ConwayLife.com

It's maybe worth noting that a few other rules can be expressed as linear maps over other rings however. For example, looking at 1d cell automata, the state transition for rule 90 is a linear map over the field with two elements. For that rule, any initial state can be viewed as a xor sum of single-...

Would it be possible to add a mode with multipliable commands like in vim, where pressing something like 5, rightarrow, would move the selection right by 5 steps ?

The totalistic step is a linear map on the other hand. Convolution with the kernel [1 1 1; 1 0 1; 1 1 1] . Followed by a very nonlinear elementwise operation (mapping 2 or 3 to one and other values to zero), and is what many of the 1-line code golf variants you'll see on the internet do. Mapping 2 o...

This Herschel period doubler can be heisenburped in one of the two states: x = 256, y = 188, rule = B3/S23 22$232bo$232b3o$235bo$64bo169b2o$64b3o155b2o$67bo155bo$66b2o155bobo$ 54b2o168b2o$55bo$55bobo$56b2o4$224bo$224bobo$224b3o$56bo169bo$56bobo8b 2o$56b3o8b2o$58bo2$217b2o$218bo$215b3o$49b2o164bo17b2...

Bandersnach Glider throws a fit and refuses to go in the direction of the arrow. Maybe this can be used to efficiently unmake one with gliders? x = 62, y = 48, rule = B3/S23 5$45bo$44bobo$20bo23bobo$21b2o20b2ob3o$20b2o9b2o16bo$31b2o10b2ob3o$43b 2obo7$46b2o$37bo8b2o$36bobo$36bo2bo$37b2o$20b2o$19bobo$...

Ah, thanks for the pointers. The github contains some really impressive work, including a very small true p64 gun which is almost as compact as the p256 gun. I'm adding it to the OP. (Incidentally, while we are mentioning documentation: right now the best lifewiki page to hit up for a list of condui...

Circuitry with power-of-two periods are generally more hashlife-friendly, assuming a vanilla HL implementation which hashes power-of-two time evolutions of its metacell interiors. Every period halvening should allow Hashlife to reach its maximal efficiency one level deeper into its tree and somewhat...

Ah, meant beehive.

Also, that pi eater is amazing and exactly what I needed, thanks! It significantly reduced the repeat time of my stable circuits, and made shorter periods viable.

Is there any pi eater that has similar good clearance to Gosper's 2-block pi-eater, but eats it faster? There's mentions of other pi eaters on the forums every so often, but it tends to be in the context of conduits that use space all around the pi. I have a glider collision setup that generates Pi'...

This configuration produces a queen bee, with a junk honeycomb. Seems mostly useless because the process is dirty enough that you're not really able to build an eater or a second shuttle in time at the active end. On the other hand, you see a huge number of pi descendents in the reaction, which migh...

And just for completeness, here's the version where the output that makes it out is the Controlled NXOR of the side outputs. That is, (Not XOR of side inputs) AND center control input: x = 150, y = 110, rule = B3/S23 19$132bo$130b2o$131b2o8$101bobo$101b2obo$104b3o$101b2o4bo$101bob5o$ 103bo$92bobo7bo...

I came up with this stable controlled half-adder. Center input (as herschel predecessor) is the control bit, the other two are the input to the CNOR and CXOR. Also has an additional pi output when the input is 011 (i.e. with control bit on, pi output is (not A) and B ), a third backwards (A and B) g...

Also, just in case some future person ends up on this thread while googling for a quick clock, here's what I eventually ended up with (p256 gun variant). It counts generations up to 2^30, registers overflow, semi-cenarks are power-of-two aligned in order to be hashlife friendly, and can easily be ex...

Thanks! Ended up building a binary clock using a simkin glider gun and a string of semi-cenarks. Works like a charm. Also built one with a p256 gun to have on on hand for cases where I want a pure power-of-two clock.

I'm playing around with various exponential-speedup algorithm and occasionally have issues figuring out exactly by how many generations I've advanced my pattern. Is there a good pattern to count the number of generations that have passed, without using escaping spaceships? For example, maybe some he...