Adjustable Probability-Based PRNG (APBP) Challenge

[qqd]

I was thinking something bizarre just now, the Simulation of Quantum Mechanics with Classical Computers (SQMCC). However, the SQMCC is prohibited by Bell's theorem, but that's only in the case of entangled particles, so I think a simulation of a single quantum spin is possible. The first obstacle is, of course, that there is no such such thing as an RNG (Random Number Generator) in classical mechanics, there are only PRNGs (P for pseudo). But PRNGs are fine for the concept of unpredictability while taking measurements of quantum systems because, I emphasize, were are NOT dealing with quantum mechanics in and of itself, but rather the SIMULATION of it. We've already built many PRNGs (most of them high-period oscillators) in CGoL, but none of them probability based (which means like for example a 60% chance of getting 0 and 40% for getting 1), and adjustable ones will be required for simulating measurement in quantum mechanics. I think it will be helpful to measure the probability of getting 0 or 1 for already known PRNG's, as these might be the components of an APBP like the p46 and p120 versions of PRNG's:

Code: Select all

x = 156, y = 75, rule = B3/S23
146b2o5b2o$146b2o5b2o8$147bo5bo$146b3o3b3o$145b2obo3bob2o3$148bo3bo$
148bo3bo5$147bo$146bobo$33bo111b2ob2o$32b2o8b2o101bo3bo$18b2o11b3obo5b
o2bo99b3ob3o$18b2o10b2o8b2ob3o99bo3bo$31b2o8b2obo100bo3bo$32bo10bo102b
obo4b2o$147bo5b2o$32bo$31b2o$18b2o10b2o13b2o30b2o$18b2o11b3obo9b2o30b
2o$b2o29b2o$b2o30bo3$41bo2bo$19b4o22bo19b4o$18bo3bo18bo3bo18bo3bo58b2o
$22bo19b4o22bo59b2o$18bo2bo42bo2bo59bo24b2o$b3o3b3o142bobo$o2bo3bo2bo
143bo$2obo3bob2o69bo73b2o$57bo5bo5b2o8b2o15b2o$21b2o19bob2o11bo5bo5b2o
7b2o16b2o$20b2o14b2o3bo2b2o2b3o28b2o2b2o$22bo13b2o3bo6b2o3b2o11b2o$41b
2o3b3o$43bo3bo9bo5bo52bo$57bo5bo15b2o2b2o31b2o$43bo3bo21b2o7b2o16b2o
17bobo$41b2o3b3o20b2o8b2o15b2o$36b2o3bo6b2o13b2o15bo$36b2o3bo2b2o2b3o
12b2o$42bob2o$33bo$32b2o58b2o$32bobo17bo38bo$b2o5b2o41b2o25b2o10bo2b2o
$b2o5b2o40b3obo9b2o12b2o10bo2bo18bo$30b2o17b2o13b2o24bobo11b2o4bo2bo$
32bo17b2o39b2o12b2o3b5o10b2o$17b2o10b2o2bo17bo52bo5b3ob2o9b2o$17b2o11b
o2bo57b2o18b2obo$31bobo17bo38bobo19b2o$31b2o17b2o26b2o10bo2bo$49b2o13b
2o12b2o10bo2b2o17b2o$31b2o17b3obo9b2o25bo19b2obo$31bobo17b2o39b2o16b3o
b2o9b2o$17b2o11bo2bo18bo57b5o10b2o$17b2o10b2o2bo76bo2bo$32bo79bo$30b2o
!

Code: Select all

x = 139, y = 126, rule = B3/S23
23bo$21bobo$11b2o6b2o$10bo3bo4b2o12b2o$9bo5bo3b2o12b2o$9bo3bob2o4bobo$
9bo5bo7bo$10bo3bo$11b2o6$11b2o$2b3o5bobo$bo3bo6bo$o5bo$o5bo2$6bo$5b2o$
5b2o$3bo2b2o$4bobo$4b2o3$2b2o3b2o$2b2o3b2o2$4b3o$4b3o$5bo6$5b2o$5b2o9$
100b2o$100b2o6$118b2o$118b2o2$119bo$98b2o3b2o13bobo$118bobo$99bo3bo15b
o$100b3o$100b3o$116b2obob2o$116bo5bo$117bo3bo$118b3o2$99bo5bo$98b3o5bo
$98b3o3b3o2$96b2o3b2o$96b2o3b2o14bo$116bo$116b3o4$101b2o$101bo17b5o$
102b3o13bob3obo$104bo14bo3bo$120b3o$121bo4$102bo17b2o$101bo18b2o$101b
3o2$79b2o$79bobo$80b3o$81b2o$78b2o$78b3o$91b3o$91bo$79b2o11bo$79b2o2$
88bo$82b2obobobo$82bob2ob2o10b2o$93b2o4bobo$94b2o3bo$93bo4$118b2o$86bo
19b3o2bo5bo3bo$86b2o14bo3bo9bo5bo$74bobo8bobo12bobo4bo8bo3bo2bo$74bo3b
o19b2o16bo$64b2o12bo10b2o7b2o17bo3bo3bo$64b2o8bo4bo7bo2bo7b2o18b2o3b2o
bo$78bo7bo7b2o4bobo23bo$74bo3bo7bo6bo2bo5bo23b2o7b2o$74bobo9bo7b2o39bo
bo$87bo2bo46bo$89b2o46b2o!

This is the start of the APBP challenge, so quantize any ideas for this you can think of!

[wwei47]

Interesting. I suspect the ones you already have to be xorshift generators. Maybe we can use that to help us.

[qqd]

I think we can make as many ordinary PRNG's and pack their 1s and 0s on a single lane using this 90-degree reflector that packs gliders as close as 15 ticks for further progress

Code: Select all

x = 128, y = 80, rule = B3/S23
8b2o$8bobo$10bo4b2o$6b4ob2o2bo2bo$6bo2bobobobob2o$9bobobobo$10b2obobo$
14bo2$2o$bo7b2o$bobo5b2o$2b2o6$44b2o$12b2o31bo$12bo32bobo$13b3o19bo10b
2o$15bo17b3o$3o29bo$2bo29b2o$bo15b2o48b2o$18bo48b2o$18bob2o$19bo2bo23b
o$20b2o24bo$35b2o9b3o$35b2o11bo4$44bo3b2o$43bobo3bo$42bobo3bo$38b2obob
o3bo$38b2obo2b4obo$42bobo3bobo$38b2ob2o2bo2bobo7b2o$39bobo2b2o3bo8b2o$
27b2o10bobo$27b2o11bo33$125b3o$125bo$126bo!

[qqd]

(Unrelated but still relevant for this topic) Here's a way of extracting a glider from every second LWSS in the p46-based PRNG using a domino filter

Code: Select all

x = 20, y = 36, rule = B3/S23
18b2o$18b2o5$7b2o2$5bo2bo$9bo$5bo3bo$6b4o11$15bo$14bobo$10bo4bo$9bobo$
8bo2bo$9b2o2$3bob2o$b3ob2o3b2o$o9b2o$b3ob2o$3bobo$3bobo$4bo!

Now we need to find a compact domino sparker which doesn't interfere with the rest of the conduit.

[pzq_alex]

(Unrelated but still relevant for this topic) Here's a way of extracting a glider from every second LWSS in the p46-based PRNG using a domino filter

Code: Select all

x = 20, y = 36, rule = B3/S23
18b2o$18b2o5$7b2o2$5bo2bo$9bo$5bo3bo$6b4o11$15bo$14bobo$10bo4bo$9bobo$
8bo2bo$9b2o2$3bob2o$b3ob2o3b2o$o9b2o$b3ob2o$3bobo$3bobo$4bo!

Now we need to find a compact domino sparker which doesn't interfere with the rest of the conduit.

Why not just apply the 45-degree LWSS-to-G and period-double the glider stream? Finding an appropriate domino sparker seems unlikely as the active region returns to the spark area quite a few times.

[qqd]

(Unrelated but still relevant for this topic) Here's a way of extracting a glider from every second LWSS in the p46-based PRNG using a domino filter

Code: Select all

x = 20, y = 36, rule = B3/S23
18b2o$18b2o5$7b2o2$5bo2bo$9bo$5bo3bo$6b4o11$15bo$14bobo$10bo4bo$9bobo$
8bo2bo$9b2o2$3bob2o$b3ob2o3b2o$o9b2o$b3ob2o$3bobo$3bobo$4bo!

Now we need to find a compact domino sparker which doesn't interfere with the rest of the conduit.

Why not just apply the 45-degree LWSS-to-G and period-double the glider stream? Finding an appropriate domino sparker seems unlikely as the active region returns to the spark area quite a few times.

Thanks for mentioning that. Here's the complete signal splitter

Code: Select all

x = 249, y = 75, rule = B3/S23
146b2o5b2o$146b2o5b2o8$147bo5bo$146b3o3b3o$145b2obo3bob2o3$148bo3bo$
148bo3bo5$147bo$146bobo$33bo111b2ob2o$32b2o8b2o101bo3bo$18b2o11b3obo5b
o2bo99b3ob3o$18b2o10b2o8b2ob3o99bo3bo$31b2o8b2obo100bo3bo22bo$32bo10bo
102bobo4b2o15b3o$147bo5b2o14bo$32bo136b2o$31b2o123b2o$18b2o10b2o13b2o
30b2o78bo$18b2o11b3obo9b2o30b2o78bobo$b2o29b2o124b2o$b2o30bo132b2o$
165bo2bo71bo$166b2o71bobo$41bo2bo195bo$19b4o22bo19b4o$18bo3bo18bo3bo
18bo3bo58b2o109b5o$22bo19b4o22bo59b2o72bo35bo4bo$18bo2bo42bo2bo59bo41b
2o31b3o36bo2bo$b3o3b3o159bo35bo35b2obo2bo$o2bo3bo2bo159b3o19bo11b2o11b
2o19bo5bobobo$2obo3bob2o69bo49b2o7b2o20bo3bo6bo17b3o24b2o18bobo4bo2bo$
57bo5bo5b2o8b2o15b2o32bo9bo19b2o3b2o22bo47bo2bo2b2o$21b2o19bob2o11bo5b
o5b2o7b2o16b2o33b9o20b2o3b2o22b2o47b2o$20b2o14b2o3bo2b2o2b3o28b2o2b2o
43b3o2b5o2b3o17bo5bo7b2o56b2o$22bo13b2o3bo6b2o3b2o11b2o60bo2bo2b3o2bo
2bo32bo56b2o$41b2o3b3o80b2o9b2o33bob2o$43bo3bo9bo5bo52bo59bo2bo$57bo5b
o15b2o2b2o31b2o59b2o$43bo3bo21b2o7b2o16b2o17bobo74b2o$41b2o3b3o20b2o8b
2o15b2o94b2o$36b2o3bo6b2o13b2o15bo146b2o$36b2o3bo2b2o2b3o12b2o162b2o$
42bob2o$33bo$32b2o58b2o106bo3b2o$32bobo17bo38bo107bobo3bo$b2o5b2o41b2o
25b2o10bo2b2o100b2obobo3bo12b2o$b2o5b2o40b3obo9b2o12b2o10bo2bo18bo82b
2obo4bo13bo$30b2o17b2o13b2o24bobo11b2o4bo2bo85b5obo12b3o$32bo17b2o39b
2o12b2o3b5o10b2o64b2obob2obo4bobo13bo$17b2o10b2o2bo17bo52bo5b3ob2o9b2o
64bob2obo2bob2o2bo$17b2o11bo2bo57b2o18b2obo69b2o12b2obob2o$31bobo17bo
38bobo19b2o70b2o$31b2o17b2o26b2o10bo2bo$49b2o13b2o12b2o10bo2b2o17b2o$
31b2o17b3obo9b2o25bo19b2obo$31bobo17b2o39b2o16b3ob2o9b2o$17b2o11bo2bo
18bo57b5o10b2o$17b2o10b2o2bo76bo2bo$32bo79bo$30b2o!