Thread for your fractal-related discoveries in OCA

[CARuler]

This is a Thread for any fractal-related discoveries you happen you make, for example:

Code: Select all

x = 1, y = 1, rule = M15,8,4,3,2,5,9,14,1,6,10,13,12,11,7,0
o!

edit; relevance clearer

[confocaloid]

How about using forum search? search.php?keywords=fractal

viewtopic.php?f=7&t=90 "Life Imitates Sierpinski"

viewtopic.php?p=98355#p98355 "Fractal thread" (merged into Random posts, which was later locked due to being high-volume and low-effort)

This is a Thread for any fractal-related discoveries you happen yo make, for example:

Code: Select all

x = 1, y = 1, rule = M15,8,4,3,2,5,9,14,1,6,10,13,12,11,7,0
o!

Unless the title says explicitly "CA-related" or something to the same effect, this is offtopic in the OCA subforum. Could belong to Sandbox.

If it is supposed to be for CA-related fractals only, then it is unclear what is the advantage of having this as a separate thread (as opposed to posting in the existing MDiOCA thread and saying "fractal" in the post while describing the posted pattern). Forum search will work to find all such posts anyway.

[CARuler]

Code: Select all

x = 3, y = 2, rule = B1c2a3i/S01c2ckn3-r45678
3o$obo!

Code: Select all

x = 3, y = 2, rule = B1c2a3i/S01c2ckn3-r45678
3o$obb!

Edit:
similar:

Code: Select all

x = 3, y = 2, rule = B1c2a3i/S01c3-r45678
3o$bo!

[eRroR_6o6]

bruh i just wanted to create a circuitry rule what is this

Code: Select all

x = 1, y = 1, rule = circuitry_attempt
A!
@RULE circuitry_attempt

@TABLE

n_states:3
neighborhood:vonNeumann
symmetries: rotate4reflect
var a1 = {0,1,2}
var a2 = {0,1,2}
var a3 = {0,1,2}
var a4 = {0,1,2}


0,1,2,0,0,2
0,1,0,0,0,1
1,a1,a2,a3,a4,2
2,1,2,2,0,0
2,2,0,0,0,0

[CARuler]

bruh i just wanted to create a circuitry rule what is this

Code: Select all

x = 1, y = 1, rule = circuitry_attempt
A!
@RULE circuitry_attempt

@TABLE

n_states:3
neighborhood:vonNeumann
symmetries: rotate4reflect
var a1 = {0,1,2}
var a2 = {0,1,2}
var a3 = {0,1,2}
var a4 = {0,1,2}


0,1,2,0,0,2
0,1,0,0,0,1
1,a1,a2,a3,a4,2
2,1,2,2,0,0
2,2,0,0,0,0

a bit like it

Code: Select all

x = 1, y = 1, rule = B1e2a/S012345678
o!

[eRroR_6o6]

The heck?

(lifeviewer doesn't let me name this for some reason lol)

Code: Select all

x = 2, y = 12, rule = whoops
B9$.A$.A$.B!

@RULE whoops

@TABLE

n_states:3
neighborhood:Moore
symmetries: rotate4reflect
var a1 = {0,1,2}
var a2 = {0,1,2}
var a3 = {0,1,2}
var a4 = {0,1,2}
var a5 = {0,1,2}
var a6 = {0,1,2}
var a7 = {0,1,2}
var a8 = {0,1,2}
var b1 = {0,2}
var b2 = {0,2}
var b3 = {0,2}
var b4 = {0,2}
var b5 = {0,2}
var b6 = {0,2}
var b7 = {0,2}
var b8 = {0,2}

0,1,0,0,0,0,0,0,0,1
2,0,a1,0,0,0,0,0,0,2
1,1,0,0,0,0,0,0,0,1
1,2,0,0,0,0,0,0,0,1
2,2,0,0,0,0,0,0,0,2
2,1,0,0,0,0,0,0,0,0
2,1,0,0,0,2,0,0,0,0
0,0,0,0,0,1,0,0,2,1
0,1,0,2,0,0,0,0,0,1
1,0,0,0,0,1,0,0,2,1
0,1,2,0,0,0,0,0,0,1
1,a1,a2,a3,a4,a5,a6,a7,a8,2
2,b1,b2,b3,b4,b5,b6,b7,b8,0
[code]

[CARuler]

looks like some sort of self-inverting Sierpiński triangle

[CARuler]

Code: Select all

x = 3, y = 3, rule = R2INT(base)
.2A$2A$.2A!



@RULE R2INT(base)
@COLORS
 0 255 255   0   0 255
1 255 255 255
@NAMES
0 dead
1 alive
@TABLE
n_states:102
neighborhood:Moore
symmetries:rotate4reflect
var al = {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
var al1 = al
var al2 = al
var al3 = al
var al4 = al
var al5 = al
var al6 = al
var al7 = al
var al8 = al
var all = {1,al}
var a = {0,all}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var s0 = {2}
var s1c = {3}
var s1e = {4}
var s2c = {5}
var s2e = {6}
var s2a = {7}
var s2k = {8}
var s2i = {9}
var s2n = {10}
var s3c = {11}
var s3e = {12}
var s3a = {13}
var s3k = {14}
var s3i = {15}
var s3n = {16}
var s3y = {17}
var s3q = {18}
var s3j = {19}
var s3r = {20}
var s4c = {21}
var s4e = {22}
var s4a = {23}
var s4k = {24}
var s4i = {25}
var s4n = {26}
var s4y = {27}
var s4q = {28}
var s4j = {29}
var s4r = {30}
var s4t = {31}
var s4w = {32}
var s4z = {33}
var s5c = {34}
var s5e = {35}
var s5a = {36}
var s5k = {37}
var s5i = {38}
var s5n = {39}
var s5y = {40}
var s5q = {41}
var s5j = {42}
var s5r = {43}
var s6c = {44}
var s6e = {45}
var s6a = {46}
var s6k = {47}
var s6i = {48}
var s6n = {49}
var s7c = {50}
var s7e = {51}
var b1c = {52}
var b1e = {53}
var b2c = {54}
var b2e = {55}
var b2a = {56}
var b2k = {57}
var b2i = {58}
var b2n = {59}
var b3c = {60}
var b3e = {61}
var b3a = {62}
var b3k = {63}
var b3i = {64}
var b3n = {65}
var b3y = {66}
var b3q = {67}
var b3j = {68}
var b3r = {69}
var b4c = {70}
var b4e = {71}
var b4a = {72}
var b4k = {73}
var b4i = {74}
var b4n = {75}
var b4y = {76}
var b4q = {77}
var b4j = {78}
var b4r = {79}
var b4t = {99}
var b4w = {100}
var b4z = {101}
var b5c = {80}
var b5e = {81}
var b5a = {82}
var b5k = {83}
var b5i = {84}
var b5n = {85}
var b5y = {86}
var b5q = {87}
var b5j = {88}
var b5r = {89}
var b6c = {90}
var b6e = {91}
var b6a = {92}
var b6k = {93}
var b6i = {94}
var b6n = {95}
var b7c = {96}
var b7e = {97}
var b8 = {98}
1,0,0,0,0,0,0,0,0,s0
1,1,0,0,0,0,0,0,0,s1e
1,0,1,0,0,0,0,0,0,s1c
1,0,1,0,1,0,0,0,0,s2c
1,1,0,1,0,0,0,0,0,s2e
1,1,1,0,0,0,0,0,0,s2a
1,1,0,0,1,0,0,0,0,s2k
1,1,0,0,0,1,0,0,0,s2i
1,0,1,0,0,0,1,0,0,s2n
1,0,1,0,1,0,1,0,0,s3c
1,1,0,1,0,1,0,0,0,s3e
1,1,1,1,0,0,0,0,0,s3a
1,1,0,1,0,0,1,0,0,s3k
1,0,1,1,1,0,0,0,0,s3i
1,1,1,0,1,0,0,0,0,s3n
1,1,0,0,1,0,1,0,0,s3y
1,1,1,0,0,0,1,0,0,s3q
1,1,0,1,1,0,0,0,0,s3j
1,1,1,0,0,1,0,0,0,s3r
1,0,1,0,1,0,1,0,1,s4c
1,1,0,1,0,1,0,1,0,s4e
1,1,1,1,1,0,0,0,0,s4a
1,1,0,1,1,0,1,0,0,s4k
1,1,1,0,1,1,0,0,0,s4i
1,0,1,1,1,0,1,0,0,s4n
1,1,1,0,1,0,1,0,0,s4y
1,1,1,1,0,0,1,0,0,s4q
1,1,0,1,0,1,1,0,0,s4j
1,1,1,1,0,1,0,0,0,s4r
1,1,0,0,1,1,1,0,0,s4t
1,0,1,1,0,1,1,0,0,s4w
1,1,1,0,0,1,1,0,0,s4z
1,1,1,1,0,1,0,1,0,s5c
1,0,1,1,1,0,1,0,1,s5e
1,0,1,1,1,1,1,0,0,s5a
1,0,1,1,0,1,1,0,1,s5k
1,1,1,1,1,1,0,0,0,s5i
1,1,1,1,0,1,1,0,0,s5q
1,1,0,1,1,0,1,1,0,s5y
1,0,1,1,1,1,0,1,0,s5n
1,1,1,1,1,0,1,0,0,s5j
1,0,1,1,1,0,1,1,0,s5r
1,1,0,1,1,1,1,1,0,s6c
1,0,1,1,1,1,1,0,1,s6e
1,1,1,1,1,1,1,0,0,s6a
1,1,1,1,1,0,1,1,0,s6k
1,0,1,1,1,0,1,1,1,s6i
1,1,1,1,0,1,1,1,0,s6n
1,0,1,1,1,1,1,1,1,s7e
1,1,1,1,1,1,1,1,0,s7c
0,0,1,0,0,0,0,0,0,b1c
0,1,0,0,0,0,0,0,0,b1e
0,0,1,0,1,0,0,0,0,b2c
0,1,0,1,0,0,0,0,0,b2e
0,1,1,0,0,0,0,0,0,b2a
0,1,0,0,1,0,0,0,0,b2k
0,1,0,0,0,1,0,0,0,b2i
0,0,1,0,0,0,1,0,0,b2n
0,0,1,0,1,0,1,0,0,b3c
0,1,0,1,0,1,0,0,0,b3e
0,1,1,1,0,0,0,0,0,b3a
0,0,1,1,1,0,0,0,0,b3i
0,1,0,1,0,0,1,0,0,b3k
0,1,1,0,1,0,0,0,0,b3n
0,1,0,0,1,0,1,0,0,b3y
0,1,1,0,0,0,1,0,0,b3q
0,1,0,1,1,0,0,0,0,b3j
0,1,1,0,0,1,0,0,0,b3r
0,0,1,0,1,0,1,0,1,b4c
0,1,0,1,0,1,0,1,0,b4e
0,1,1,1,1,0,0,0,0,b4a
0,1,0,1,1,0,1,0,0,b4k
0,1,1,0,1,1,0,0,0,b4i
0,0,1,1,1,0,1,0,0,b4n
0,1,1,0,1,0,1,0,0,b4y
0,1,1,1,0,0,1,0,0,b4q
0,1,0,1,0,1,1,0,0,b4j
0,1,1,1,0,1,0,0,0,b4r
0,1,0,0,1,1,1,0,0,b4t
0,0,1,1,0,1,1,0,0,b4w
0,1,1,0,0,1,1,0,0,b4z
0,1,1,1,0,1,0,1,0,b5c
0,0,1,1,1,0,1,0,1,b5e
0,0,1,1,1,1,1,0,0,b5a
0,0,1,1,0,1,1,0,1,b5k
0,1,1,1,1,1,0,0,0,b5i
0,0,1,1,1,1,0,1,0,b5n
0,1,1,1,0,1,1,0,0,b5q
0,1,1,1,1,0,1,0,0,b5j
0,0,1,1,1,0,1,1,0,b5r
0,1,0,1,1,1,1,1,0,b6c
0,0,1,1,1,1,1,0,1,b6e
0,1,1,1,1,1,1,0,0,b6a
0,1,1,1,1,0,1,1,0,b6k
0,0,1,1,1,0,1,1,1,b6i
0,1,1,1,0,1,1,1,0,b6n
0,0,1,1,1,1,1,1,1,b7e
0,1,1,1,1,1,1,1,0,b7c
0,1,1,1,1,1,1,1,1,b8
1,1,1,1,1,1,1,1,1,1
#transitions
0,0,b1c,b1e,b1c,0,0,0,0,1
b1e,b1c,b3a,s3i,b3a,b1c,0,0,0,1
b1c,b1e,s3i,b3a,b1c,0,0,0,0,1

#defaults
all,a,b,c,d,e,f,g,h,0

[wwei47]

Can things like sierpinki generators and other fractal generators go in here?

[CARuler]

Can things like sierpinki generators and other fractal generators go in here?

yes

[wwei47]

One must remember that replicators and fractals are inextricably linked. I have made some weird fractal generators during my time here, but now I have a dedicated thread for them as opposed to posting them with the replicators themselves, so I'm listing out all the fractal generators that I could find by going through my old posts.

The pascal mod 3 replicator that started it all for me. Linked is a 23-cell generator, which to my knowledge is the smallest known:
viewtopic.php?f=7&t=6518&p=185813&hilit ... an#p185813
Today, I found another 3-engine design, though it has a lot more than 23 cells:

Code: Select all

x = 32, y = 20, rule = B2e35y7e/S1c2ace3an
2o$2bo8bo2bo$2o5bo3b4o3bo$7b2o2bo2bo2b2o$7bo3b4o3bo$11bo2bo3$29b2o$28b
o2bo$29b2o5$26bo2bo$25bo4bo$13bo12bo2bo$12b2o$13bo!

As far as I know, there is one known example of a pascal mod 3 replicator before this, but there is no known generator for it.
viewtopic.php?f=11&t=376&hilit=rep%2A&start=725#p60494

Fractal generators with fractal dimensions of log5(12) and log3(5). Unfortunately, neither are "full density" (one replicator cycle per puffer cycle), due to sparks getting in the way and forcing half density.
viewtopic.php?f=11&t=3752&start=125#p84333

The final edit in this post contained another pascal mod 3 generator, but it is unfortunately pseudo-period.
viewtopic.php?f=11&t=1971&p=64263&hilit ... tor#p64722

The discord link here is dead, but I can now directly attach the file. This one likely isn't really a fractal generator, but it is a generator for a chaotic replicator, so I think I think it's worth listing.

WIP1.mc

(2.12 MiB) Downloaded 167 times

viewtopic.php?f=11&t=1971&p=64759&hilit=rep%2A#p64759
There's also a sierpinski generator in there:

Code: Select all

x = 4, y = 3, rule = B2ek3cei4ckrz5jkny6c8/S1c2cek3acjkn4cjnq5ajy6-ae8
b2o$o2bo$b2o!

This one has a generator for a log4(8)=1.5-dimensional fractal. Unfortunately, it's only quarter density. There's another log3(5) one there, also at quarter density.
viewtopic.php?f=11&t=3752&p=84439&hilit=rep%2A#p84439
It also has a generator that I thought was a noninteger replication order, but actually it's just puffing out two replicators at an offset that somehow doesn't break either of them. When we delete one, it becomes clear that it's just log4(11).

Code: Select all

x = 21, y = 17, rule = B2e3aiky4jnqtwz5cjqry6aei/S1c2-k3ajry4cjkrt5-eqr6i
3o9b3o$bo11bo$bo11bo$3o9b3o$5bo3bo$4bobobobo$4bobobobo$5bo3bo2$19bo$
18bobo$18bobo$19bo2$bo11bo$3o9b3o$obo9bobo!

This post has two pascal mod 5 generators. These give a fractal dimension of log5(15). The first one is full density but the second one has a density of 1/3.
viewtopic.php?f=11&t=3752&p=84439&hilit=rep%2A#p84682

In this post, I improve the second log5(15) generator, and one of the log3(5) generators. In addition, I increased the density of the second generator to half density.
viewtopic.php?f=11&t=3752&p=84439&hilit=rep%2A#p84979

Heavpoot and I massively improve the chaotic replicator generator mentioned earlier.
viewtopic.php?f=11&t=3752&p=101097&hilit=rep%2A#p101097
Today I found an even better solution at 3 engines and 22 cells:

Code: Select all

x = 12, y = 16, rule = B2e3eijkq4j5aey6a8/S1c2aci3a4c5kq6n
7bo$8bo$7bo$bo$obo$9bo$2bo7bo$bo7bo2$7bo2bo$6bo4bo$7bo2bo2$b2o$b2o$2bo
!

Two generators here. One is just an XOR replicator with linear annihilation time, and one is a half density generator with a fractal dimension of log5(13).
viewtopic.php?f=11&t=3752&p=105791&hilit=rep%2A#p105791

Another generator for a chaotic replicator.
viewtopic.php?f=11&t=3752&p=105950&hilit=rep%2A#p105950

viewtopic.php?f=11&t=1971&p=117029&hilit=rep%2A#p117029
Edit 18 appears to have a fractal generator that works like H-trees.

Code: Select all

x = 4, y = 4, rule = B2n35ejkn/S23
3o$o2bo$obo$bo!

EDIT: From digging through Golly 4.3's collection:

This post has a pseudo-pascal mod 4 generator. Dimension is log4(10). It also has a pascal mod 5 generator (log5(15)).
viewtopic.php?p=65074#p65074

This is a reduction of my log5(13) fractal generator by FWKnightship.
viewtopic.php?p=105822#p105822

Edit 2: I have no way of proving whether or not this eventually blows up due to all the colliding spaceships, but this appears to be a pascal-mod-3 spaceship-emitting replicating wave that generates a fractal of dimension log3(4).

Code: Select all

x = 3, y = 3, rule = B3-y4j5cy/S2-in3-ak4n5jqr6cn78
2o$obo$bo!

Edit 3: (5,2)c/19 P152 ship-pair-generating sierpinski replicating wave

Code: Select all

x = 3, y = 3, rule = B3-cqy4j5cy/S2-in3-ak4n5jqr
2o$obo$bo!

Edit 4: Actually made sure to put edit 3's replicator into a code block, and fixed the wording in edit 2.

Edit 5: Another log3(4) fractal generator. Both of these are (5,2)c/19;(-2,-5)c/19, but the first one is P228 while this one is P57.

Code: Select all

x = 3, y = 3, rule = B3-cey4jq5cejy6ek/S2-in3-ak4n5jqr6c8
2o$obo$bo!

Edit 6: Another one, but P342 this time.

Code: Select all

x = 3, y = 3, rule = B3-ceky4jqt5cy6ek/S2-in3-ak4nr5jkqr6c
2o$obo$bo!

[CARuler]

lol

Code: Select all

x = 117, y = 78, rule = MAPabcdeQ
b2obo8b2obo6b2obo2b3obo2b2o3bob2obo2b3ob3o3b4o3bo2b2ob2ob2o4b4o3b3obo
bobo5b3o3b2o2bobobo$4bob5o4bo2b2o2bobo4bo2bo2bo2bob4ob2obo3bobo2bo3bo
bob4o6b3obob2o6b2o2b2obob3o2b3o3bo2bobo$2b5obob5o2bo5b2o2b2o3bob2obo6b
2o4bo2bob2o3b2ob2o4b4o2b3o2b2o2b3o3bo2bo3b4o2bo3b4ob5o$o2b2o3b2o3b2ob
4obo3bob2ob3o6bob3o2b2ob2obo2b6obobo3bo2b3ob2ob3o2bob2o3bob3o2bo3b2o2b
o3bobobobo$b2ob2obobob6o2b2obobobo7b8obo2bob3obo2b2ob2o2b5obo4b2ob3ob
2obob5obobob2o4b3ob2ob3obo$obob3o2bo2bo2bo3bo2b4o2bo2b2o2b5o2bo5bo2bo
2b4ob3o2b2ob2obo5bob4o3bo3bo8bobobob2o3bo2bob2o$bo3b2ob6obo3bob3obobo
11bo2b2o2bob2obob2o2b4o3bo3b2o2b2ob3obobobob3ob4obo2b2ob2o4b4obobob2o
$3b2ob2o2b3o2b3obob2obobob4o2bo3bo2b2o2b3o4bobob2o5bo2bo2bob2o2b4ob2o
b5o2bo3b3o2bo4bob2obo2b5o$6b3ob2o2b4obo2bobo2b4o3bo3b3o5b4o4b4obobobo
12bo3b2obob3o4b2obo3b2ob2ob5o3bob2o$bo4bob3obo3b4ob3obob2ob3ob3ob7o2b
2o2b3ob2ob3ob3o2bob2ob3o6b3obo2b2obobobob2o2bob2o2b2o4b3o$obo4bobo4bo
bobob2o3b3o4b2ob2o2bob6obo7b2ob7o3b5o2b2obo2bo4bo3bo4bo5b4obobob6o$3o
2b2ob4o2bo2bo2bo2b2o2b2obo2b2o4b3ob2o3bob2obobobo2bo2b5o2bobobobo2b2o
bob2obobobo2bobo2bobob2ob2obo2b2ob2o$bob3ob2o4b2obob2o2bo2bobo3b2obob
obobob2obo2b2o2b2o2bob2o2bobo2bo3bob2o4bobob3ob7ob2obo3bo3bo2bo2b2obo
$4obo2bo2b2o3b2o2b2ob2ob3o4b3o2b2o2b2o2b3o2bob2obob4o2bobob2o3bob2ob5o
2b4ob2o3b2o7bobo2b2o5bo$b2o3b2o4b3obobo2bo2b2o2b2ob3o2bobob3ob5o2b2o2b
2obo3bo2bo3b4obobo4b3obo4bob5o3b2o2b5o3bobo$ob3ob3o3b2ob2obo3bo3bo4bo
4b2ob2o3bo3b4ob2ob3o5bo2b8obob3o2b2o2b3o2b2obo2bo2b2o2b4ob2o3bo$o2bob
o2b2o2bob2ob5o4b2o2bo4bo2bobobobobobobo2b3o4b2obo5bo3bo5bob2obob7obo2b
o3bob2o3bo2b5o$b2o2bob6obobobob2o5b3o2bobo3bo3b6ob9o3b2o3b2o3b2obobo4b
o3b2obo3b2obobob2o4b2ob2obobo$bobo2bo2b3o3b2obob5o2bo2b3ob2o5b2o2b2ob
2o4bo2bo3b4obo5b2o2b2o2b2o7b3ob4ob7o2b4o4bo$2o2bo2b2obo3b3obob2ob5obo
bo2b2obo2bobo2b2ob5obobob3o2bob3o2bobo7b3ob5o2bob2o2bob3o2bob5obob2o$
b2o2bobob2o3b7o3b3ob3o2bobobo2bob2o2bobob2obo2b2o6bobob2o4b5o4bobob7o
2bo2b2o2b4o2b3o$4o2b4o7b2ob2o2b2o2b5o2b2ob2obo4bo2b4o6bo3bo2b7o4b3obo
2b2obobo2bo4b2ob2ob5ob2o2b4o$2obob2ob6obo2bob2o5b2ob3o2b2o4bo2b5obo2b
2o2bo3b3o3b5o3b2o5b2o2b2o2bo2bob5ob4ob3o4b3o$2bobo2bo4b3o2b3obob3o2bo
bob2o2bobobob2obob3ob2o5bob2obob3obob2o2b4ob2o3b4obo2bobob6ob4ob8o$b2o
6b2o4bo3bob3ob4o4b3o3bo3bobob5o2bobobob2obobobob2ob2ob4o2b2o2bo2b2ob3o
2bo2b6ob2ob3o2bobo$2b5ob2ob4obo2bobobo3b4o2b2ob2obob3o2bo2b3obo3bobob
ob3obo2b4o2b8o3bo3b3ob2ob2ob2ob2o5bo2bobo$3obob2o3bob4obob3obobo2b2o2b
ob2o2b2o2bob2ob2obobo3bobo7b2o4b2o4b2ob5o3b3ob4o2b4obobobob2o2bo$bo7b
3ob3obob2o3bob2obob2o4b3obo2b2ob2obob3ob2obo2b2obob2obo3bob4o2bob3o2b
o2bob2o3bo2bobobo2b5o2bo$6obob4obobo3bo2b5o3b2ob4ob3ob6obobo2bo3bo5bo
2bob3ob3o2bob2ob2o2bo3bobo4b2obobob4o5b2o$2o3b3ob2ob4o2bob2obob4obo2b
3o2b2o5bo2bob3o5b2o7bobobob2obob5o2b3o5b2o3bo9bo2bo3bo$o2b2o6bobo2b3o
bo3bo3bobo2bobobo3b3ob5o2b4o2bo2bo3b2ob3obo2b2obo3bobo2bob2o2bo2bo3bo
b2obo4b3o2bo$bo4bob3ob2o2b2o2bobo6b2ob2obo2b4o3b2o2bo2bob2o2bo5bo2bob
ob2o2bobob4o3bob3o3b2o2b2ob2obob2ob5ob2o$5bobob3ob3o2bob4o2b3o2bobo4b
obo2b2o2b3o2bo2bo3b2o2b3o3bobo2bo2b2ob3obo2b7o2b3obo5b2obo2bob2o$3bo2b
ob5o2bobobobob2o3bobob2obo4b2o2bobob3ob2ob4ob3ob5ob4obobob3o2bo2b2obo
3bo2bo6bo2b3ob3obo$3b3o2bo2b2o3b2o5b3ob2o9bo3bobob2obo3b2obobobo2b4o2b
4o3b4obo3bo2b2o2b4obob2obobo4bobob2obo$3o2bo3bobo3b2o4b2o2b2o2b2obobo
2b2o3b3ob2ob2ob2o2b2ob2o3b9ob3ob2o3bo2bob2o2bobob2o6bob4o2bobo$2ob2o4b
ob4obo2bo2b2o4b2o3b2o2bobo2bobobo2bo3bobobobobob2obob2o2bo3bob2o3bob2o
bobo2bobo4b2o4bobo$2o2bobo2b4obobo2b4o3bo2bobo3b3ob2o2bob2obob2obo3bo
b3obo2bo6b3obo3b4obo6bo3bobo3b2o6bo2bobo$obo2bob2o5b5obo3b2o3bo3bob2o
6bo2bo2bo4bobo2b2o5bo2bobob3obo2b2obo2bobob2obob7obo6bo2b2obo$3ob4o4b
2o2b2ob4o3b2obob3ob3obo2b3ob5o3b2o3b3o2b4o3bo2bo2b2o4bob4o4bo2bo3b7ob
4o$bo2b2obob5ob3o4bob2o4bobo6bo2b5ob4ob2o3bobob2o3b2ob3o2b2ob7obo6b2o
bob2obobob4ob2ob4o$b2obobobobo2b3ob2o3b2o2b2ob2ob2o2bob2ob2o3b5o2bobo
bo4b10o3bob2obob3o3b2o2b5o2bo2bo3b2obo$ob2o2bo2bobo11b3o2b2o3bobo5bo2b
obo3bo5b5ob4ob2ob2o5b3o2bo2bobob3ob3ob4o5b3obo5bo$2b2o6bo2b2o3bo2b6ob
ob4obo3bobobobobob5o3bob2ob3ob2ob2obobob3ob3o2b2o2bo9bo2bo2b3ob2ob3ob
o$4ob2o5bob3obobob2o7bob3o2b2o4bo2b2ob3o2bobobo3b4o3b2obob2o2bo3b2o2b
2o5bobo2b2o4bob3obo2bo$b2o3bobo2b2obob4obob5o2bob2ob3o2bo3bob2o2b2obo
2b3o3b3o5b2ob4ob2o2b2o4bo3bo2b2ob4o2bo3b2o2b2ob2o$bo2b10o2b5o2b3o6b2o
bo2b2o3b2o3b2o2b2o3bo2bo2b6o5b3obo3bobobob2o2bobo3b2o2bobob3o2bob2obo
$o4b3o2bo2bobobobob2ob2o2b3obo3bob2obo5bo2b3o2bobobobo2bo5b3ob2ob9ob3o
2bo3b4o3b2ob5o2bo$2bobobob2ob4obobo3bob2o3b5ob5obo2b2o2b2ob3o4b2ob3ob
ob2o3b2o2bob4obobo2bob2o3bobob3ob2o3bob3o2bo$b2o2bobob2o3b3o4bobo2b6o
3b3obo2bob3obo5b2o2bob7ob4o2bo3bo2bobobob2obo2bo4b4obobo2b2ob3obo$3o3b
o3bobo4b2ob2o3b5ob4o2bo2b2o5b4ob2ob2ob3obob2ob6o2bo4b2ob3ob3obob2obob
3obo2b2o3b2o2b3o$o2bo4b3ob3o2bob3o4b2obo5bo5b5o2bob8o7b4o4bob4o2b2o4b
ob2ob2ob2ob2o2bo2b4o3bo2b2o$o3bo3bo3bob3o2bob6o2bo2bobobo2bobob2ob2ob
obob7o3b3ob3o3b5obob2obo2bobob3ob2ob2ob5obo7bo$bo2bo8b4ob4ob7o5b3obob
ob5ob3o2bo3bo3bo3bob2obo2bo5b2o3b3o2b2o7b3obo2bo3bo4bo$2obo3b2ob4obob
4ob2o4b5o4bo2bob3o2bo2b3ob2o2bob5o2b3obo6b2ob5o7b3obo3b2obo3b4o2b3o$4b
ob3obobob2ob4o7bobob3obo3bob2o2b3o5b5o2b2ob2ob3obobobobob3o5bo2b2ob2o
3bo2b2obo2bo4bobo$2ob2o2b2ob2o2bob3o2bob2obob4ob3ob2o4bo2b3ob2ob5ob5o
bo4bobob2obo2b2ob2obo4bo2b3obo4bob2o3bob2o2bo$4b6o2bo3b2ob2ob2o4bob9o
3b3obo2bobo3b2o3bobo6b4o2bo2b3ob2obob4o3b3ob3obobobobob2o3b2o$2bob3ob
o2b2o3bobobob2o2b4o3b4ob4ob2obo2b4ob2obobob4ob2obo7bob2obo3b2obo2bo3b
o8bo2b2o2bobobo$bo7bobo3bobo2bo2b2ob3ob2obo3bobob3obo2b2ob3obo2bob2ob
o2bo2bob2o2b2o2b3o2b2obob2o3bob2obo3bob2o3b3obobo$2bobo4b2o2b6ob3o4bo
b7obob2ob3o4bobob4o3b8ob2ob9o2bobobo2bo2bo3b2o5bo3bo4b4o$b3ob2ob2obob
o3bobo6b5o2b2ob2ob2ob2obo4b5o2b2o2bo4b3o3bo2bo3bobo3bob3obo2bo2bobob2o
b3obo3bob2o$3bo3bobob2o4b4o7bo3bob4ob3o3b2ob4o2b2o2b5o4bobobo3bob4ob3o
b5obo5bobob6obob4o$b2obob3obo3b3ob2o2b2o2b2o3bobobob3obobo3b2o2b2ob3o
2b2o2b3o2bobob2o6b3ob3o3bo2b2obo2b3o2b5ob2obo$5b2ob4ob4ob4ob7o2bo2bo3b
obo3b3o3b4o5bo2bo3bob2ob3o3b2o2bo4bo2bob2ob3ob2o2bob2o2b2o2bo2bo$9o2b
2obob4o3bob2o5b4obo2bobob5obo2bo2b2ob3obob4o2b2o2bo3b4o2b2obob2ob6o6b
o2b2obo3bo$obob2o5b3ob3obo4b2obo3b4o3bob4o3bobobo8bobo3bo3bo3bo3b7o6b
3ob2ob2o2bobob2o4bo2bo$4bo2bobo2b2obob2ob5o3b2o3b2ob2obobo5b2o3bobobo
2b2ob2ob2obobobob2ob2o3bob5o2bo4bo2b2o5b3o3bo2b2o$2o2bobob5ob2obo4bo2b
2o3bob6ob3o4b2o3b3o2bobobo3bo2b2ob4ob2obobobobo2b4obo4bo2b3o2bo2b3ob3o
bo$3obob2ob3o2b3obobobo2bo2bo2bo3b3o2b2ob4o2bobo2bo4bo2b4o3b2ob3obo2b
2o3bo2b4obo3bo5bo2b2ob3o2b4o$4ob2o3b2ob13obo2bob3o3b2o6b2ob5ob2o2b2ob
ob2o3b3ob2o4bobo3b4ob3o6bobo7b2o5bo$3ob3o5bo3bo3b5obobo2b6o2bob2obo2b
o2b3o2b2obo2bo6bo4b3ob3obob5ob3ob2ob3o4b3o5b2ob2o$o2bob2ob2ob2ob2obob
2o2b2obobo3bobobo2b2o6bo3b2o3b2ob2o5bo2b2ob4ob4o2b3ob2ob3ob2ob3o3bo2b
3obob2o$b2ob3o4b2obob3obo2b5ob2ob2o5bob3o3bo3b2o2bo3bob4o2bob3o5bo6b2o
2b3obobobobobob2o4bob2ob3o$ob2obobobobobob3o4bob2o2bo4bobob3ob3o2bob2o
b2ob2o2b3obob2o5bob7o3bobo2bo2bobob3obob2o2bo2b2o2b2obo$o5bo2b5o2b12o
2b3ob2o2b3o2b2o2b3o2bobo3bo3bob2o2bobob2ob4ob3o5b2o3bob3obob3ob2o4bob
4o$o2b5ob4o4b2o2bo3bo3bo4bobo2bo2bobo2b3ob5obob3ob5o7bob2o2bo5b4o2b4o
bob2o4bob5obo$2o3b3obo4bobob3o3b3obob3o2b3ob3ob2o4bobo2b4o2bob2obobo4b
4ob3o2bobobob4o2b4o7bo3bob2obobo!

[wwei47]

viewtopic.php?f=11&t=3752&p=84439&hilit=rep%2A#p84439
It also has a generator that I thought was a noninteger replication order, but actually it's just puffing out two replicators at an offset that somehow doesn't break either of them. When we delete one, it becomes clear that it's just log4(11).

Code: Select all

x = 21, y = 17, rule = B2e3aiky4jnqtwz5cjqry6aei/S1c2-k3ajry4cjkrt5-eqr6i
3o9b3o$bo11bo$bo11bo$3o9b3o$5bo3bo$4bobobobo$4bobobobo$5bo3bo2$19bo$
18bobo$18bobo$19bo2$bo11bo$3o9b3o$obo9bobo!

3 engines:

Code: Select all

x = 11, y = 17, rule = B2e3aiky4jnqtwz5cjqry6aei/S1c2-k3ajry4cjkrt5-eqr6i
3o$bo$bo$3o$5bo$4bobo$4bobo2bo$5bo2bobo$8bobo$9bo5$bo$3o$obo!

EDIT: I'm really starting to wish that past-me had labeled the patterns that they had posted. Anyways, reviewing some of my MDIOCA posts from late 2018.

Page 37:
42c/84 pascal-modulo-3 replicator; emits spaceships every cycle:

Code: Select all

x = 4, y = 3, rule = B2ei3iy4knt5y6i8/S1c2-k3jqy4ntwyz5q6ek8
b2o$o2bo$b2o!

7c/14 XOR replicators; emit spaceships every 2 cycles:
'

Code: Select all

x = 4, y = 3, rule = B2e3ijk4cjkqy5ry8/S1c2-in3aey4ac5kq6ae7c
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2ek3cij4cjkt5c6a7c8/S1c2-in3aejq4wyz5jknq6i7e8
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2en3ijny4nq5ejy7e8/S1c2-in3aijny4e5akry6-kn8
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2ek3aij4cetz5-aekr6e/S1c2-in3aekq4acy5jqry6-kn7e
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2e3ein4ajz5jkn6ain/S1c2-i3-jky4ajkty5en6in7c
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2ek3acik4acjtwz5-ceij6in7c8/S1c2-k3acqr4kn5aqr6an7e
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2en3-cnry4cejqwy5kry6ek8/S1c2-kn3ajq4qwz5ar6aen7c8
b2o$o2bo$b2o!

Page 38:
[Edit 4: This is also a 7c/14 XOR replicator that emits spaceships every other cycle.]

Code: Select all

x = 4, y = 3, rule = B2e3eijqr4cijqtw5iky6an7/S1c2ac3ajk4wy5ekry6n7e
b2o$o2bo$b2o!

28c/56 pascal-modulo-3 replicator; emits spaceships every 3 cycles:

Code: Select all

x = 4, y = 11, rule = B2ei3aikny4ctw5-ceiq6k7c/S1c2-kn3qy4knrt5jnqy6ikn7e
b2o$o2bo$b2o6$b2o$o2bo$b2o!

Two fractal generators that I posted in 2020 that apparently never made it off the discord:
log6(21); full density

Code: Select all

x = 27, y = 9, rule = B2ek3eiq4jkrtz5ciy6cn7/S1c2-ek3acnqy4iny5n6-ai8
o14bo$2o12b2o8bo$o14bo9bo$9bo7bo7b2o$9b2o6b2o$11bo4bo2bo$2bo13b2o$bo
16bo$2bo14bo!

log6(17); half density

Code: Select all

x = 50, y = 40, rule = B2en3-cnqr4cikqtw5aeny6ck7e/S1c2acn3-eiry4krwy5ae6k7e
47bo$27b3o2b3o10bo2bo$23b2o9b2ob2o$23b6o3bo4b2o5bo2b2o$23b2o5bo2b2o2b
2o6bobo$29bo$31b3o$31b3o$22bo2bo12bo2bo$22b4o12b4o$22bo2bo12bo2bo8$47b
3o$47b3o3$47b3o$47b3o5$15bo2bo15bo$11b2o2b4o2b2o11bo2b2o$11b2o2bo2bo2b
2o10b2o2b2o$11b2o2b4o2b2o10b2o2b2o$15bo2bo14b2o2$5b2o14b2o$bo2bo2bo2bo
10b2o$o4b2o4bo$bo2bo2bo2bo8b2o5bo$5b2o12bo$26bo!

EDIT 2: To be clear, I also reviewed page 36, but didn't see anything there that was postable in this thread. I have some boat research that will likely show up in this thread once I'm ready to post results.
Edit 3: While reviewing my 2019-era posts in the interesting replicators thread, I found this thing that has three different fractal dimensions (1; log2(3); 2:

Code: Select all

x = 27, y = 20, rule = B2ek3-knqr4ac5y/S1c2-a3aqry4a5j6a
18bo4bo$18bo4bo2$4bo11bobo4bobo$4bo10bo10bo$4bo11bobo4bobo2$18bo4bo$
18bo4bo2$9b2o$9b2o11b4o$22b4o$9b2o11b4o$9b2o2$bo$obo$obo$bo!

[CARuler]

Code: Select all

x = 1, y = 1, rule = RepCount
o!
@RULE RepCount
@COLORS
0   0   0   0
1 255 255   0
2   0   0 255
3 148   0 255
4 255   0 255
@TABLE
n_states:5
neighborhood:vonNeumann
symmetries:none
var a = {0,1,2,3,4}
var b = a
var c = a
var d = a

0,0,1,0,0,1
0,0,0,0,1,1
0,0,1,0,1,2
0,0,0,2,0,3
0,3,1,0,0,1
0,3,0,0,1,1
0,3,1,0,1,2
3,a,b,2,c,4
3,a,b,4,c,4
0,0,0,4,0,3

#defaults
1,a,b,c,d,0
2,a,b,c,d,0
4,a,b,c,d,3

edit:
emulation of the first fractal

Code: Select all

x = 1, y = 1, rule = RepThing
o!

@RULE RepThing
@TABLE 
n_states:3
neighborhood:vonNeumann
symmetries:rotate4reflect
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = {0,2}
var f = e
var g = e
var h = e

e,1,f,g,h,1
0,2,2,2,2,2
2,2,2,0,0,0

#defaults
1,a,b,c,d,2

edit2:
turns out i didn't need 3 states lol

Code: Select all

x = 1, y = 1, rule = B1e2i4e/S
o!

[eRroR_6o6]

well it's not that weird but it's still quite cursed and the t-square appears during its evolution
the pop plot of this is also just downright goofy

Code: Select all

x = 2, y = 2, rule = B2ae4w/S
2o$2o!

Edit: so i tried to change the rule and somehow got the alternating checkerboard version of last post

Code: Select all

x = 2, y = 2, rule = B2ae4ew/S
2o$2o!

[wwei47]

Old post review dug this up in edit 5 of this post: viewtopic.php?f=11&t=3752&p=106588#p106588

5c/42 XOR replicator; emits spaceships every cycle

Code: Select all

x = 4, y = 3, rule = B2e3-cnqy4qrtwy5jkny6cek7c8/S1c2-kn3ajkq4-acetw5e6cik8
b2o$o2bo$b2o!

I am trying to find (old) "interesting" replicators to make fractal generators from.
EDIT: I should add the additional note that stuff I bump into from myself in other threads will likely get crossposted here; if this thread had existed back then, I would have posted them here in the first place, and I want to "move" them to the right thread.

EDIT 2: (16,34);(-34,-16)c/119 P238 sierpinski generator

Code: Select all

x = 4, y = 4, rule = B2en35qr/S2-i3-a5r
3o$o2bo$obo$bo!

Edit 3: Did I actually forget the code box bruh.

[eRroR_6o6]

The heck?

(lifeviewer doesn't let me name this for some reason lol)

Code: Select all

x = 2, y = 12, rule = whoops
B9$.A$.A$.B!

@RULE whoops

@TABLE

n_states:3
neighborhood:Moore
symmetries: rotate4reflect
var a1 = {0,1,2}
var a2 = {0,1,2}
var a3 = {0,1,2}
var a4 = {0,1,2}
var a5 = {0,1,2}
var a6 = {0,1,2}
var a7 = {0,1,2}
var a8 = {0,1,2}
var b1 = {0,2}
var b2 = {0,2}
var b3 = {0,2}
var b4 = {0,2}
var b5 = {0,2}
var b6 = {0,2}
var b7 = {0,2}
var b8 = {0,2}

0,1,0,0,0,0,0,0,0,1
2,0,a1,0,0,0,0,0,0,2
1,1,0,0,0,0,0,0,0,1
1,2,0,0,0,0,0,0,0,1
2,2,0,0,0,0,0,0,0,2
2,1,0,0,0,0,0,0,0,0
2,1,0,0,0,2,0,0,0,0
0,0,0,0,0,1,0,0,2,1
0,1,0,2,0,0,0,0,0,1
1,0,0,0,0,1,0,0,2,1
0,1,2,0,0,0,0,0,0,1
1,a1,a2,a3,a4,a5,a6,a7,a8,2
2,b1,b2,b3,b4,b5,b6,b7,b8,0

so i discovered something similar on complete accident while trying to make a stable generations b1e rule

Code: Select all

x = 1, y = 1, rule = 1e2i3a/1e/3
A!

[CARuler]

what the heck is this

Code: Select all

x = 1, y = 1, rule = B13/SVInvestigator
J!

edit: again

Code: Select all

x = 1, y = 1, rule = B13/SVInvestigator
L!

[eRroR_6o6]

replicator-like rule but it's actually r2 von neumann

Code: Select all

x = 5, y = 3, rule = R2,C0,S0,2,4,6,8,10,12,B1,3,5,7,9,11,NN
2bo$3bo$bobo!

I don't know what it emulates on the edges.

[CARuler]

what is this

Code: Select all

x = 3, y = 3, rule = B13/SVInvestigator
E.E$.H$E.E!

[wwei47]

(±3,2)c/11 P44 sierpinski generator; emits blinker pairs every cycle

Code: Select all

x = 5, y = 4, rule = B3ai4ae5cy678/S2-n3-a567
2bo$2ob2o$obobo$2ob2o!

[ThePlayzr]

Hmm.

Code: Select all

x = 2, y = 2, rule = B2ae4e/S
2o$o!

Best I can describe it is a spacefiller with an anti-replicator destroying the output.
Block does the same thing:

Code: Select all

x = 2, y = 2, rule = B2ae4e/S
2o$2o!

Edit: population graph is hillarious

[wwei47]

By nolovoto. 18c/36 engine (which is itself a failed replicator!); emits 9c/18 replicators every 2 replication cycles:

Code: Select all

x = 12, y = 37, rule = B2ek3ij5ir/S12-a3j6cn
2b3o$b2obo$6b3o$6bob2o$9bo$4b2ob2obo$4b2obo$8bo$4b2obo$4b2ob2obo$9bo$
6bob2o$6b3o$b2obo$2b3o6$3bo3bo$b2o5b2o$2o3bo3b2o$o9bo$2o7b2o2$2o7b2o$
o9bo$2o3bo3b2o$b2o5b2o$3bo3bo4$3bo$2bobo6bo$3bo7bo!

EDIT: By sylvie: 6c/12 engine; emits 3c/3 replicators every 4 replication cycles:

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x = 35, y = 18, rule = B2aci/S
2bobo25bobo$bo3bo23bo3bo2$bo3bo23bo3bo$16bobo2$o2bo10bo5bo10bo2bo$3bo
5bo15bo5bo$3bo5bo4bob3obo4bo5bo$o3b2o3bo15bo3b2o3bo$3bo9bo7bo9bo$6bo8b
2ob2o8bo$3bo11bo3bo11bo$3bo12bobo12bo$3bobo23bobo$3bo27bo$13bobo3bobo
$13bobo3bobo!

[yyh_baboon]

Strange Sierpinski generator(I don't even think that's a Sierpinski triangle)

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x = 4, y = 3, rule = B3-kn4ce6ik/S2-i34i5r
3o$o2bo$ob2o!
[[ THEME INVERSE ]]

[wwei47]

By Docsy on the discord.

Code: Select all

x = 13, y = 7, rule = B2c3a/S2cn3acin4aq5acejn6-i78
obobo3bobobo$b3o5b3o$4o5b4o$b4o3b4o$o2b2o3b2o2bo$5bobo$6bo!

These seem to be able to get up to some wacky shenanigans.

Code: Select all

x = 17, y = 9, rule = B2c3a/S2cn3acin4aq5acejn6-i78
obobo7bobobo$b3o9b3o$4o9b4o$b4o2bo4b4o$o2b2obobo3b2o2bo$5bobobobo$6bo
bobo$7bobo$8bo!

Code: Select all

x = 17, y = 9, rule = B2c3a/S2cn3acin4aq5acejn6-i78
obobo7bobobo$b3o9b3o$4o4bo4b4o$b4o2bobo2b4o$o2b2obobobob2o2bo$5bo5bo$
6bo3bo$7bobo$8bo!

EDIT: Pascal mod 3 generator+decaying wicks by rabbit. 6c/12 engine; generates block pairs every 3 cycles.

Code: Select all

x = 3, y = 3, rule = B3ai/S3-c4-w5-q6i7e
2bo$b2o$3o!

Edit 2: Double sierpinski+line generator by hibiscus; engine is (+/-13,12)c/94 and emits spaceships every 2 cycles.

Code: Select all

x = 5, y = 3, rule = B3aijy4ajqrwz5ai6ac/S2aek3-acky4eiqrt5jy6ci
b3o$obobo$2ob2o!