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Awhile back, I posted a script that converts the three examples you gave (Life, Just Friends, and Callahan's non-totalistic hex rule), but it doesn't convert any arbitrary rule table. It only converts rules that can be expressed in totalistic B/S notation or Hensel's non-totalistic notation. See htt...

Newcomers to this forum may want to know that this rule was also discussed here:
viewtopic.php?f=11&t=949

(And the problem of reversed states was discussed there as well!)

Yes, I meant to change the 2nd order reversible rule script but I accidentally changed the 2 state version instead. I think everything is changed the way it should be now. I'd be very interested in hearing about the larger context of your work. Are you trying to describe the entire universe or are y...

About the states, good point! Thanks. I edited the script and Alexander's snakes rule above so that state 2 and state 3 are swapped. For fun, here's a hexagonal version. It is adapted from the non-totalistic hexagonal script for two state rules posted here: http://www.conwaylife.com/forums/viewtopic...

If anyone reading this thread is utterly perplexed by what is going on, you might find it helpful to compare Wolfram's Rule 214 with Wolfram's description of the 2nd order technique applied to rule 214. That's what helped me figure it out! Wolfram's elementary CA Rule 214: http://atlas.wolfram.com/0...

Using the script, I found an interesting simplification of your ant rules. My guess is that you already discovered it(!), but maybe someone else will find it interesting. The rule is B1e/S1e (or, in other words, the rule is B1/S1 in the von Neuman neighborhood, so Hensel's notation is overkill for t...

And here's almost the exact same script, but slightly modified at the bottom, so that it uses the 2nd order technique to produce a four state reversible CA rule for Golly: # Reversible2ndOrder.py # by Eric Goldstein, March 7, 2014 # All but a few lines of this code are from HenselNotation->WeightedL...

To play with Hensel's notation using Golly, here's a script that accepts Hensel's notation and outputs the corresponding the two state CA. Again, just to be clear, this one produces two state CAs - it is just to show how Hensel's notation works: # HenselNotation->WeightedLife2.0.py # by Eric Goldste...

Alexander, Thank you very much for slow ants! From a game of life perspective, slow ants is my favorite rule of the bunch, since it doesn't explode quite as easily. I look forward to playing with it. But it raises questions for me! Do you hope to someday see these ant rules implemented physically as...

I just wanted to post some feedback: this has been a terrific thread!

Alex, when you feel ready, it would be great to see Slow Ants (SlAnt).

Here's a puffer that produces p999s: x = 131, y = 95, rule = B2/S1H/C3 3.2A.B$3.2A$3AB2.A$A2B3.B$2.B.A2.B$A.BA.B3A$A2B2AB.A15.A2.A2.A$.ABA.A .2A14.2B6A$5.A.2A12.B.ABA5.A$4.2A3.A17.2A2BA$5.A3.B11.B.B3.B4A$5.A2.A .A15.A$5.2A2.2BA13.A2BA$6.2A2.2B14.A.B$9.2B16.3A$6.A3.B$5.A.A2.2B$4. 2AB.2AB26.A$4.A2.B2....

The script posted here: http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1328&p=11073#p11073 can also be used for Hexagonal Generations rules (unlike the one above, this script makes files in the .rule format rather than .tree). You can input a string with the format B2/S1/C3 to produce a .rule...

"If you find infinite growth in this rule [..] please post immediately." Here you go. This puffer, made from three ships, makes the p4 oscillator. x = 77, y = 85, rule = Hex_B2_S1_C3 3.2A$3.3BA$3.AB.BA$ABA2.3B$A2B.A2B$.B.2B2.A$.A3B2.B$2.AB.ABA$11.2A.B$ 12.B$12.ABA$13.ABA$14.ABA$13.A2.A$13.AB2A$15.A1...

Paul Callahan's original essay which explains his non-totalistic notation can be found here:
http://www.mirekw.com/ca/files/hexrule.txt

c0b0p0 , I'm glad to see people experimenting with rules related to Callahan's hex rule, and sharing their results! Awhile back, I was interested in extending Callahan's non-totalistic hexagonal rule notation so that it applies to more than just two neighbors. I tried out the following: ExtendedCall...

Here's a Golly script for hexagonal generations I posted awhile back: http://www.conwaylife.com/forums/viewtopic.php?f=9&t=933#p6818 Edit: I just remembered: the script should be updated for the new .rule format, and could also benefit from using hexagonal icons. Unfortunately no time for that just ...

If you need further help, have a look at:
viewtopic.php?f=9&t=826
and
viewtopic.php?f=9&t=828

There has already been work done with this rule and very closely related rules which support the oblique spaceship, and many of the other patterns described above, See this link: http://www.conwaylife.com/forums/viewtopic.php?f=11&t=861 <-- click It describes the "9:43 at Knight" rule (237/34578/4)....

Breeder 1: Here's a 5c/12 speed breeder - it leaves behind Slowships which form 5c/12-producing rakes: x = 134, y = 588, rule = 23567/358/4 3.C8.A.A$12.4A$11.B2A.A$11.2ABA$13.A4$3.A15.A$.B3AB11.5A3.A$A2CA2CA 10.AB.BA2.A.A$BAB.BAB10.ABABA3.A$A2C.2CA11.2A$.B3AB12.2AC$2.3A14.CB$ 10.A$9.AB2A3.2A$9.AB.2A...

5c/12 ships can reflect off the Slowship resulting in each ship changing direction! For example, here a 5c/12 ship and Slowship travel towards each other, collide, and each ship reverses direction without damage or uncleaned up debris: x = 63, y = 93, rule = 23567/358/4 17$37.B$36.C.C$41.2A$42.A$42....

The Slowship itself is fantastic -- play around with its sparks and you'll keep finding new tricks for them. For starters, Slowships can be used to make rakes firing in all directions, and they can be used as moving reflectors and splitters and eaters. In the pattern below, Slowships are used to mak...

The slowship rules also have a rather amazing p85 mega oscillator I call the "The Chomper" (you'll see why). Chompers can be used to make shuttles (it reflects 5c/12 ships 180 degrees), loops (it reflects 90 degrees), and guns. Here are two p2040 guns. The first gun uses shuttles and 2nd-order shutt...

The slowship rules have a p7 oscillator which works as both a reflector and an eater. Two shuttles can interact with a tub to create a "tub gun". Here are four patterns to illustrate. Top pattern: a tub gun. Second pattern: a tub gun + eater. Third pattern: Multiple tubs to make a "machine gun". Fou...

I have *a lot* of patterns for this rule, and for other rules that support the 5c/12 spaceship. I hardly know where to start! The 5c/12 bullet ship rules come in four groups: 1st group: 2356/35/4 + B7 or B8 or B78 includes the original rule found by Tropylium which supports an orthogonal p72 tumbler...

Towerator, Yup, I love that rule. Earlier in this tread, Tropylium introduced 2356/357/4 and suggested it would be a good rule for engineering. I had so much fun thanks to that suggestion! Thanks Tropylium! I spent a couple of weeks with 2356/357/4 and with some related rules which support the 5c/12...