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Ok, my previous hypothesis for a "natural" upper limit for the densitiy (numCells/2, or numCells/2+1) is completely shattered, with the pattern shown below. This is a period 3 oscillator on a 7x7 torus (shown 9-fold on a 3x3 grid) that oscillates with 14-14-28 cells. The 14-cell patterns have two ce...

I was wondering whether we can observe oscillators on small tori where at least one generation has a density > 0.5. My results so far show that there is a 13-cell 'ash pattern' (these include all stages of oscillators) for a 5x5 torus and a 25-cell ash pattern for a 7x7 torus, so the answer is Yes....

A seven-period oscillator on a 7x7 torus (b3/s23)? Does not sound too exciting ... But: So far, I have only identified one single p7 oscillator on T7 - in contrast, there were several oscillators with period 6 on T6 This oscillator consists of only one (!) canonical pattern which is shifted by 3 row...

Dear all, I have been quiet for a few weeks, but the work on the 7x7 torus has progressed continuously. I have now done more than the first one trillion patterns in the brute force approach (so all patterns of the first 40 bits, out of 49 cells/bits), and about another half trillion of randomly sam...

Have FPGAs been considered for this type of search? You could easily do one generation per clock cycle at around 200Mhz. This would give about 9 hours to run each of the 2^36 possible 6x6 grids (without canonicalization) for 100 generations if it were completely sequential. Since this problem can b...

As written earlier, there are 351 canonical ash patterns on a 6x6 torus in the B3S23 world. Here is the overview of the periodicity of these 351 patterns, and the respective frequency. T6 CAP_PC table.PNG Period 24 / count 2 is a simple glider in its two 'canonical' forms. Period 12 / count 6 are ac...

Apologies if this should go to a more general Golly thread. When using Golly with Torus rules, it would be very nice to have under the Edit menu - next to Flip and Rotate - also a " Shift horizontally " and a " Shift vertically " command (more precisely, it should be "Rotate" but this may be potenti...

That drop-off at precisely 90 generations is quite weird. What could the reason be for chaotic behaviour not being able to extend for more generations? Because otherwise it would be similar to finding methuselae, where for a longer lifetime one would expect a (probably exponential) decay in the pro...

Thanks a lot, done, including downsizing the original PNG files (to approx 660 x 360) to avoid scroll bars.
Frank

I have now updated my 6x6 results with the detection of the (initial) canonical patterns as well as the canonical ash patterns (CAP). My software found the expected number of 239,123,150 initial canonical patterns (see http://oeis.org/A255016) out of 68.7 billion (2^36) initial patterns. - 241 of th...

I will post my thoughts on the 'small tori' discussion from the apgsearch 4.0 thread to here. I agree that this really needs to be a separate client program (with Catagolue as the server, of course, for simplicity). At this stage, before anyone programs anything, it's worth discussing how best to re...

Here is the p4 on T7 that has one of its 4 generations with a density of just above 0.5 (25/49): x = 21, y = 21, rule = B3/S23:T21,21 2o3bob2o3bob2o3bo$3b2obo3b2obo3b2obo$3obob4obob4obobo$2bobobo2bobobo2b obobo$obobob2obobob2obobobo$obobo2bobobo2bobobo$ob2obobob2obobob2obo$ 2o3bob2o3bob2o3bo$3b2obo3...

I was wondering whether we can observe oscillators on small tori where at least one generation has a density > 0.5. My results so far show that there is a 13-cell 'ash pattern' (these include all stages of oscillators) for a 5x5 torus and a 25-cell ash pattern for a 7x7 torus, so the answer is Yes ....

My wish for the next or one of the next versions of apgsearch / apgluxe is the support of (small) tor i (via the rulestring) so that we can do a joint distributed effort to fully explore at least the 7x7 and 8x8 tori. This would then not start with a random soup (and the unique seed for the random g...

This is a p3 on T6 (potentially, the only p3): x = 18, y = 18, rule = B3/S23:T18,18 b4o2b4o2b4o$2o4b2o4b2o$3bobo3bobo3bobo$2o2b4o2b4o2b2o$b2o4b2o4b2o$3bob o3bobo3bobo$b4o2b4o2b4o$2o4b2o4b2o$3bobo3bobo3bobo$2o2b4o2b4o2b2o$b2o 4b2o4b2o$3bobo3bobo3bobo$b4o2b4o2b4o$2o4b2o4b2o$3bobo3bobo3bobo$2o2b4o 2b4o...

Not unexpectedly, p24 is a single glider on the 6x6 torus plane. p12 is (mostly?) a group of c (orthogonal) agars (I think that is what they are called) - during my initial 16x16 experiments, I used to call these patterns "light speed walls". At this point I cannot exclude the possibility of some ra...

This is my first attempt at the analysis of all possible patterns (2^36 = 68,719,476,736) on a 6x6 torus (under B3/S23 rules). I have not done the CAP analysis that I have provided for the smaller tori. This may follow at a future timepoint with an improved software handling large (gigabyte-size) ar...

p20 on T5 is the standard glider, it needs two across-torus runs (each 10 generations) to be identically positioned. There are three different p10's on a T5, all shown on a grid of 3x3 tori (of tSize=5): p10 - 'A-U-A-U': x = 15, y = 14, rule = B3/S23:T15,15 2ob4ob4ob2o$bobo2bobo2bobo$2ob4ob4ob2o$bob...

My motivation to look into Ubuntu (within a Virtual Machine) and/or WSL (Windows Subsystem for Linux) was the fact that apgluxe ran extremely slow unter CygWin, much slower than the number of soups per second that Adam was suggesting. Maybe there is an easy fix to that (that I did not know), but for...

And last but not least here the analysis of the 5x5 torus: Torus Size: 5x5 # of cells: 25 # of states (raw): 33554432 # of states (canonical): 172112 Start torus: 0 Finish torus: 33554431 [Start] 2018-05-10 17:01:18.401 [Finish] 2018-05-10 17:05:30.620 ### ALL PATTERNS analysis: ### Patterns analyze...

Torus Size: 4x4 # of cells: 16 # of states (raw): 65536 # of states (canonical): 805 Start torus: 0 Finish torus: 65535 [Start] 2018-05-10 16:43:34.346 [Finish] 2018-05-10 16:43:35.105 ### ALL PATTERNS analysis: ### Patterns analyzed:65536 Generations analyzed: 228315 Canonical patterns found: 805 ...

Torus Size: 3x3 # of cells: 9 # of states (raw): 512 # of states (canonical): 26 Start torus: 0 Finish torus: 511 [Start] 2018-05-10 17:31:27.191 [Finish] 2018-05-10 17:31:27.195 ### ALL PATTERNS analysis: ### Patterns analyzed:512 Generations analyzed: 469 Canonical patterns found: 26 ashPixCount|...

Torus Size: 2x2 # of cells: 4 # of states (raw): 16 # of states (canonical): 6 Start torus: 0 Finish torus: 15 [Start] 2018-05-10 16:36:48.478 [Finish] 2018-05-10 16:36:48.479 ### ALL PATTERNS analysis: ### Patterns analyzed:16 Generations analyzed: 11 Canonical patterns found: 6 ashPixCount|0:12|2...

Dear all, in the following posts I will present my first results for quadratic tori of size 2 to 5. Size 6 is in the making, 68 billion initial patterns take a while ... but the computational work is mostly done :D :!: . For each torus size ('tSize', from 2 to 5, until now) I have analysed all patt...

Guys, I may need your help with the established terminology, I am still a newbie in your world. Please correct me if you think a different term should be used. So I looked into the "canonical" states (states? hmm...), in other words: by how much can we reduce our initial 2^(torus size) 'soups' (they...