD$.D 2ABABABABA2BAB3AB3A2BD$.DB2A6BA2B5A3B2ABD$.DA...

Can you give insight into how you found it? It was found by an algorithm similar to Nicolay Beluchenko's OEIS sequence A196447 - try next cell on and off, skip first level GoEs, choose minimum number of grandparents, where minimum number is not the exact number but just a minimal distance between f...

Would you please help me to verify following pattern? It has parents but all of them are Gardens of Eden, so it has no grandparent: XXXXXXXX.XXXXX.XXXX.XXX. X.X..XX..XXX..XXXX.XX..X XX.X.XXXX.XXXX.XX.X..XXX XXX.X.X.X.X..X.XXX.XXX.. X.XX......X..XXXXX...XX. .X.X.XXXXXXXXX.X.X...... X.X.XX....X..X.XXX...

If you go to the paper linked to from the Garden of Eden 6 wiki page, this orphan appears as one of their almost-record results. The paper was wrotten three years ago, so this GoE is around that old, argh, "what an impact from the classics", i totally miss this although i was in fact inspired by th...

Hello again, FractalFusion! What is the program you used to verify this orphan, and others like it? I'm interested in knowing. it's some custom made bruteforcer with backtracking and some optimizations, a bit too dirty to publish it as is. you just gave me an idea to re-verify it with SAT generator ...

D8-symmetric Garden-of-Eden, bounding box is 11x11, orphan size is 93, number of on-cells is 65. x = 11, y = 11, rule = B3/S23 4bobo$bobobobobo$2b7o$b4ob4o$ob3ob3obo$b2o2bo2b2o$ob3ob3obo$b4ob4o$2b 7o$bobobobobo$4bobo! orphan is with corners cut off: ????X.X???? ?X.X.X.X.X? ?.XXXXXXX.? ?XXXX.XXXX? X....