dvgrn wrote:Naszvadi wrote:Hensel isotropic rulestring: B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78 (published here earlier by a conwaylife forum member)
More on this rule in the examples delivered with
golly and the rule is defined there is a built-in.
It's kind of funny that the rule is so much simpler than the isotropic rulestring makes it out to be -- it's just
Code: Select all
neighborhood:vonNeumann
symmetries:rotate4reflect
111000
011101
011111
... but the isotropic rulestring has to mention not only those birth and survival conditions based on orthogonal neighbors, but also all the combinations of ways that corner-neighbor cells can happen to be ON or OFF, even though we don't really care about them.
Yes, this was the bait
So, basically Banks-I rule is a (von)Neumann isotropic rule, but as a ruletable, with so little number of transitions.
Just a reminder: it would be nice if
Golly could support nontotalistic isotropic Neumann rules e.g. with rulestrings B34/S012n34V , where n in 2n strands for "near", and "o" for "opposite" in other cases.
Well, the (rather) incomplete background story of creating the W110 unit cell in Banks-I:
First of all, tried to create an XOR-gate in several weeks, and constructed this working instance:
Code: Select all
x = 119, y = 353, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
68bo$66b3o$67b2o$67b2o$67b2o$67b2o$67b2o$67b2o$67bobo$64b3o$65b3o$65b
3o$65b3o$65b3o8bo$65b3o8b3o$65b3o8bo2bo$65b3o8bo2bo$65b3o9b2o$65b3o$
65b3o$65b3o$65b3o$65b3o$65b3o$65bobo$65b2o$65b3o$65b3o$65b3o$65b3o$65b
3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$62bo2b3o$62b6o$62b3ob2o2bo31b2o
$54b5o3bo4b4o30bo2bo$55b3o8b5o30bo2bo$55b3o8b5o31b4o$47bo8b11o3bo$45b
3o3b3obob10o$46b2o4b3o3b9o$46b2o4b3o4bo4b3o$46b2o4b3o3b2o4b3o$46b2o4b
3o2b4o3b3o16b5o$46b2o4b3o6bo2b3o17b3o23bo$46b2o4b3o6b6o17b3o24b8o$46bo
bo3b3o6b6o17b9ob15ob8o$43b3o3bo2b3o6bo3b13ob15ob15o7bo$44b3o2b6o10b14o
b4o4b22o$44b3o2bobob2o10b19o3b2o20bo$41bo2b3o2bo4b12o3bo11b3o4bo$41b6o
6bob11o15bobo2b4o$41b6o6b2ob10o15b2o$41bo3b7obo3bo5b3o15b3o$45b8o10b3o
15b3o$45b9o9b3o15b3o$42b4o3bo3bo8b4o15b3o$43b3o17bobo5bo9b3o$43b3o17b
3o5b9ob3o$43b3o17bob9ob4o2b3o$43b3o13b12o7bo2b3o$31bo11b3o14b3o4b4o10b
3o$21b2o2bo2bob3o10b3o14bobo3b2o2bo7bo2b3o$20bo2bobo2bo2bo11b3o14b2o4b
2o10b6o$20bo2bobo2bo2bo11b3o14b3o2b4o9bob4o2bo$21b2o3b2o4bo10b3o11bo2b
3o15bo3b5o$43b3o11b6o19b5o$43b3o11b6o20b4o$40bo2b3o11bo3b6ob15o3bo$40b
6o15b7ob14o$40b6o15b22o$40bo3b18o3bo16bo$44b18o$o43b18o$45o3bo12bo$45o
$45o$o43bo8$68bo$66b3o$67b2o$67b2o$67b2o$67b2o$67b2o$67b2o$67bobo$64b
3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b4o$
65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b
3o$65b3o$65b3o$65b3o$65b3o$62bo2b3o$62b6o$62b6o2bo31b2o$54b5o3bo3b5o
30bo2bo$55b3o8b5o30bo2bo$55b3o8b5o31b4o$47bo7b12o3bo$45b3o3b16o$46b2o
4b3o3b9o$46b2o4b3o3b2o4b3o$46b2o4b3o3b2o4b3o$46b2o4b3o2b4o3b3o16b5o$
46b2o4b3o6bo2b3o17b3o23bo$46b2o4b3o6b6o17b3o24b8o$46bobo3b3o6b6o17b9ob
15ob8o$43b3o3bo2b3o6bo3b13ob15ob15o7bo$44b3o2b6o10b14ob4o4b22o$44b3o2b
6o10b19o3b2o20bo$41bo2b3o2bo3b13o3bo11b3o4bo$41b6o6b13o15bobo2b4o$41b
6o6b13o15b2o$41bo3b9o3bo5b3o15b3o$45b9o9b3o15b3o$45b9o9b3o15b3o$42b4o
3bo3bo8b4o15b3o$43b3o17bobo5bo9b3o$43b3o17b3o5b9ob3o$43b3o17bob9ob4o2b
3o$43b3o13b12o7bo2b3o$31bo11bobo14b3o4b4o10b3o$21b2o2bo2bob3o10b2o15bo
bo3b2o2bo7bo2b3o$20bo2bobo2bo2bo11b3o14b2o4b2o10b6o$20bo2bobo2bo2bo11b
3o14b3o2b4o9bob4o2bo$21b2o3b2o4bo10b3o11bo2b3o15bo3b5o$43b3o11b6o19b5o
$43b3o11b6o20b4o$40bo2b3o11bo3b6ob15o3bo$40b6o15b7ob14o$40b3ob2o15b22o
$40bo3b18o3bo16bo$44bobob14o$o43b18o$9ob15ob15ob3o3bo12bo$10ob15ob15ob
2o$45o$o43bo8$68bo$66b3o$67b2o$67b2o$67b2o$67b2o$67b2o$67b2o$67bobo$
64b3o$65b3o$65b3o$65b3o$65b3o8bo$65b3o8b3o$65b3o8bo2bo$65b3o8bo2bo$65b
3o9b2o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65bobo$65b2o$65b3o$65b3o$
65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$62bo2b3o$62b6o$
62b3ob2o2bo$54b5o3bo4b4o$55b3o8b5o$55b3o8b5o$47bo8b11o3bo$45b3o3b3obob
10o$46b2o4b3o3b9o$46b2o4b3o4bo4b3o$46b2o4b3o3b2o4b3o$46b2o4b3o2b4o3b3o
16b5o$46b2o4b3o6bo2b3o17b3o23bo$46b2o4b3o6b6o17b3o7bo16b8o$46bobo3b3o
6b2ob3o17b25ob8o$43b3o3bo2b3o6bo3b45o7bo$44b3o2b6o11b18o3b23o$44b3o2b
6o10bob17o3b2o20bo$41bo2b3o2bo3b12o4bo11b3o3b2o$41b6o6b13o15b3o2b4o$
41b6o6b13o15b3o$41bo3b9o3bo5b3o15b3o$45b9o9b3o15b3o$45b9o9b3o15b3o$42b
4o3bo3bo8b4o15b3o$43b3o17b3o5bo9b3o$43b3o17b3o5b9ob3o$43b3o17b11ob4o2b
3o$43b3o13b12o7bo2b3o$31bo11bobo14b3o3b5o10b3o$21b2o2bo2bob3o10b2o15b
3o3b2o2bo7bo2b3o$20bo2bobo2bo2bo11b3o14b3o3b2o10b6o$20bo2bobo2bo2bo11b
3o14b3o2b4o9b6o2bo$21b2o3b2o4bo10b3o11bo2b3o15bo3b5o$43b3o11b6o19b5o$
43b3o11b6o19b5o$40bo2b3o11bo3b22o3bo$40b6o15b22o$40b3ob2o15b22o$40bo3b
18o3bo16bo$44bobob14o$o43b18o$9ob15ob15ob3o3bo12bo$10ob15ob15ob2o$45o$
o43bo8$68bo$66b3o$67b2o$67b2o$67b2o$67b2o$67b2o$67b2o$67bobo$64b3o$65b
3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b4o$65b3o$
65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b3o$65b
3o$65b3o$65b3o$65b3o$62bo2b3o$62b6o$62b6o2bo$54b5o3bo3b5o$55b3o8b5o$
55b3o8b5o$47bo7b12o3bo$45b3o3b16o$46b2o4b3o3b9o$46b2o4b3o3b2o4b3o$46b
2o4b3o3b2o4b3o$46b2o4b3o2b4o3b3o16b5o$46b2o4b3o6bo2b3o17b3o23bo$46b2o
4b3o6b6o17b3o7bo16b8o$46bobo3b3o6b6o17b25ob8o$43b3o3bo2b3o6bo3b45o7bo$
44b3o2b6o10b19o3b23o$44b3o2b6o10b19o3b2o20bo$41bo2b3o2bo3b13o3bo11b3o
3b2o$41b6o6b13o15b3o2b4o$41b6o6b13o15b3o$41bo3b9o3bo5b3o15b3o$45b9o9b
3o15b3o$45b9o9b3o15b3o$42b4o3bo3bo8b4o15b3o$43b3o17bobo5bo9b3o$43b3o
17b3o5b9ob3o$43b3o17bob9ob4o2b3o$43b3o13b12o7bo2b3o$31bo11bobo14b3o4b
4o10b3o$21b2o2bo2bob3o10b2o15bobo3b2o2bo7bo2b3o$20bo2bobo2bo2bo11b3o
14b2o4b2o10b6o$20bo2bobo2bo2bo11b3o14b3o2b4o9b6o2bo$21b2o3b2o4bo10b3o
11bo2b3o15bo3b5o$43b3o11b6o19b5o$43b3o11b6o19b5o$40bo2b3o11bo3b22o3bo$
40b6o15b22o$40b6o15b22o$40bo3b10ob7o3bo16bo$44b11ob6o$o43b18o$45o3bo
12bo$45o$45o$o43bo!
After finishing the above gate, in 4-5 minutes constructed this much more smaller and stable XOR gate:
Code: Select all
x = 27, y = 59, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
11b5o$12b3o5b5o$2b5o5b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b
3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3bobo6b3o6b3o$4b2o6b
3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b
3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b
3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b
3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6bobo$3b3o6b3o6b2o$3b3o6b3o6b
3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b
3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b3o6b3o$3b3o6b
3o6b3o$3bobo6b3o6b3o$4b2o6b3o6b3o$3b3o6b3o6bobo$3b3o6b3o3bo2b2o$3b3o2b
o3b3o3b6o$3b6o3b3o3b6o2bo$o2b6o3b3o3bo3b5o$5o3bo3b3o7b5o$5o7b3o7b5o$5o
7b11o3bo$o3b19o$4b8o3b8o$4b8o3b2o5bo$4bo6bo3b2o$14b4o!
After that, combining with signal splitters from Banks and the (x)and(not(y)) gate also from Banks, inclusive OR gate could be constructed and used in the unit cell. No crossroads were needed, just appropriate timings with delaying tricks (corners and side-changers, a right-angle turn from 1971 changes the side of the signal).
Also used an observation: the signal splitter is similar to the old (x)and(not(y)) gate, and they can be interbreed trivially, so the gate's output were duplicated immediately:
Code: Select all
x = 39, y = 41, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
15bo$15b3o$15b2o$15b2o$15b2o$15b2o$15b2o$15b2o$15b2o$15b2o$15b2o$15b2o
$15b2o$15b2o$15b2o$15b2o$14bobo$17b3o$16b3o$16b3o$16b3o$16b4o$8bo7b3o$
8o8b3o$b8ob9o19bo$bo7b15ob14o$9b6o4b4ob15o$9bo4b2o3b20o$14bo4b3o16bo$
13b4o2bobo$20b2o$19b3o$19b3o$19b3o$19b3o$19b3o$19b3o$19b3o$19b3o$19b3o
$18b5o!
Unit cell has two states - and there is a generation among the 256 ones in which they differ only one cell, see here (the ON state cell is on top):
Code: Select all
x = 398, y = 281, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
2b5o38b5o$3b3o40b3o$3b3o40b3o$3b3o40b4o$3b3o38b3o$3b3o39b2o$3b3o39b2o$
3b3o39b2o$3b3o20bo18b2o$3b3o20b21o$3b3o20b22o$3b3o16bo3b19o$3b3o16b6o
13bo2bo$3b3o16b6o$3b3o16bo2b3o$3b3o19b3o$3b3o18b4o$3b3o21b3o$3b3o21b2o
$3b3o21b2o$3b3o21b2o$3b3o21b2o8bo$3b3o21b11o$3b3o20b12o$3b3o23b9o3bo$
3b3o23bo2bo3b6o$3b3o30b6o$3b3o30b3o2bo$3b3o30b3o2bo$3b3o6b5o19b6o$3b3o
7b3o20b6o$3b3o7b3o20b6o$3b3o7b24o4bo$3b3o3b28o$3b3o4b3o3b21o3bo$3b3o4b
3o3b2o17b6o$3b3o4b3o3b2o17b6o$3b3o4b3o2b4o16b3o2bo$3b3o4b3o22b3o$3b3o
4b3o22b3o$3b3o4b3o22b4o$3b3o4b3o20b3o$3b3o4b3o21b2o$3b3o4b3o21b2o$3b3o
4b3o21b2o$3b3o4b3o12bo8b2o$3b3o4b3o12b11o$3b3o4b3o12b12o$3b3o4b3o8bo3b
9o$3b3o4b3o8b6o6bo$3b3o4b3o8b6o$3b3o4b3o8bo2b3o$3b3o4b3o11b3o$3b3o4b3o
10b4o$3b3o4b3o13b3o$3b3o4b3o13b2o$3b3o4b3o13b2o$3b3o4b3o13b2o$3b3o4b3o
13b2o8bo$3b3o4b3o13b11o$3b3o4b3o12b12o$3b3obo2b3o15b9o3bo$3b3ob6o15bo
6b6o$3b3ob6o9bo2bo9b6o$3b3obo3b15o9b3o2bo$3b3o5b18o6b3o$3b3o5b17o7b3o$
3b3o5bo14b2o7b3o$3b3o20b2o7b3o$3b3o20b2o7b3o$3b3o20b2o7b3o$3b3o19b3o7b
3o$3b3o21b4o4b3o$3b3o21b3o5b3o$3b3o14b4o3b3o2bo2b3o$3b3o15b2o4b6o2b3o$
3b3o15b2o4b6o2b3o$3b3o15b8o3bo2b3o$3b3o11b12o6b3o$3b3o12b11o6b3o$o2b3o
12b3o7bo6b3o$6o5b4o3b3o2bo11b3o$6o2bo3b2o4b6o11b3o$o3b5o3b2o4b6o11b3o$
4b5o3b8o3bo5b4o2b3o$4b16o10b2o3b3o$4bo4b11o6bo3b2o3b3o$9b3o7bo6b6o3b3o
$9b3o7bo6b13o$9b3o7b4ob11o$9b3o7b7o6b3o$9b3o2bo2b4o4bo6b3o$9b6o3b3o8bo
2b3o$5bo3b6o3b3o8b6o$5b6o3bo2b4o8b6o38bo2bo$5b6o7b3o8bo3b44o$bo3b6o7b
3o12b47o$b6o3b11o5bo6b46o$b6o3b17o6bo43b2o$bo2b3o3b8o3b6o50b2o$bo2b3o
3bo5b2o3b6o3bo46b2o$b6o9b2o3bo3b6o46b2o$b6o8b4o6b6o45b3o$b6o3bo14b3o2b
o47b4o$bo4b5o14b3o50b3o$6b5o14b3o6b4o40b3o2bo$2bo3b5o14b3o7b2o41b6o$2b
6o2bo14b3o7b2o41b6o$2b6o17b3o7b45o3bo$2bo2b3o17b3o3b49o$2bo2b3o17b3o4b
48o317bo$2b6o17b3o4b3o44b319o$2b6o17b3o4b3o44b319o$2b6o3bo13b3o4b3o44b
319o$2bo4b5o13b3o4b3o44b3o315bo$7b5o13b3o4b3o44b3o$3bo3b5o13b4o3b3o44b
3o$3b6o2bo11b3o6b3o30b4o10b3o2bo$3b6o15b2o6b3o31b2o11b6o$3bo2b3o15b2o
6b3o31b2o11b6o$6b3o15b2o6b3o31b15o3bo$5b4o15b2o6b3o27b19o$8b18o6b3o28b
18o$8b19o5b3o28b3o14bo$4bo3b16o8b3o28b3o$4b6o9bo3bo8b3o28b3o$4b6o22b3o
28b3o$4bo2b3o2b9o11b3o28b3o$7b3o3b2o2b3o2b4o6b3o2bo25b3o$7b3o3b2o2b3o
3b2o7b6o25b3o$7b3o3b7o3b2o7b6o25b3o$6b14o3b11o3bo25b3o$10b24o29b3o$10b
3o7b14o29b3o$10b3o7b3o10bo29b3o$9b5o6b3o40b3o$19b5o39b3o$62b5o6$2b5o
38b5o$3b3o40b3o$3b3o40b3o$3b3o40b4o$3b3o38b3o$3b3o39b2o$3b3o39b2o$3b3o
39b2o$3b3o20bo18b2o$3b3o20b21o$3b3o20b22o$3b3o16bo3b19o$3b3o16b6o13bo
2bo$3b3o16b6o$3b3o16bo2b3o$3b3o19b3o$3b3o18b4o$3b3o21b3o$3b3o21b2o$3b
3o21b2o$3b3o21b2o$3b3o21b2o8bo$3b3o21b11o$3b3o20b12o$3b3o23b9o3bo$3b3o
23bo2bo3b6o$3b3o30b6o$3b3o30b3o2bo$3b3o30b3o2bo$3b3o6b5o19b6o$3b3o7b3o
20b6o$3b3o7b3o20b6o$3b3o7b24o4bo$3b3o3b28o$3b3o4b3o3b21o3bo$3b3o4b3o3b
2o17b6o$3b3o4b3o3b2o17b6o$3b3o4b3o2b4o16b3o2bo$3b3o4b3o22b3o$3b3o4b3o
22b3o$3b3o4b3o22b4o$3b3o4b3o20b3o$3b3o4b3o21b2o$3b3o4b3o21b2o$3b3o4b3o
21b2o$3b3o4b3o12bo8b2o$3b3o4b3o12b11o$3b3o4b3o12b12o$3b3o4b3o8bo3b9o$
3b3o4b3o8b6o6bo$3b3o4b3o8b6o$3b3o4b3o8bo2b3o$3b3o4b3o11b3o$3b3o4b3o10b
4o$3b3o4b3o13b3o$3b3o4b3o13b2o$3b3o4b3o13b2o$3b3o4b3o13b2o$3b3o4b3o13b
2o8bo$3b3o4b3o13b11o$3b3o4b3o12b12o$3b3obo2b3o15b9o3bo$3b3ob6o15bo6b6o
$3b3ob6o9bo2bo9b6o$3b3obo3b15o9b3o2bo$3b3o5b18o6b3o$3b3o5b17o7b3o$3b3o
5bo14b2o7b3o$3b3o20b2o7b3o$3b3o20b2o7b3o$3b3o20b2o7b3o$3b3o19b3o7b3o$
3b3o21b4o4b3o$3b3o21b3o5b3o$3b3o14b4o3b3o2bo2b3o$3b3o15b2o4b6o2b3o$3b
3o15b2o4b6o2b3o$3b3o15b8o3bo2b3o$3b3o11b12o6b3o$3b3o12b11o6b3o$o2b3o
12b3o7bo6b3o$6o5b4o3b3o2bo11b3o$6o2bo3b2o4b6o11b3o$o3b5o3b2o4b6o11b3o$
4b5o3b8o3bo5b4o2b3o$4b16o10b2o3b3o$4bo4b11o6bo3b2o3b3o$9b3o7bo6b6o3b3o
$9b3o7bo6b13o$9b3o7b16o$9b3o7b7o6b3o$9b3o2bo2b4o4bo6b3o$9b6o3b3o8bo2b
3o$5bo3b6o3b3o8b6o$5b6o3bo2b4o8b6o38bo2bo$5b6o7b3o8bo3b44o$bo3b6o7b3o
12b47o$b6o3b11o5bo6b46o$b6o3b17o6bo43b2o$bo2b3o3b8o3b6o50b2o$bo2b3o3bo
5b2o3b6o3bo46b2o$b6o9b2o3bo3b6o46b2o$b6o8b4o6b6o45b3o$b6o3bo14b3o2bo
47b4o$bo4b5o14b3o50b3o$6b5o14b3o6b4o40b3o2bo$2bo3b5o14b3o7b2o41b6o$2b
6o2bo14b3o7b2o41b6o$2b6o17b3o7b45o3bo$2bo2b3o17b3o3b49o$2bo2b3o17b3o4b
48o317bo$2b6o17b3o4b3o44b319o$2b6o17b3o4b3o44b319o$2b6o3bo13b3o4b3o44b
319o$2bo4b5o13b3o4b3o44b3o315bo$7b5o13b3o4b3o44b3o$3bo3b5o13b4o3b3o44b
3o$3b6o2bo11b3o6b3o30b4o10b3o2bo$3b6o15b2o6b3o31b2o11b6o$3bo2b3o15b2o
6b3o31b2o11b6o$6b3o15b2o6b3o31b15o3bo$5b4o15b2o6b3o27b19o$8b18o6b3o28b
18o$8b19o5b3o28b3o14bo$4bo3b16o8b3o28b3o$4b6o9bo3bo8b3o28b3o$4b6o22b3o
28b3o$4bo2b3o2b9o11b3o28b3o$7b3o3b2o2b3o2b4o6b3o2bo25b3o$7b3o3b2o2b3o
3b2o7b6o25b3o$7b3o3b7o3b2o7b6o25b3o$6b14o3b11o3bo25b3o$10b24o29b3o$10b
3o7b14o29b3o$10b3o7b3o10bo29b3o$9b5o6b3o40b3o$19b5o39b3o$62b5o!