New growth type

[Dr. Monstaa]

Starting work on a single engined rake that fires gliders to a 2-engined pattern that duplicates and/or reflects the gliders to go into a 4-engined pattern which again, duplicates and/or reflects gliders into an 8-engined pattern and eventually go as far as this likes.

Looking at a graph of cells-generations it should end up as quadratic but made up as a linear graph. I'll call this linear-quadratic growth.

As far as I know this has not been done before and if anyone has any parts for this please post

[Dr. Monstaa]

Oh, and while i'm on the subject of rakes, does anyone have a tagalong that makes the shapeship it follows a rake?

[p46beth]

If you were hoping for the duplication to continue indefinetly, that would make it exponential growth, which is impossible. If it stopped after the kth duplication, for some finite k, it would ultimately just be linear growth. Still, it would make a cool rake.

[Wojowu]

Could you put some rle of your pattern? I don't understand what you mean in your pattern

[Dr. Monstaa]

If you were hoping for the duplication to continue indefinetly, that would make it exponential growth, which is impossible

What I'm saying is that this can continue as long as it likes anyone could limit it at anything

Could you put some rle of your pattern? I don't understand what you mean in your pattern

Haven't made it yet. The point of the post was to get someone to help

[calcyman]

If you were hoping for the duplication to continue indefinetly, that would make it exponential growth

Not if the generation time increases exponentially, in which case it would be ordinary polynomial growth.

[Wojowu]

If you were hoping for the duplication to continue indefinetly, that would make it exponential growth

Not if the generation time increases exponentially, in which case it would be ordinary polynomial growth.

If distance between such engines will grow linearly will generation time grow exponentially? If so, if we know glider synthesis of our pattern we can make backward Cordership rakes running in two opposite directions, and 2 gliders bumping between them in such way, that gliders hitting Corderships will be reversed and will start chain reaction which produces two glider salvos into middle of pattern, which produces copy of our Corderships and gliders. Only thing to do is shifting patterns in such way that they don't interact

[Dr. Monstaa]

If you were hoping for the duplication to continue indefinetly, that would make it exponential growth

Not if the generation time increases exponentially, in which case it would be ordinary polynomial growth.

If distance between such engines will grow linearly will generation time grow exponentially? If so, if we know glider synthesis of our pattern we can make backward Cordership rakes running in two opposite directions, and 2 gliders bumping between them in such way, that gliders hitting Corderships will be reversed and will start chain reaction which produces two glider salvos into middle of pattern, which produces copy of our Corderships and gliders. Only thing to do is shifting patterns in such way that they don't interact

The distance between the engines ideally shouldn't grow....

Idea is interesting but I personally would like more details or if my preferences hinder your mechanism we can design new one.

Anyway a suitable first rake can be most, if not any from Golly.

[p46beth]

If distance between such engines will grow linearly will generation time grow exponentially?

No, the generation time would only grow polynomialy.

The distance between the engines ideally shouldn't grow....

Well if the engines are identical, then it will have to grow, or else we would get exponential growth.

[Wojowu]

But in this pattern each glider flight takes two times more time than before, so isn't that exponential growth of generation time?

Code: Select all

x = 131, y = 128, rule = B3/S23
88b2o$89bo$89bobo5b2o$90b2o5bo2bo$81b2o18bo9bobo$81b2o18bo7bo3bo$67bo
10b2o21bo7bo$67bobo7b3o17bo2bo7bo4bo8b2o$70b2o6b2o17b2o10bo12b2o$56b2o
12b2o9b2o5b2o19bo3bo$56b2o12b2o9b2o5bobo9bobo8bobo$67bobo20bo9b2o$67bo
11bo10b2o9bo$77bobo$78b2o4$106bo$105b2o$105bobo2$95b2o21b2o$96bo21bobo
$96bobo9bo4b2o6bo7b2o$97b2o8bobo2bo2bo2bo2bo7b2o$107b2obob3o6bo$107b2o
b2o6bobo$107b2obo7b2o$107bobo$108bo31$22b2o$22b2o6$35bob2o$14b2o14bo2b
obob2o$14b2o13bo3bo2bo$30bo6bobo$31bo5bo$29bo$29bo12bo$44b2o$41b2ob2o$
6b2o35bo$6b2o36b2o2$43b2o2$41bo$42bobo$39b2o2bo4$b3o$3bo16b2o$bo19b2o$
3bo16bo$b3o$b2o$2bo58bob2o$b3o52bo2bobob2o$o3b3o48bo3bo2bo$5b2o49bo6bo
bo$5b2o50bo5bo$2bo21bobo28bo12b2o$2bo22bob2o3b2o21bo12b2o$2bo18b2o3b2o
b5o$21b2o3bobob2obo$20bo2b2obo4b3o10bo$21bobobo7bo9bobo$21bobo18bo3bo$
42bo2bo$42bo2bo14b2o$42bobo15b2o$13b3o$13b3o$15bo$16bo2b2ob2o$10b3o3b
4o3bo$16bob2obobo3b3o$15bo13bo15bo6b2o$27bo16b3o5b2o$29bo14bo2bo$27b3o
16bo$27b2o15b3o$28bo15b3o$27b3o15bo$26bo3b3o11b2o$31b2o12b2o$31b2o$28b
o$28bo$28bo!

(pattern is part of Fermat primes calculator)

[p46beth]

"Exponential generation time" is not clearly defined. Usually, we say something has exponential growth with respect to time, so generation will always increase linearly. It the pattern you just posted, the time between new gliders being fired increases exponentially...so the population exhibits logarithmic growth.

[Wojowu]

Code: Select all

x = 158, y = 168, rule = B3/S23
94bo$86b3o3b4o$86bobo3b2ob2o$86b3o2bo$91b2o3bo$92b4o$93b3o10b2o$106b2o
7$114b2o$101bo12b2o$90b2o9b3o$89bobobo7b3o$89bo3b2o5bo3bo$90b2o8b4o$
90b3o7bob2o3$80bo6b2o$79bobo3bo3bo$78bo3bobo3b2o$79bobo2bobob2o$80bo3b
o2b2o$84bo4bo$85bo2bo$64bo22bo$56b3o3b4o$56bobo3b2ob2o$56b3o2bo$61b2o
3bo$62b4o$63b3o10b2o$76b2o3$78b2obo$78bo4bo$78bo5bo$81bo2bo$80bo2b2o$
71bo7bo2bo$60b2o9b3o6bobo$59bobobo7b3o$59bo3b2o5bo3bo$60b2o8b4o6b2o$
60b3o7bob2o4b2o2bo$79bob2o$76b2ob2o$76b3o$76bo67b2o$76b2o2bo63b2o$32b
5o7bo19b2o11b3o$30b2o5b2o4bobo18b2o11b2o$30bo7bo4bo$30b2o7bo3bo2bo28bo
$32b2o6bo3b3o26b3o$35bo36bo2bo$35bo4bo13b2o17bo2bo53b2o9b2o2bo6b2o$36b
2obo14b2o18bobo54b2o8bobob3o4b2o$74b3o53bo14bobo$136b3o$134bob2o$134bo
2b2o$134b2obo$135b2o$51bo3bo6b2o71bo$49bo2bob3o5b2o$52bobobo$40bobo7bo
81bo$34b2o4b3obob2ob2o79bo2bo14bob2o$34b2o6bo2b2o3bobo3bo90bo4bo$50bob
o76bo22bo$38b2o91b2o8b3o3bo6b2o$26b3o8b4o100bo2bo3bo7b2o$24b7o5b2o2bo
103bo4bo7bo$23b9o3bob3o102bobo4b2o5b2o$22bo7b3o3b2obo88bo14bo7b5o$23b
3o6bo54b3o39bo$24b2o43bo17bo42bo$27bo42bo17bo43b2o$28bo39b3o54bo6b3o$
2b5o7bo14bo88bob2o3b3o7bo$2o5b2o4bobo102b3obo3b9o$o7bo4bo103bo2b2o5b7o
$2o7bo3bo2bo100b4o8b3o$2b2o6bo3b3o8b2o91b2o$5bo22bo76bobo$5bo4bo90bo3b
obo3b2o2bo6b2o$6b2obo14bo2bo79b2ob2obob3o4b2o$25bo81bo7bobo$101bobobo$
94b2o5b3obo2bo$22bo71b2o6bo3bo$21b2o$20bob2o$19b2o2bo$20b2obo$19b3o$
10bobo14bo53b3o$4b2o4b3obobo8b2o54bobo18b2o14bob2o$4b2o6bo2b2o9b2o53bo
2bo17b2o13bo4bo$82bo2bo36bo$82b3o26b3o3bo6b2o$82bo28bo2bo3bo7b2o$114bo
4bo7bo$79b2o11b2o18bobo4b2o5b2o$78b3o11b2o19bo7b5o$12b2o63bo2b2o$12b2o
67bo$79b3o$77b2ob2o$75b2obo$75bo2b2o4b2obo7b3o$76b2o6b4o8b2o$83bo3bo5b
2o3bo$84b3o7bobobo$75bobo6b3o9b2o$75bo2bo7bo$73b2o2bo$73bo2bo$73bo5bo$
74bo4bo$76bob2o3$80b2o$80b2o10b3o$92b4o$91bo3b2o$96bo2b3o$91b2ob2o3bob
o$92b4o3b3o$70bo22bo$69bo2bo$68bo4bo$69b2o2bo3bo$68b2obobo2bobo$68b2o
3bobo3bo$68bo3bo3bobo$69b2o6bo3$54b2obo7b3o$54b4o8b2o$53bo3bo5b2o3bo$
54b3o7bobobo$54b3o9b2o$42b2o12bo$42b2o7$50b2o$50b2o10b3o$62b4o$61bo3b
2o$66bo2b3o$61b2ob2o3bobo$62b4o3b3o$63bo!

Consider that we are changing this pattern (loggrow.rle from Golly pattern library) in such way that instead of shotting gliders in opposite directions (NE and SW) it shots two glider salvos in same direction (NE for example) or two *WSS salvos into same point (E and N for example) to construct our copy of modified pattern and shift our first pattern to SW to not allow salvo pairs to collide. If it is impossible to prevent collisions for infinite time I'm almost sure we could move it as far as we want so we can stop cloning after any number of generations

[Dr. Monstaa]

Code: Select all

x = 158, y = 168, rule = B3/S23
94bo$86b3o3b4o$86bobo3b2ob2o$86b3o2bo$91b2o3bo$92b4o$93b3o10b2o$106b2o
7$114b2o$101bo12b2o$90b2o9b3o$89bobobo7b3o$89bo3b2o5bo3bo$90b2o8b4o$
90b3o7bob2o3$80bo6b2o$79bobo3bo3bo$78bo3bobo3b2o$79bobo2bobob2o$80bo3b
o2b2o$84bo4bo$85bo2bo$64bo22bo$56b3o3b4o$56bobo3b2ob2o$56b3o2bo$61b2o
3bo$62b4o$63b3o10b2o$76b2o3$78b2obo$78bo4bo$78bo5bo$81bo2bo$80bo2b2o$
71bo7bo2bo$60b2o9b3o6bobo$59bobobo7b3o$59bo3b2o5bo3bo$60b2o8b4o6b2o$
60b3o7bob2o4b2o2bo$79bob2o$76b2ob2o$76b3o$76bo67b2o$76b2o2bo63b2o$32b
5o7bo19b2o11b3o$30b2o5b2o4bobo18b2o11b2o$30bo7bo4bo$30b2o7bo3bo2bo28bo
$32b2o6bo3b3o26b3o$35bo36bo2bo$35bo4bo13b2o17bo2bo53b2o9b2o2bo6b2o$36b
2obo14b2o18bobo54b2o8bobob3o4b2o$74b3o53bo14bobo$136b3o$134bob2o$134bo
2b2o$134b2obo$135b2o$51bo3bo6b2o71bo$49bo2bob3o5b2o$52bobobo$40bobo7bo
81bo$34b2o4b3obob2ob2o79bo2bo14bob2o$34b2o6bo2b2o3bobo3bo90bo4bo$50bob
o76bo22bo$38b2o91b2o8b3o3bo6b2o$26b3o8b4o100bo2bo3bo7b2o$24b7o5b2o2bo
103bo4bo7bo$23b9o3bob3o102bobo4b2o5b2o$22bo7b3o3b2obo88bo14bo7b5o$23b
3o6bo54b3o39bo$24b2o43bo17bo42bo$27bo42bo17bo43b2o$28bo39b3o54bo6b3o$
2b5o7bo14bo88bob2o3b3o7bo$2o5b2o4bobo102b3obo3b9o$o7bo4bo103bo2b2o5b7o
$2o7bo3bo2bo100b4o8b3o$2b2o6bo3b3o8b2o91b2o$5bo22bo76bobo$5bo4bo90bo3b
obo3b2o2bo6b2o$6b2obo14bo2bo79b2ob2obob3o4b2o$25bo81bo7bobo$101bobobo$
94b2o5b3obo2bo$22bo71b2o6bo3bo$21b2o$20bob2o$19b2o2bo$20b2obo$19b3o$
10bobo14bo53b3o$4b2o4b3obobo8b2o54bobo18b2o14bob2o$4b2o6bo2b2o9b2o53bo
2bo17b2o13bo4bo$82bo2bo36bo$82b3o26b3o3bo6b2o$82bo28bo2bo3bo7b2o$114bo
4bo7bo$79b2o11b2o18bobo4b2o5b2o$78b3o11b2o19bo7b5o$12b2o63bo2b2o$12b2o
67bo$79b3o$77b2ob2o$75b2obo$75bo2b2o4b2obo7b3o$76b2o6b4o8b2o$83bo3bo5b
2o3bo$84b3o7bobobo$75bobo6b3o9b2o$75bo2bo7bo$73b2o2bo$73bo2bo$73bo5bo$
74bo4bo$76bob2o3$80b2o$80b2o10b3o$92b4o$91bo3b2o$96bo2b3o$91b2ob2o3bob
o$92b4o3b3o$70bo22bo$69bo2bo$68bo4bo$69b2o2bo3bo$68b2obobo2bobo$68b2o
3bobo3bo$68bo3bo3bobo$69b2o6bo3$54b2obo7b3o$54b4o8b2o$53bo3bo5b2o3bo$
54b3o7bobobo$54b3o9b2o$42b2o12bo$42b2o7$50b2o$50b2o10b3o$62b4o$61bo3b
2o$66bo2b3o$61b2ob2o3bobo$62b4o3b3o$63bo!

Consider that we are changing this pattern (loggrow.rle from Golly pattern library) in such way that instead of shotting gliders in opposite directions (NE and SW) it shots two glider salvos in same direction (NE for example) or two *WSS salvos into same point (E and N for example) to construct our copy of modified pattern and shift our first pattern to SW to not allow salvo pairs to collide. If it is impossible to prevent collisions for infinite time I'm almost sure we could move it as far as we want so we can stop cloning after any number of generations

Intersting. I'm going to work on that.

[Wojowu]

I've made 17-state automata which represents my idea. Save as Expgrowth.table

Code: Select all

n_states:17
neighborhood:Moore
symmetries:none
var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}
9,a,b,c,d,4,f,g,h,3
10,6,b,c,d,e,f,g,h,5
0,1,b,c,d,4,f,g,h,3
0,6,b,c,d,2,f,g,h,5
3,0,0,0,0,7,0,0,0,0
5,8,0,0,0,0,0,0,0,0
4,a,b,c,d,2,f,g,h,7
6,1,b,c,d,e,f,g,h,8
1,a,b,c,d,2,f,g,h,2
2,1,b,c,d,e,f,g,h,1
1,a,b,c,d,e,f,g,h,0
2,a,b,c,d,e,f,g,h,0
0,1,b,c,d,e,f,g,h,1
0,a,b,c,d,2,f,g,h,2
3,a,b,c,d,e,f,g,h,4
4,a,b,c,d,e,f,g,h,0
5,a,b,c,d,e,f,g,h,6
6,a,b,c,d,e,f,g,h,0
0,a,b,c,d,4,f,g,h,3
0,6,b,c,d,e,f,g,h,5
7,a,b,c,d,e,f,g,h,0
8,a,b,c,d,e,f,g,h,0
0,a,b,3,7,e,f,g,h,9
0,a,8,5,d,e,f,g,h,10
9,a,b,c,d,10,f,g,h,13
10,9,b,c,d,e,f,g,h,14
9,a,b,c,d,e,f,g,h,0
10,a,b,c,d,e,f,g,h,0
0,a,9,10,d,e,f,g,h,0
0,a,b,9,10,e,f,g,h,0
0,a,9,c,d,e,f,g,h,9
0,a,b,c,10,e,f,g,h,10
0,a,b,c,d,e,7,3,h,11
0,a,b,c,d,e,f,5,8,12
0,a,b,c,d,e,f,11,h,3
0,a,b,c,d,e,f,g,11,1
0,a,b,c,d,e,12,g,h,2
0,a,b,c,d,e,f,12,h,5
11,a,b,c,d,e,f,g,h,0
12,a,b,c,d,e,f,g,h,0
0,a,b,c,15,e,f,g,h,3
0,a,b,15,d,e,f,g,h,1
0,a,b,16,d,e,f,g,h,2
0,a,16,c,d,e,f,g,h,5
13,a,b,c,d,e,f,g,h,0
14,a,b,c,d,e,f,g,h,0
15,a,b,c,d,e,f,g,h,0
16,a,b,c,d,e,f,g,h,0
0,a,b,c,13,e,f,g,h,15
0,a,14,c,d,e,f,g,h,16

Seed pattern:

Code: Select all

x = 1, y = 6, rule = Expgrowth
C2$A$B2$E!

Rule table is not ideal, because some state 9 destroy state 4. It is clearly visible that pattern is a breeder, and number of engines grow (I think) like in my idea.
Edit:
Now pattern should work, but I haven't tested that. But if we look Dr. Monstaa first post we can read that he means something different than my idea. If i understand that good, he means array of glider duplicators and something like this: first glider is hitting duplicators, and these two gliders fly away to two different duplicators, and they fly to another duplicators and again and again. This is possible in Life as far as there is finite number of duplicators. I will try to make something like that, but today I don't have enough time. Tomorrow I will try to do it