Glider circuits: components and contraptions

PM 2Ring · Post by **PM 2Ring** » April 3rd, 2010, 2:48 am

calcyman wrote:
Collatz sequence generator
I am absolutely stunned! You've probably found more uses for that adder circuit than anyone else.

Thanks, calcyman! It's fun building these things, and actually I'm a little surprised that there aren't more patterns floating around that use that adder circuit.

From what I can see, it appears to operate in binary, with a LWSS read-out device at the top of the pattern. I guess that tripling a number is accomplished by shift addition, whereas halving a number is a simple binary shift.

Yes. Binary shifting is easy, and can generally be performed by a simple delay (although some of my circuits have used the inline advancer). The adder circuit is used to add n & 2n+1, the 2n+1 is formed by inserting a copy of the parity bit (which is the LSB of n) in front of n. That was rather tricky to synchronize in space and time.

What are you using the bistable switch for?

It's part of the switchable glider reflector subsystem. If n is odd, the reflector gets turned on before the data arrives, and it needs to be turned off before the next cycle. The reflector gets turned on by one copy of the parity bit, and it's essentially turned off with another copy. A delay circuit of period around 7000 would be too large (although I did build a pretty Herschel based one), so instead I use the bistable switch as a simple 1 bit memory.

A copy of the parity bit sets the switch (from block to boat), so when the reflector reset bit arrives from the p7680 gun in the southeast corner it get's reflected by the switch into the p60 stream that controls the switchable p60 LWSS gun that is the heart of the switchable glider reflector. If the bistable switch is off, the reset bit travels through the switch & hits an eater.

The switchable glider reflector is a toggle switch, so attempting to turn it on when it's already on will turn it off, and vice versa. The former would never happen in this application, since an odd number in the Collatz sequence must always be followed by an even one. But it's nice to make these things work properly.

I'm sure there are other applications for a mechanism that converts a toggle switch into one with separate on & off inputs.

That's very compact as well; if I attempted to make such a device, it would have been larger than 20000 * 20000.

Your computation-oriented structures do tend to be very large!

I think I need to upgrade Golly (& my OS) before I can play with your recent constructions. I'd love to see how your efforts at display circuitry are going.

I suppose I could've made my Collatz generator a little bit smaller, but once I realized the period was going to be around 7000, I decided to make it p7680 so I could use that very compact p7680 glider gun. And so I didn't bother optimizing the space that much, and besides, I needed some space for all those Buckaroos that were required to get the glider spacing & timing correct.

It's a shame that your device only has finite memory. Since you like p30-oriented technology so much, I recommend that you have a look at Paul Callahan's extensible delay-line memory:
[...]
The data is contained in a loop of MWSSes, which circulate between two eaters. LWSSes can be launched to extend the delay-line memory, in order to accommodate more bits. I'd like to see a pattern exploting this beautiful mechanism; you might be the first to use it in an arithmetic/logic circuit.

Alternatively, you might want to use sliding-block memory, but I think that delay-line memory is more suited to your style of computation.

Thanks for that! I'll certainly play around with it, and see what I can do with it. I've looked at the sliding-block memory, but you're right, it's not my style. It's too bulky, and I prefer to work with bitstrings. OTOH, I do have a soft spot for any reactions that push, pull, or otherwise transform still-lifes, as you may have noticed from my avatar.

TLUL · Post by **TLUL** » May 24th, 2010, 2:49 am

calcyman wrote: It's a shame that your device only has finite memory. Since you like p30-oriented technology so much, I recommend that you have a look at Paul Callahan's extensible delay-line memory: