ConwayLife.com

There still aren't many usable conduits, whether for b or for pi. But at least Turing completeness and universal construction are theoretically possible. x = 43, y = 25, rule = B34q/S23-k 40bobo$40b2o$41bo$36bo$36bo$36bo12$18bo$17bo$17b3o14b2o$35bo$35bobo$2o 16bo17b2o$b2o14b2o$o16bobo! Hotwheels's 4...

x = 70, y = 26, rule = B2-a5y/S0235-y78 8bo23bo6bo22bo4bo$2b2o2b5o2b2o45b2obo2bob2o$2b4obobob4o16bobo4bobo19bo b2o2b2obo$4bo3bo3bo17bobobo2bobobo18bo8bo$4bobo3bobo17bo3bo2bo3bo18bo 8bo$4bo3bo3bo17bo10bo$6bo3bo19bobo2b2o2bobo$6b2ob2o19bo2bo4bo2bo$30bo 10bo$30bo10bo$7bobo20bo10bo$4bobo3bobo17bo10bo$2...

ln(9-e^e+(9e^√π)/π) ≈ 2.370787065 (+0.000000090933)

Edit 2: nvm those numbers were meaningless now that the gaps are of the order of 10^-16.

(7+20e/(6+e^(√(e))))/5 ≈ 2.3707867023 (+0.000000185)

(11/4)^(5/(π+e)) ≈ 2.3706382 (+0.00000308)

e^(5-e)-3*e/ln(3) ≈ 2.3706326 (+0.0000045)

√(4π/√(5)) ≈ 2.370622 (+0.000007475), found by computer search

x = 16, y = 16, rule = B34q/S23-k 7b2o$3bob2o2b2obo$2b2o8b2o$b2obobo2bobob2o$bobo8bobo$bobobo4bobobo$2ob ob2o2b2obob2o$bobo8bobo$2b2obo4bob2o$bobobo4bobobo$3bob2o2b2obo$2obob 2o2b2obob2o$5bo4bo$obobo6bobobo$bo5b2o5bo$7b2o! A 4c/8 block puffer, might be useful for creating low-period rakes. x = 15, ...

This rule is a close variant of B2a/S12 except duoplets can be changed. I found some basic circuitry, which includes a reflector (that does not work in B2a/S12): x = 106, y = 81, rule = B2a4k/S12 6bo24bo7bo25bo2bo29bo2bo$bo5bo22bo9bo23bo4bo27bo4bo$o11bo22bo$5bo5bo 24bo$6bo23bo5bo$o5bo24bo3bo2bo30bo$...

x = 8, y = 12, rule = B34q/S23-k 6bo$4b3o$3bo$3b2o6$3o3b2o$obo3b2o$obo! Hotwheels's new pi rotating conduit, which is compact enough to be chained. Edit: @below I mean x = 35, y = 35, rule = B34q/S23-k 13bo$11b3o$10bo$10b2o6$13b2o$13b2o8bo$21b3o$20bo$20b2o6$23b2o$2b2o19b 2o8bo$bobo27b3o$bo28bo$2o7b...

I ran a 60x60 radiolife soup on B3-ckq4q/S23-cey4i (rule by HotWheels9232) and decay probability 1/1000; after 48612 or so generations it stabilized with bounding box 1765/1541. The soup began in the western half of the southmost area, and only the upper right started expanding; it quickly grew to w...

x = 56, y = 31, rule = B34q6-ik/S23-cq4i6c 16b2o$16b2o$10bo$10bo$14bo$14b2o$14bo$10bo$10bo$16b2o$16b2o10$16b2o$ 16b2o$10bo$10bo$14bo$14b2o$14bo$3b2o5bo41b2o$2bobo5bo41bobo$2bo13b2o 36bo$b2o13b2o36b2o! The T-tetromino is very common in this rule; it evolves into two identical halves which are essent...

x = 21, y = 17, rule = B34q/S23-k 2bo$obo$b2o8$19bo$18bo$18b3o2$14bobo$15b2o$15bo! Gliders can be pushed out using 2 gliders from one lane so we can make arbitrarily high clearance controlled edge shooting guns, which means we can make periodic slow salvos (using glider loops) and also universal co...

import golly as g, random, time const = { 'B2n3-q4q5y6kn/S023-kq4c6i8':(0.0002,0) } rule = g.getrule() if rule in const.keys(): (c,d) = const[rule] else: (c,d) = (0.001,0.05) g.show(str(c) + ' ' + str(d)) while True: if g.empty(): g.show('Life ended at generation ' + str(g.getgen())) break cells = ...

If we change a standard cellular automaton so that after the transition is complete each alive cell has a very low probability of turning off then it might cause these changes (I didn't run any experiments but this is probably going to be the case when using a life-like rule): 1. Common simple thing...

Here is a 4g infinite growth! x = 58, y = 54, rule = B34q/S23-k 48bo$46bobo$47b2o4$52bo$51bo$51b3o2$56bo$55b2o$55bobo39$3o$2bo$bo! I used a 3g SE from life(currently my favourite not because it was used in this synthesis but a still life synthesis in life), and threw gliders at the SE, hoping for t...

x = 37, y = 37, rule = B34q/S23-k 19bo$18bobo$18bobo$16b3ob2o6bo$15bo10b3o$16b3ob2o3bo$18bob2o3b2o$12b2o $3b2o7b2o$4bo$4bobo$5b2o$28b2o$12b3o13b2o$12bobo$3bob2o5bobo17bo$b3ob 2o24bobo$o9bo20bobo$b3ob2o2bobo18b2ob3o$3bobo30bo$3bobo24b2ob3o$4bo5bo bo17b2obo2$7b2o$7b2o$30b2o$30bobo$32bo$23b2o7b2o$23b2...

Mazing glider synthesis: x = 43, y = 27, rule = B34q/S23-k 27bo$28b2o$27b2o8$30bo9b3o$31bo8bo$5bo23b3o9bo$4bo29b2o$4b3o17bo9bobo$ 23bobo8bo$bo21bobo$b2o21bo$obo2$39b2o$38b2o$40bo2$15b3o$17bo$16bo! I looked at soups producing a half-bakery in Catagolue, and the first one was a beehive, double TL (or ...

Edit 1:Totally unrelated, but could anybody make a synthesis for this spaceship? x = 55, y = 50, rule = B34q/S23-k 5bobo$6b2o$6bo15$20bo$19b3o$18b5o$17b2o3b2o$18b5o$19b3o$20bo$33bo$33bo $33bo2$25bo3b3o3b3o$23b2ob2o$25bo7bo$18b2o13bo$17bo2bo12bo$17bobo$18bo 6$3o$2bo$bo5$53b2o$52b2o$54bo! x = 26, y =...

Smaller breeder: x = 50, y = 20, rule = B34q/S23-k 3b3o30b3o$4bobo30bobo$5b2o31b2o12$15b2o31b2o$15bo32bo$o32bo$2o31b2o$b 2o31b2o$2bo32bo! x = 37, y = 21, rule = B34q/S23-k 9bo$9b2o6$bo32bo$o32bo$bobo30bobo$2b2o31b2o5$o$2o3$35bo$35b2o! Population 21, better than original 32, but the bounding box is ...

Edit: added c/5d from obviously rlifesrc. Actually zfind has already found it earlier (see the second post). Also, crab and the tubstretcher still work, and the tub can burn also in a new way (based on the r spark) x = 40, y = 45, rule = B34q/S23-k 8b2o$7b2o$9bo$11b2o$10bo2$9bo2bo$b2o5b2o$2o5bo$2bo...

This would be a p2 reflector but I cannot find a stable solution, so it is supported by a unix instead: x = 26, y = 18, rule = B34q/S23-k 22bo$22bobo$22b2o$4bo$4obo$3obobo$5bobo$6bo$5b2o8bo$5b2o8bo$5b2o8bo6b 2o$22bobo$24bo$24b2o$20b2o$10b2o8bobo$10bobo9bo$11b2o9b2o! x = 21, y = 26, rule = B34q/S23-...

Here is a selection of spaceships by zfind: (Updated Dec 22, several are from others, notably hotwheels's c/3 searches and the width 10 c/5o) x = 253, y = 420, rule = B34q/S23-k 3b3o5b3o5b3o12bo27bo5bo24bo28bo11bo19bo5bo21b2o2b2o26bo25b2o$2bo3bo3bo 3bo3bo3bo10bobo25b3o3b3o23bo27b5o5b5o17bobo3bobo22b...