Travelling Ts(b3s23-a5) and its variants

[yujh]

This script should hopefully be working:

Code: Select all

import golly as g

P = 2 ** 10 - 2
p = 146

g.setalgo("HashLife")
g.setstep(0)
# g.autoupdate(False)

T = P//p
t = bin(T)[3:][::-1]  # Leading digit should be covered in step 1
l = []

for i in range(len(t)):
    l.append(g.getcells(g.getrect()))
    g.setstep(i // 3)  # idk why hashlife is 8^n not 2^n
    for j in range(p << i % 3):
        g.step()
    g.putcells(l[-1], 0, 0, 1, 0, 0, 1, "xor")


for i in range(len(t)):
    if t[i] == "1":
        # g.warn(str(i))
        g.setstep(i // 3)
        for j in range(p << i % 3):
            g.step()
        g.putcells(l[i], 0, 0, 1, 0, 0, 1, "xor")

I suppose there are some ways to optimize this, I currently have no clue if this is better than the naive version. (I suppose there might be some way to paste efficiently)
To use you need to have the base oscillator present and change P and p as needed.

Edit: this seems to be running faster than the script below on my machine..

[PK22]

Here is a lifelib version, which I think should be faster (it automatically installs lifelib and Cygwin if you haven't already):

Code: Select all

#Import lifelib, and install it with pip if it isn't installed:
import os
try:
    import lifelib
except:
    print('Installing lifelib...')
    os.system('pip install lifelib')
    import lifelib
    import platform
    if platform.system() == 'Windows':
        lifelib.install_cygwin()
import time

sess = lifelib.load_rules('B3/S25')
#Outer-totalistic rules should be slightly faster to simulate,
#and B3/S25 supports Margolus oscillators.
lt = sess.lifetree(n_layers=1, memory=1000)
targetperiod = int(input('Enter your desired period.\n>>>'))
if targetperiod%2 != 0:
    raise ValueError('Can only create oscillators of even periods.')
starttime = time.time()
#Figure out some of the values that we need to use:
tempperiod = targetperiod
powerof2 = 0
while tempperiod%2 == 0:
    powerof2 = powerof2 + 1
    tempperiod = tempperiod//2
newpowerof2 = 1
while ((2**newpowerof2)-1)%tempperiod != 0:
    newpowerof2 = newpowerof2 + 1
width = 2 * (2**newpowerof2) * (2**(powerof2-1))
height = 2 * (2**(powerof2-1))
baseoscperiod = (2**(newpowerof2) - 1) * (2**(powerof2))
iterationsneeded = int(baseoscperiod/targetperiod) - 1
print(str(iterationsneeded)+' iterations needed to produce oscillator...')
initialrle = str(width)+'o'
initialrle = (height - 1) * (initialrle + '$') + initialrle + '!'
#Alright, let's make this oscillator!
x = lt.pattern(initialrle)
pattern = x
for i in range(iterationsneeded):
    pattern = pattern[targetperiod]
    pattern = pattern ^ x
if pattern.period == targetperiod:
    #If the pattern's period matches the target period entered by the user, then we are done.
    print('Success!')
    print('Oscillator created in '+str(round(time.time() - starttime, 4))+' seconds.')
    print('Saved as \'Margolus p'+str(targetperiod)+'.mc\'.')
    pattern.save('Margolus p'+str(targetperiod)+'.mc')
else:
    #Sometimes it doesn't work. Fortunately, if we reduce the length of the initial line by two Margolus cells, then it will work.
    print('Error: Resultant oscillator has period '+str(pattern.period)+'.')
    print('Retrying with different parameters...')
    tempperiod = targetperiod
    powerof2 = 0
    while tempperiod%2 == 0:
        powerof2 = powerof2 + 1
        tempperiod = tempperiod//2
    newpowerof2 = 1
    while ((2**newpowerof2)-1)%tempperiod != 0:
        newpowerof2 = newpowerof2 + 1
    width = (2 * (2**newpowerof2) - 4) * (2**(powerof2-1))
    height = 2 * (2**(powerof2-1))
    baseoscperiod = (2**(newpowerof2) - 1) * (2**(powerof2))
    iterationsneeded = int(baseoscperiod/targetperiod) - 1
    print(str(iterationsneeded)+' iterations needed to produce oscillator...')
    initialrle = str(width)+'o'
    initialrle = (height - 1) * (initialrle + '$') + initialrle + '!'
    #Alright, let's make this oscillator!
    x = lt.pattern(initialrle)
    pattern = x
    for i in range(iterationsneeded):
        pattern = pattern[targetperiod]
        pattern = pattern ^ x
    if pattern.period == targetperiod:
        #If the pattern's period matches the target period entered by the user, then we are done.
        print('Success!')
        print('Oscillator created in '+str(round(time.time() - starttime, 4))+' seconds.')
        print('Saved as \'Margolus p'+str(targetperiod)+'.mc\'.')
        pattern.save('Margolus p'+str(targetperiod)+'.mc')
    else:
        print('Sorry, both attempts to create an oscillator with the target period failed.')

As an example, it takes 12.848 seconds to create a p46, which took 88 iterations.
Note that it saves the resultant oscillator as a macrocell file with rule B3/S25, but you can open it in Golly and change the rule.

[hotcrystal0]

2 things.
Firstly, are we going to include every oscillator or just the small ones and sparky ones?
Secondly, you forgot to embed a viewer into the wiki page, it's just an RLE currently.

I’m including only the small ones and sparky ones.

Unfortunately, I can’t. Several people tried to add LifeViewer to esolangs wiki, but none of the attempts worked.

[yujh]

Code: Select all

# Import lifelib, and install it with pip if it isn't installed:
import os
try:
    import lifelib
except:
    print('Installing lifelib...')
    os.system('pip install lifelib')
    import lifelib
    import platform
    if platform.system() == 'Windows':
        lifelib.install_cygwin()
import time

sess = lifelib.load_rules('B3/S25')
# Outer-totalistic rules should be slightly faster to simulate,
# and B3/S25 supports Margolus oscillators.
lt = sess.lifetree(n_layers=1, memory=1000)
targetperiod = int(input('Enter your desired period.\n>>>'))
if targetperiod % 2 != 0:
    raise ValueError('Can only create oscillators of even periods.')
starttime = time.time()
# Figure out some of the values that we need to use:
tempperiod = targetperiod
powerof2 = 0
while tempperiod % 2 == 0:
    powerof2 = powerof2 + 1
    tempperiod = tempperiod//2
newpowerof2 = 1
while ((2**newpowerof2)-1) % tempperiod != 0:
    newpowerof2 = newpowerof2 + 1
width = 2 * (2**newpowerof2) * (2**(powerof2-1))
height = 2 * (2**(powerof2-1))
baseoscperiod = (2**(newpowerof2) - 1) * (2**(powerof2))
# iterationsneeded = int(baseoscperiod/targetperiod) - 1     # ok what the is int(a/b) :sob:
T = baseoscperiod // targetperiod
t = bin(T)[3:][::-1]  # Leading digit should be covered in step 1
l = []
# print(str(iterationsneeded)+' iterations needed to produce oscillator...')
initialrle = str(width)+'o'
initialrle = (height - 1) * (initialrle + '$') + initialrle + '!'
# Alright, let's make this oscillator!
x = lt.pattern(initialrle)
pattern = x
# for i in range(iterationsneeded):
#     pattern = pattern[targetperiod]
#     pattern = pattern ^ x

for i in range(len(t)):
    l.append(pattern)
    pattern = pattern[targetperiod << i]
    pattern ^= l[-1]

for i in range(len(t)):
    if t[i] == "1":
        pattern = pattern[targetperiod << i]
        pattern ^= l[i]

if pattern.period == targetperiod:
    # If the pattern's period matches the target period entered by the user, then we are done.
    print('Success!')
    print('Oscillator created in ' +
          str(round(time.time() - starttime, 4))+' seconds.')
    print('Saved as \'Margolus p'+str(targetperiod)+'.mc\'.')
    pattern.save('Margolus p'+str(targetperiod)+'.mc')
else:
    print('Unsuccessful')  # nah im too lazy for this
    print('Oscillator not created in ' +
          str(round(time.time() - starttime, 4))+' seconds.')
    exit()

    # Sometimes it doesn't work. Fortunately, if we reduce the length of the initial line by two Margolus cells, then it will work.
    print('Error: Resultant oscillator has period '+str(pattern.period)+'.')
    print('Retrying with different parameters...')
    tempperiod = targetperiod
    powerof2 = 0
    while tempperiod % 2 == 0:
        powerof2 = powerof2 + 1
        tempperiod = tempperiod//2
    newpowerof2 = 1
    while ((2**newpowerof2)-1) % tempperiod != 0:
        newpowerof2 = newpowerof2 + 1
    width = (2 * (2**newpowerof2) - 4) * (2**(powerof2-1))
    height = 2 * (2**(powerof2-1))
    baseoscperiod = (2**(newpowerof2) - 1) * (2**(powerof2))
    iterationsneeded = int(baseoscperiod/targetperiod) - 1
    print(str(iterationsneeded)+' iterations needed to produce oscillator...')
    initialrle = str(width)+'o'
    initialrle = (height - 1) * (initialrle + '$') + initialrle + '!'
    # Alright, let's make this oscillator!
    x = lt.pattern(initialrle)
    pattern = x
    for i in range(iterationsneeded):
        pattern = pattern[targetperiod]
        pattern = pattern ^ x
    if pattern.period == targetperiod:
        # If the pattern's period matches the target period entered by the user, then we are done.
        print('Success!')
        print('Oscillator created in ' +
              str(round(time.time() - starttime, 4))+' seconds.')
        print('Saved as \'Margolus p'+str(targetperiod)+'.mc\'.')
        pattern.save('Margolus p'+str(targetperiod)+'.mc')
    else:
        print('Sorry, both attempts to create an oscillator with the target period failed.')

Here's a slightly faster version. Probably. Note that I didnt change a lot of stuff due to laziness, so this might not work correctly as often. This only takes O(log(iterationsneeded)) copy and paste operations instead of O(iterationsneeded) in the original.
Also it is probably preferable to change pattern.period == targetperiod to pattern[targetperiod]==pattern to prevent an extremely high period.
Edit: I dont think pip3 install lifelib is working (for python3)
This still runs slower than the golly script i posted above on my machine.

Edit2: Stepping the pattern seems to take a very long time, which i do not understand.

Edit3: Here's a p26, which took about a minute to make. The original script took slightly less than 2 minutes.

[LuveelVoom]

I recall doing LLSSS searches for 3c/7 at fairly high symmetric width and finding only partials, but i'd have to check what width.

[PK22]

AND is simple. Just do this:

Code: Select all

x = 15, y = 15, rule = B3/S23-a5
9bo$7b3o$6bo$6b2o5b2o$13bo$11bobo$11b2o$bo$2o$bo4$3b3o$4bo!

If there are 2, the T gets lane shifted, escaping the eater. OR will be difficult though, because they have to end on the same lane.
Also, what about AND OR, AND NOT, or OR NOT? Won't we need these?

According to the wiki, we can simulate W110 for a cell q with neighbours p and r using:

Code: Select all

XOR(OR(p, q), AND(p, q, r))

Turns out we don't need a NOT gate - we can just make an XOR gate using two Ts which mutually annihilate, then in the two potential outcomes where 1 T is inputted, shift them using sparkers so that they would be in the same position.

For an OR gate, does anyone know of any 2T collisions where one T cleanly annihilates the other without being phase-shifted or pushed forward? If so, we can use a similar technique to the XOR gate by using sparkers to shift the Ts back onto the same lane.

The image below is a rough diagram of how the logic gates in the planned metacell will work. The output, Q', will be sent north of the logic area, duplicated into multiple signals, and then these will sent back south towards the logic gates for the next period. To ensure that it is clear W110 is being emulated, a T will be fired north of the metacell.

[hotcrystal0]

Slightly updated oscillator stamp collection:

Code: Select all

x = 296, y = 204, rule = B3/S23-a5Super
196.2A8.2A28.6pA2.6pA$75.6D25.M8.A3.A35.4D4.6D9.A16.A2.A6.A2.A27.6pA2.
6pA$75.6D17.4A4.2M5.2A2.2A2.3A3.2A26.4D4.6D8.2A16.A.2A6.A.2A31.2pA2.2pA
2.2pA$79.2D4.3M3.4A3.4A4.2M4.3A2.2A2.2A4.A.A27.2Q4.2Q2.2Q9.A17.3A7.3A
31.2E2.2E2.2E7.3A$79.2D26.M8.A3.A8.A27.2Q4.2Q2.2Q6.A60.6E2.2E2.2E7.A2.
A$75.6D48.2A10.A15.2M4.2M2.2M5.3A59.6E2.2E2.2E8.3A$75.6D50.2A8.A.A13.
2M4.2M2.2M12.3A52.2E6.2E2.2E8.2A$75.2D50.A5.2A5.A.A14.2P4.2P2.2P13.A6.
2A45.2I6.2I2.2I8.2A$75.2D10.A6.2A6.M7.3A7.2M5.A.A5.2A5.A14.2P4.2P2.2P
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6H10.2A7.A.2A7.A9.A26.6I2.6I$75.6D4.A.A.A3.A.A.A3.2M5.A.A2.A14.A10.2A
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13.M38.2M17.2A12.A5.A.A5.A$29.A.A47.2D11.A7.A11.2A7.A2.A16.M70.5A3.5A
$19.A11.A47.2D31.2A8.2A16.2M72.A7.A13.6D2.2D2.2D$17.2A12.A.2A201.6D2.
2D2.2D$19.A4.3A2.A.2A.A205.2D2.2D2.2D$15.A9.A3.A210.2D2.2D2.2D8.2A13.
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2M62.4A9.4A20.A.A21.6D2.6D7.2A.A.3A8.3A5.3A$14.3A14.A43.6D13.M.M4.2M6.
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20.M.M5.M.M8.M.2M7.A.6A.A33.2A.2A9.2A.2A18.2A.2A20.2D10.2D$9.A.A17.2A
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13.4A17.4A$9.A.A73.2M15.M2.M6.2M64.A.A.A.A.A.A$10.2A90.2M76.3A.3A14.4A
17.4A$18.2A2.3A2.2A149.2A2.A.A2.2A12.A2.2A.2A9.2A.2A2.A$18.A9.A145.4A
.A.A3.A.A.4A13.A2.A7.A2.A$19.4A.4A146.3A.A9.A.3A14.A2.A5.A2.A16.6D2.6D
$22.A.A80.M2.M65.2A.2A9.2A.2A13.2A3.A3.A3.2A15.6D2.6D10.A4.A$21.A3.A99.
M48.A.3A9.3A.A13.A.2A.A3.A.2A.A19.2D2.2D13.2A4.2A$21.2A.2A63.A2.A11.M
4.M2.M12.M18.M30.4A9.4A15.2A.A5.A.2A20.2D2.2D12.A.A4.A.A$89.2A.2A8.3M
.2M.4M6.2M9.2M11.M.M65.A3.A20.6D2.6D7.3A6.3A$87.2A3.2A7.M3.M2.M11.M2.
M.M.M2.M12.M.M65.2A.2A20.6D2.6D$86.7A.2A5.M.2M.2M.2M8.M3.5M3.M8.2M.M2.
2M64.A.A21.2D10.2D$89.A2.A.A7.M2.M3.M.M.2M4.4M5.4M12.M.M65.A.A21.2D10.
2D$11.3N.3N5.3N61.A.A2.A10.M.M.M3.2M.M7.M5.M10.M.M.2M2.M63.2A.2A20.6D
2.6D$13.N.N.N2.N2.N62.2A.7A8.2M.3M9.4M2.M2.4M5.3M.M3.2M89.6D2.6D7.3A6.
3A$11.3N.N.N.3N.3N.2N59.2A3.2A11.M4.3M4.M2.M2.M.M2.M2.M3.M4.M.2M113.A
.A4.A.A$13.N.N.N2.N4.N.N.N58.2A.2A13.M.M.M2.M4.2M5.M5.2M3.2M3.2M.M114.
2A4.2A$11.3N.3N5.3N.N.N59.A2.A14.2M.2M148.A4.A$110.M44.4A4.6A13.A16.A
18.4A$110.M.M42.4A4.6A13.A14.2A.2A16.4A$111.2M44.2U8.2U7.A7.A12.A3.A16.
4A$9.2A5.A5.2A133.2U8.2U8.4A2.A14.A.A17.4A$9.A2.A2.A.A2.A2.A133.2M4.6M
5.2A2.2A2.2A13.A3.A16.4A$10.4A2.A2.4A134.2M4.6M13.2A9.2A.A5.A.2A12.4A
$13.A5.A55.6S76.2T4.2T12.A5.A9.A.A7.A.A12.4A$10.4A5.4A52.6S18.2A10.A3.
A12.A3.A24.2T4.2T12.2A13.A13.A11.4A36.2A6.2A$10.A3.5A3.A52.2V22.2A6.2A
.A5.A.2A3.2A2.A5.A2.2A17.6F2.6F8.2A2.2A2.2A6.A.A7.A.A12.4A37.A6.A$11.
A2.A.A.A2.A14.2A37.2V12.2A8.2A6.A11.A3.A13.A17.6F2.6F8.A2.4A9.2A.A5.A
.2A12.4A14.6D2.6D8.3A4.3A$10.2A9.2A7.A.2A.A.A37.6M5.A.A.2A7.2A7.3A.A.
A.3A5.4A.A.A.4A39.A7.A12.A3.A16.4A14.6D2.6D7.A3.A2.A3.A$16.A13.2A.A.A
39.6M5.A5.A6.2A11.A.A14.A.A46.A19.A.A17.4A18.2D2.2D2.2D6.A.A2.A2.A2.A
.A$16.A16.A.2A38.2V2.2V6.2A.A.A6.2A7.4A3.4A7.3A3.3A43.A18.A3.A16.4A18.
2D2.2D2.2D7.A3.A2.A3.A$33.2A40.2V2.2V7.2A9.2A7.A9.A7.A7.A62.2A.2A16.4A
14.6D2.6D8.A8.A$19.A11.2A42.6S18.2A8.A7.A81.A18.4A14.6D2.6D$17.2A10.A
2.A3.A38.6S27.2A7.2A99.4A14.2D6.2D2.2D$19.A4.3A2.A.A3.A.A198.2D6.2D2.
2D$15.A9.A3.A2.A3.A199.6D2.6D$15.A15.2A203.6D2.6D14.8A$33.2A229.8A$3.
2A9.3A16.A.2A118.4D4.6D10.A9.A14.2A7.2A49.8A$3.A.A.2A.A19.2A.A.A103.2A
3.2A9.4D4.6D11.2A5.2A15.A3.A.A3.A49.8A$5.A.A.2A19.A.2A.A.A37.6D26.M13.
A.3A.A11.A.A.A.A11.2D8.2D10.A.2A3.2A.A13.6A.6A$4.2A.A16.3A9.2A37.6D6.
A8.A9.M.M11.A.5A.A12.A.A13.2D8.2D10.A9.A12.A13.A$6.2A71.2D5.A3.A2.A3.
A7.M.M.M9.A.2A3.2A.A10.A.A.A12.2D4.6D6.A.2A.A2.A.A2.A.2A.A6.3A2.9A2.3A
$8.2A15.A53.2D4.A.A2.A2.A2.A.A6.M.M.M8.A.A7.A.A4.2A3.A3.A3.2A7.2D4.6D
7.A2.A3.A.A3.A2.A7.A.A.A9.A.A.A$4.A3.A2.A3.A9.A53.2D5.A3.A2.A3.A4.2M.
M3.M.2M6.2A7.2A5.A2.2A5.2A2.A7.2D8.2D7.2A4.A3.A4.2A9.A.A9.A.A$3.A.A3.
A.A2.3A4.A57.2D6.3A4.3A5.M.M4.M.M.M4.2A9.2A5.2A9.2A8.2D8.2D8.A3.A5.A3.
A10.A.A9.A.A$4.A3.A2.A10.2A55.2D7.A6.A9.4M3.M5.2A9.2A7.A7.A8.6D2.6D10.
2A7.2A11.2A.A9.A.2A76.2A$8.2A11.A57.2D6.2A6.2A21.2A9.2A5.2A9.2A6.6D2.
6D35.A9.A79.2A$6.2A71.2D26.2M10.2A7.2A5.A2.2A5.2A2.A29.2A7.2A11.2A.A9.
A.2A59.A16.2A$4.2A.A16.A54.2D26.M.M8.A.A7.A.A4.2A3.A3.A3.2A27.A3.A5.A
3.A10.A.A9.A.A19.6D2.6D22.2A.A2.A15.2A$5.A.A.2A13.A83.M10.A.2A3.2A.A10.
A.A.A31.2A4.A3.A4.2A9.A.A9.A.A19.6D2.6D22.A6.A14.2A$3.A.A.2A.A7.2A9.2A
89.A.5A.A12.A.A32.A2.A3.A.A3.A2.A7.A.A.A9.A.A.A21.2D2.2D2.2D15.A8.2A.
2A15.2A$3.2A14.A2.A.A.A2.A91.A.3A.A11.A.A.A.A29.A.2A.A2.A.A2.A.2A.A6.
3A2.9A2.3A21.2D2.2D2.2D16.A6.2A19.2A$18.A3.5A3.A108.2A3.2A33.A9.A12.A
13.A19.6D2.2D2.2D15.A28.2A$18.4A5.4A148.A.2A3.2A.A13.6A.6A20.6D2.2D2.
2D15.A5.A2.A19.2A$21.A5.A61.M24.M65.2A5.2A15.A3.A.A3.A25.2D2.2D2.2D16.
2A5.2A19.2A$18.4A2.A2.4A58.M7.M16.M64.A9.A14.2A7.2A25.2D2.2D2.2D15.A2.
A25.2A$17.A2.A2.A.A2.A2.A62.M2.3M3.2M14.2M7.2M106.6D2.6D15.A28.2A$17.
2A5.A5.2A55.M3.M2.3M3.M2.M8.M3.M2.M2.M.2M.M2.M105.6D2.6D17.A26.2A$85.
3M.M.3M4.2M.M.M6.3M.M.3M2.2M.M3.M.M133.2A28.2A$84.M4.M4.4M.M.M2.2M3.M
4.M4.2M5.2M.M71.A61.A.A28.2A$84.2M.2M.3M8.2M.M4.2M.2M.3M4.4M.M27.4D4.
2D2.2D10.2A19.A.A59.A.A29.2A$88.M.M3.2M.M.M4.M8.M.M3.2M4.M.M27.4D4.2D
2.2D10.2A20.A59.A.A30.2A$88.M.M.M4.2M.M.M.2M7.M.M.M4.4M.2M28.2D4.2D2.
2D10.2A72.A.2A.2A.2A31.2A$87.2M.M.4M6.M.M7.2M.M.4M.M2.M.M29.2D4.2D2.2D
10.2A73.A2.A36.2A$91.M4.6M2.M11.M4.M2.M2.M29.2D4.6D10.2A16.A7.A51.A2.
A33.2A$93.M2.M2.M4.2M11.3M5.2M30.2D4.6D10.2A15.2A3.A3.2A51.A35.2A$92.
2M25.2M36.2D8.2D10.2A14.A.A2.3A2.A.A86.2A$157.2D8.2D10.2A13.3A9.3A85.
2A$155.6D6.2D10.2A113.2A$11.2N2.3N5.3N129.6D6.2D10.2A113.2A$12.N2.N4.
N2.N.N90.A.A60.2A9.A5.A9.A5.A81.2A$12.N2.3N.3N.3N.2N46.6D22.A9.A.2A.2A
.A57.2A8.A.A3.2A9.2A3.A.A80.2A$12.N2.N.N2.N2.N.N.N.N45.6D10.A8.A.2A9.
A2.A.A2.A11.A3.A3.A3.A44.A5.A9.A5.A81.2A$11.3N.3N5.3N.N.N45.2D2.2D5.2A
2.2A8.A10.2A.2A3.2A.2A8.A.A.A.3A.A.A.A$75.2D2.2D6.A.A8.2A.2A2.2A6.A7.
A9.A2.A.A2.A2.A.A2.A88.6D2.6D$75.6D7.A.A9.A2.A.A5.A.A7.A.A8.2A2.A.A.A
.A2.2A47.3A9.3A27.6D2.6D9.2A$75.6D8.A.A6.A.A2.A6.3A9.3A11.A.A.A.A52.A
.A2.3A2.A.A32.2D6.2D9.A.A$31.A4.A38.2D2.2D6.2A2.2A4.2A2.2A.2A26.4A.A.
A.A.4A49.2A3.A3.2A33.2D6.2D11.2A$31.6A38.2D2.2D6.A15.A6.3A9.3A6.A4.A5.
A4.A49.A7.A30.6D2.6D$4.A4.A21.6A38.6D19.2A.A7.A.A7.A.A8.A.2A7.2A.A89.
6D2.6D$4.6A21.A4.A38.6D19.A12.A7.A10.2A2.A5.A2.2A93.2D2.2D$4.6A17.4A6.
4A70.2A.2A3.2A.2A8.A.2A7.2A.A54.A38.2D2.2D15.2A$4.A4.A18.2A3.2A3.2A73.
A2.A.A2.A9.A4.A5.A4.A52.A.A33.6D2.6D12.A.A$4A6.4A14.2A2.A2.A2.2A73.A.
2A.2A.A10.4A.A.A.A.4A54.A34.6D2.6D13.2A$.2A3.2A3.2A6.A8.2A2.A2.A2.2A76.
A.A17.A.A.A.A$.2A2.A2.A2.2A6.2A7.2A3.2A3.2A50.8A34.2A2.A.A.A.A2.2A$.2A
2.A2.A2.2A6.A7.4A6.4A49.8A33.A2.A.A2.A2.A.A2.A7.4F4.6F23.2A$.2A3.2A3.
2A18.A4.A53.8A34.A.A.A.3A.A.A.A8.4F4.6F7.A16.A$4A6.4A17.6A53.8A35.A3.
A3.A3.A11.2T4.2T10.A2.A.2A9.A$4.A4.A21.6A53.8A17.A4.A36.2T4.2T9.A6.A7.
A.A$4.6A21.A4.A53.8A17.6A36.2T4.6T6.2A.2A$4.6A80.8A17.6A36.2M4.6M10.2A
6.A.A$4.A4.A80.8A17.A4.A36.2M8.2M$90.8A13.4A6.4A32.2M8.2M10.A2.A2.A.A
$90.8A14.2A3.2A3.2A31.6H2.6H10.2A$90.8A14.2A2.A2.A2.2A31.6H2.6H15.2A$
90.8A14.2A2.A2.A2.2A14.3A41.A$90.8A14.2A3.2A3.2A13.2A2.A40.2A$90.8A13.
4A6.4A11.A2.A$90.8A17.A4.A14.A.2A.A$90.8A17.6A13.A.A2.A.2A$115.6A12.2A
.A2.A3.A$115.A4.A12.A.A.2A.A$133.A2.A2.A15.4D4.6D$134.A2.A17.4D4.6D13.
2A$137.A19.2D4.2D13.A.A2.A$138.A18.2D4.2D12.2A.3A$157.2D4.6D7.2A$114.
A3.A38.2D4.6D10.2A$75.6D8.2M22.A.A.A.A37.2D4.2D2.2D7.2A.A.A$75.6D9.M2.
2M19.2A.2A38.2D4.2D2.2D8.A2.A$75.2D2.2D6.M2.M.M.M16.3A.A.A.3A33.6D2.6D
6.A.A$75.2D2.2D5.M.M.M2.M16.A11.A32.6D2.6D6.2A$75.6D6.2M.M18.A.3A5.3A
.A$75.6D9.2M16.A.A.A7.A.A.A$79.2D9.M7.2M8.A.2A9.2A.A$79.2D10.2M4.M.M6.
A.A.A11.A.A.A$75.6D12.M4.M6.A.A17.A.A49.2A7.2A$75.6D12.M.M10.3A15.3A28.
4pA4.6pA9.A7.A$94.7M54.4pA4.6pA8.A9.A$100.M5.3A15.3A30.2pA4.2pA2.2pA8.
4A3.4A$96.2M7.A.A17.A.A29.2pA4.2pA2.2pA12.A.A$96.M.M7.A.A.A11.A.A.A30.
2H4.6H8.3A.A.A.3A$97.M10.A.2A9.2A.A32.2H4.6H7.A11.A3.2A$108.A.A.A7.A.
A.A32.2B4.2B2.2B7.2A.A5.A.2A4.A$109.A.3A5.3A.A33.2B4.2B2.2B11.A3.A3.A
.3A$110.A11.A32.6B2.6B19.A.A$111.3A.A.A.3A33.6B2.6B16.2A.A2.2A$114.2A
.2A70.A.A$113.A.A.A.A64.A.A.2A2.A$114.A3.A63.3A.A3.2A$181.A4.A.2A$181.
2A3.2A.A!

Also, is a gun possible using this over-unity reaction?

Code: Select all

x = 74, y = 27, rule = B3/S23-a5
71bo$72b2o$71b2o4$bo71bo$2o70b2o$bo57b3o11bo17$54b3o$55bo!

[PK22]

Also, is a gun possible using this over-unity reaction?

Code: Select all

x = 74, y = 27, rule = B3/S23-a5
71bo$72b2o$71b2o4$bo71bo$2o70b2o$bo57b3o11bo17$54b3o$55bo!

Yes - here is a p420 glider gun:

Code: Select all

x = 75, y = 155, rule = B3/S23-a5
65bo$63b2obo$63b2ob2o$62bob2o$61bo2bo2$62b2o4$45b3o$45bo3b2o$45b2o$46b
ob3o$47b3o2$54b3o2$55bo$55bo10$2b2o$b3o$bobobobo$b2o2b2o$2b5o$3b2o49bo
$54bo$53b3o$55bo$53bobo$54bobo$51b2ob2o$53bo3$3b2o$2bobo$2bo$b2o2$38b
3o$35b2o3bo$13b2o24b2o$12b2o21b3obo$14bo21b3o3$71b2o$22b2o46bob3o$21b
3o46bob3o$22b2o46b2o4$22b3o$22bo$23bo17b2o$41bo$42b3o$44bo19$30bo$30b
3o$33bo$32b2o$33b3o$35bo$34bobo3$b2o$b2o$b3o$o2bo$3o2$36bobo$36bob2o$
38b2o$35bo3bo$8b3o24bob2o$35b3o$9bo$9bo5$22bo$22bo$18bobo2bo$16b3o2b2o
$18b3obo$21bo50bo$70b2o$70b3o$69b2o$58bo10b2ob3o$56b2o12b2ob2o$58bo12b
3o16$25bobo$24b2obo$24b2o$24bo3bo$25b2obo$26b3o2$10bo$9bo2bo$7b2o3bo$
7b4o$6bo2bo$7b2o$8bo!

This gun has three major advantages compared to existing guns.
1). Its period is very divisible, so it is compatible with p3, p5, p6, p7, p10, and p20 reflectors.
2). It outputs a glider without the need for a Margolus oscillator.
3). Since its only components are spaceships, fishhooks, and p20s, this is probably synthesisable. If we can construct this, it will be the first synthesis of any linear growth pattern in this rule. (It would also imply a MSM breeder given backrakes and forerakes with a high enough period).
My estimate for the cost is:

Code: Select all

3 x fishhook = 3 * 2G = 6G
12 x p20 = 12 * 3G = 36G
1 x G = 1 * 2G (in case of kickbacks) = 2G
4 x T = 4 * 2G = 8G
Add 8G to account for potential kickbacks.
Total: ~60G

3G synth for p20:

Code: Select all

x = 23, y = 20, rule = B3/S23-a5
$5bobo5bo$5b2o4b2o$6bo5b2o6$3b2o$2bobo$4bo!

I will start work on the synthesis tomorrow.
EDIT: Miscalculation fixed.

[hotcrystal0]

Here is a promising lead for an OR gate (technically a NOR fed into a NOT but nobody cares). The marked Ts are the inputs. This works for three out of four cases, with the one that doesn’t work being when the top signal is on but the bottom is off:

Code: Select all

x = 30, y = 28, rule = B3/S23-a5History
A27.D$.2A24.2D$A27.D4$26.3A$26.A.A$25.A2.2A$7.A17.2A.2A$7.3A16.3A$10.
A$9.2A4$6.C$7.2C17.A$6.C17.2A$26.A$11.3C$12.C7.A$19.A.A$21.2A$22.A$19.
A2.A$18.2A.2A$20.A!

Edit: Unrelated, but P18 SKOP reduced again to 46 cells by using a P3 instead of a P6:

Code: Select all

x = 14, y = 15, rule = B3/S23-a5
b2o$bo2$b2o$2b2ob2o$o6bo$2obo2bo3bo$5bo3bobo$9bobo$6b2obo2b2o$10bobo$
2b2obobob2o2bo$2bob2obo3b2o$7bob2o$7b2obo!

[ThePlayzr]

OR gate:

Code: Select all

x = 29, y = 32, rule = B3/S23-a5History
25.2A$24.5A$24.A3.A$24.2A.2A$25.2A5$.C$2C$.C6$4.A$4.A$3.A.A10$16.A$16.
A$15.A.A!

The Ts travelling vertically are the 2 signals.
NOT gate:

Code: Select all

x = 30, y = 32, rule = B3/S23-a5History
26.2A$25.5A$25.A3.A$25.2A.2A$26.2A5$.C$2C$.C6$4.A$4.A$3.A.A10$16.A$16.
A$15.A.A!

XOR gate:

Code: Select all

x = 34, y = 67, rule = B3/S23-a5History
30.2A$29.5A$29.A3.A$29.2A.2A$30.2A5$.C$2C$.C3$23.A$22.A.A$24.2A$4.A20.
A$4.A17.A2.A$5.A15.2A.2A$23.A9$16.A$16.A$15.A.A33$31.C$30.3C$30.3C!

The marked Ts are required, the normal Ts are the inputs.
Do we need XAND or XNOT? If no, then we have everything we need.
PK22, are you going to do another search for 3c/7?

[PK22]

OR gate:

Code: Select all

x = 29, y = 32, rule = B3/S23-a5History
25.2A$24.5A$24.A3.A$24.2A.2A$25.2A5$.C$2C$.C6$4.A$4.A$3.A.A10$16.A$16.
A$15.A.A!

The Ts travelling vertically are the 2 signals.
(...)
PK22, are you going to do another search for 3c/7?

1). That is an XOR gate. Here is the truth table for the gate you posted, where A and B are the inputs and C is the output:

Code: Select all

A B C
0 0 0
0 1 1
1 0 1
1 1 0

We do not need XAND or XNOT - we just need XOR, AND, and OR, and that should be sufficient to emulate W110.
It would be easier to work with an OR gate that has two perpendicular inputs in the same phase, I think.

2). I think my computing power is better spent on other searches for this rule, such as Mateon1_Glider8_4_5_Test.

Here is where I am at with synthesising the p420 gun:

Code: Select all

x = 253, y = 355, rule = B3/S23-a5History
32.A.A$33.2A$33.A2$26.A$24.A.A$25.2A17$36.A$34.A.A$35.2A2$250.A$250.A
.A$250.2A15$226.A.A$226.2A$227.A7$21.A$19.A.A$20.2A3$4.A.A$5.2A$5.A
31$231.A$230.A$230.3A2$155.D$153.2D.D$153.2D.2D$152.D.2D75.A$151.D2.D
76.A.A$231.2A$152.2D4$135.3D$135.D3.2D$135.2D$136.D.3D$137.3D2$144.3D
2$145.D$145.D6$2.A$3.A$.3A2$92.2D$91.3D$91.D.D.D.D$2.A88.2D2.2D$A.A
89.5D$.2A90.2D49.D$144.D$143.3D$145.D$143.D.D$144.D.D$141.2D.2D$143.D
3$93.2D$92.D.D$92.D$91.2D2$128.3D$125.2D3.D$129.2D$125.3D.D$126.3D3$
161.2D$112.2D46.D.3D$111.3D46.D.3D$112.2D46.2D4$112.3D$112.D$113.D17.
2D$131.D$132.3D$134.D19$120.D$120.3D$123.D$122.2D6$91.2D$91.2D$91.3D$
90.D2.D$90.3D2$126.D.D$126.D.2D$128.2D$125.D3.D$98.3D24.D.2D$125.3D$
99.D$99.D5$112.D$112.D131.2A$108.D.D2.D123.3A4.A.A$106.3D2.2D124.A6.A
$108.2D128.A$162.D$160.2D$160.3D$159.2D$148.D10.2D.3D$146.2D12.2D.2D$
148.D12.3D16$115.D.D$114.2D.D$114.2D$42.2A70.D3.D$43.2A70.2D.D$42.A
73.3D2$100.D$25.2A72.D2.D$24.A.A4.3A63.2D3.D$26.A6.A63.4D$32.A63.D2.D
$97.2D$98.D30$243.A$242.2A$242.A.A15$239.2A$239.A.A$239.A5$20.2AD$21.
2A$20.A47$232.2A$231.2A$233.A!

[ThePlayzr]

OR gate:

Code: Select all

x = 29, y = 32, rule = B3/S23-a5History
25.2A$24.5A$24.A3.A$24.2A.2A$25.2A5$.C$2C$.C6$4.A$4.A$3.A.A10$16.A$16.
A$15.A.A!

The Ts travelling vertically are the 2 signals.
(...)
PK22, are you going to do another search for 3c/7?

1). That is an XOR gate. Here is the truth table for the gate you posted, where A and B are the inputs and C is the output:

Code: Select all

A B C
0 0 0
0 1 1
1 0 1
1 1 0

No, as the T coming from the left is coming from a gun that is part of the gate. The two Ts coming from below are 2 different signals.

[Resu]

AND gate?

Code: Select all

x = 92, y = 32, rule = B3/S23-a5History
15.2A$15.A.A.2A.A24.2A31.2A$17.A.A.2A24.A.A.2A.A25.A.A.2A.A$15.A.A.A29.
A.A.2A27.A.A.2A$14.A4.A27.A.A.A28.A.A.A$17.2A27.A4.A27.A4.A$49.2A31.2A
$17.2A$2.2A10.A4.A29.2A31.2A$.A.A11.A.A.A14.2A10.A4.A15.2A10.A4.A$.A15.
A.A.2A10.A.A11.A.A.A14.A.A11.A.A.A$2A13.A.A.2A.A10.A15.A.A.2A11.A15.A
.A.2A$15.2A15.2A13.A.A.2A.A10.2A13.A.A.2A.A$47.2A31.2A7$5.A$4.2A31.A$
5.A30.2A$23.2A12.A$23.A.A29.2A31.2A$25.A29.A.A30.A.A$25.2A30.A32.A$57.
2A31.2A$11.A$11.A64.A$10.A.A63.A$75.A.A!

Edit: Wait, how did I not see this post? viewtopic.php?p=215635#p215635

[ThePlayzr]

AND gate?

Code: Select all

x = 92, y = 32, rule = B3/S23-a5History
15.2A$15.A.A.2A.A24.2A31.2A$17.A.A.2A24.A.A.2A.A25.A.A.2A.A$15.A.A.A29.
A.A.2A27.A.A.2A$14.A4.A27.A.A.A28.A.A.A$17.2A27.A4.A27.A4.A$49.2A31.2A
$17.2A$2.2A10.A4.A29.2A31.2A$.A.A11.A.A.A14.2A10.A4.A15.2A10.A4.A$.A15.
A.A.2A10.A.A11.A.A.A14.A.A11.A.A.A$2A13.A.A.2A.A10.A15.A.A.2A11.A15.A
.A.2A$15.2A15.2A13.A.A.2A.A10.2A13.A.A.2A.A$47.2A31.2A7$5.A$4.2A31.A$
5.A30.2A$23.2A12.A$23.A.A29.2A31.2A$25.A29.A.A30.A.A$25.2A30.A32.A$57.
2A31.2A$11.A$11.A64.A$10.A.A63.A$75.A.A!

Edit: Wait, how did I not see this post? viewtopic.php?f=11&t=6970&start=350

Umm, did you mean This post?

[Resu]

Edit: Wait, how did I not see this post? viewtopic.php?f=11&t=6970&start=350

Umm, did you mean This post?

Yep. I tried to change the link, but it just caused me to edit the post again.
Edit: Why is https://conwaylife.com/forums/viewtopic.php?p=215635#p215635 and viewtopic.php?p=215635#p215635 different???
Edit 2: A lane shifter would be so useful, has one been found?

[PK22]

No, as the T coming from the left is coming from a gun that is part of the gate. The two Ts coming from below are 2 different signals.

My point still stands. An OR gate should return 1 if any of its inputs are 1, but if both bottom Ts are present, then it returns 0. The gate only returns 1 if there is one T approaching from the south, which makes it an XOR gate.

A lane shifter could be achieved by taking the below AND gate and having the eastbound input permanently provided by a gun. It does phase shift the T, though.

AND is simple. Just do this:

Code: Select all

x = 15, y = 15, rule = B3/S23-a5
9bo$7b3o$6bo$6b2o5b2o$13bo$11bobo$11b2o$bo$2o$bo4$3b3o$4bo!

[ThePlayzr]

No, as the T coming from the left is coming from a gun that is part of the gate. The two Ts coming from below are 2 different signals.

My point still stands. An OR gate should return 1 if any of its inputs are 1, but if both bottom Ts are present, then it returns 0. The gate only returns 1 if there is one T approaching from the south, which makes it an XOR gate.

Oh, I though OR meant it produced a signal if it received 01 or 10, and receiving 11 makes it not produce a signal. You are correct.
Edit: here is a OR gate, that produces a T if it receives 01, 10, or 11.

Code: Select all

x = 44, y = 60, rule = B3/S23-a5History
42.C$42.C2$41.3C25$26.2A$25.5A$25.A3.A$25.2A.2A$26.2A5$.C$2C$.C6$4.A$
4.A$3.A.A10$16.A$16.A$15.A.A!

[PK22]

I got the gun synthesis finished! It uses 55G (5G below my initial target of 60G) to create a stator variant of the p420 gun with one of the capping eaters in a different position:

Code: Select all

x = 762, y = 760, rule = B3/S23-a5
759bobo$759b2o$760bo94$118bo$116bobo$117b2o7$654bobo$654b2o$655bo4$97b
o$98bo$96b3o11$497bo$495b2o$496b2o4$167bo$168bo$166b3o16$496bo$495bo$
253bobo239b3o$254b2o$254bo2$247bo$245bobo$246b2o5$602bo$601bo$601b3o3$
598bobo$598b2o$599bo5$257bo$255bobo$256b2o2$491bo$491bobo$491b2o15$
467bobo$467b2o$468bo4$285bo$286bo$173bobo108b3o$174b2o66bo$174bo65bobo
$241b2o2$285bo$225bobo55bobo$226b2o56b2o$226bo31$472bo$471bo$471b3o5$
472bo$472bobo$472b2o20$223bo$224bo$222b3o5$223bo$221bobo$222b2o17$435b
obo5bo$435b2o4b2o$436bo5b2o65$275b2o$276b2o$275bo4$276bo$276b2o$275bob
o9$485b2o$478b3o4bobo$478bo6bo$479bo26$263b2o$264b2o$263bo3$246b2o$
245bobo4b3o$247bo6bo$253bo3$503b2o$502b2o$504bo27$484bo$164b2o317b2o$
165b2o316bobo$164bo2$161b2o$160bobo$162bo10$480b2o$480bobo$480bo5$241b
2o$242b2o$241bo25$473b2o$466b3o4bobo$466bo6bo$467bo7$528bo$527b2o$527b
obo4$221b2o$220bobo$222bo4$473b2o$472b2o$474bo21$105b3o$107bo$106bo
538b2o$645bobo$645bo31$596b2o$596bobo$596bo4$172bo$172b2o$171bobo30$
599bo$598b2o$598bobo4$83b2o$84b2o$83bo4$84bo$84b2o$83bobo18$3o$2bo$bo
650b2o96b2o$651b2o97bobo$653bo96bo45$724b3o$724bo$725bo56$757b2o$756b
2o$758bo!

This is, to my knowledge, the first synthesis of any infinite growth pattern in this rule.
Unfortunately, it is rather complex, and it might be difficult to create a MSM breeder using it.
EDIT: Synthesis for a T tagalong (xq4_8mnwss8z013) in 16G!

Code: Select all

x = 83, y = 78, rule = B3/S23-a5
61bo$60bo$60b3o$6bo$4bobo$5b2o$57bo$57bobo17bo$57b2o16b2o$76b2o2$3bob
o55bobo$4b2o55b2o$4bo57bo4bo$66bo$66b3o4$59bobo$59b2o$60bo$53bobo$53b
2o$54bo$15bo$13bobo$14b2o22$44b2o$43b2o8b2o$45bo7bobo$53bo5$55bo$54b2o
$54bobo$60b2o$60bobo$60bo9$b2o$obo$2bo2$80b2o$80bobo$80bo!

This should be gunnable - the glider salvos are a little tight, especially the top-right one, but clock insertion works in this rule, so if the 2G inserter (the 2G collision producing a glider perpendicular to both input gliders) fails, I can use that - especially since the clock is more common in this rule and should be easier to synthesise.

The repeat time is, sadly, >420, so we cannot use my small glider gun to create a gun for this, but I will adjust it to p540 and use that as the basis for the T tagalong gun.

[ThePlayzr]

I got the gun synthesis finished! It uses 55G (5G below my initial target of 60G) to create a stator variant of the p420 gun with one of the capping eaters in a different position:

Code: Select all

x = 762, y = 760, rule = B3/S23-a5
759bobo$759b2o$760bo94$118bo$116bobo$117b2o7$654bobo$654b2o$655bo4$97b
o$98bo$96b3o11$497bo$495b2o$496b2o4$167bo$168bo$166b3o16$496bo$495bo$
253bobo239b3o$254b2o$254bo2$247bo$245bobo$246b2o5$602bo$601bo$601b3o3$
598bobo$598b2o$599bo5$257bo$255bobo$256b2o2$491bo$491bobo$491b2o15$
467bobo$467b2o$468bo4$285bo$286bo$173bobo108b3o$174b2o66bo$174bo65bobo
$241b2o2$285bo$225bobo55bobo$226b2o56b2o$226bo31$472bo$471bo$471b3o5$
472bo$472bobo$472b2o20$223bo$224bo$222b3o5$223bo$221bobo$222b2o17$435b
obo5bo$435b2o4b2o$436bo5b2o65$275b2o$276b2o$275bo4$276bo$276b2o$275bob
o9$485b2o$478b3o4bobo$478bo6bo$479bo26$263b2o$264b2o$263bo3$246b2o$
245bobo4b3o$247bo6bo$253bo3$503b2o$502b2o$504bo27$484bo$164b2o317b2o$
165b2o316bobo$164bo2$161b2o$160bobo$162bo10$480b2o$480bobo$480bo5$241b
2o$242b2o$241bo25$473b2o$466b3o4bobo$466bo6bo$467bo7$528bo$527b2o$527b
obo4$221b2o$220bobo$222bo4$473b2o$472b2o$474bo21$105b3o$107bo$106bo
538b2o$645bobo$645bo31$596b2o$596bobo$596bo4$172bo$172b2o$171bobo30$
599bo$598b2o$598bobo4$83b2o$84b2o$83bo4$84bo$84b2o$83bobo18$3o$2bo$bo
650b2o96b2o$651b2o97bobo$653bo96bo45$724b3o$724bo$725bo56$757b2o$756b
2o$758bo!

This is, to my knowledge, the first synthesis of any infinite growth pattern in this rule.
Unfortunately, it is rather complex, and it might be difficult to create a MSM breeder using it.
EDIT: Synthesis for a T tagalong (xq4_8mnwss8z013) in 16G!

Code: Select all

 x = 83, y = 78, rule = B3/S23-a5
61bo$60bo$60b3o$6bo$4bobo$5b2o$57bo$57bobo17bo$57b2o16b2o$76b2o2$3bob
o55bobo$4b2o55b2o$4bo57bo4bo$66bo$66b3o4$59bobo$59b2o$60bo$53bobo$53b
2o$54bo$15bo$13bobo$14b2o22$44b2o$43b2o8b2o$45bo7bobo$53bo5$55bo$54b2o
$54bobo$60b2o$60bobo$60bo9$b2o$obo$2bo2$80b2o$80bobo$80bo!

This should be gunnable - the glider salvos are a little tight, especially the top-right one, but clock insertion works in this rule, so if the 2G inserter (the 2G collision producing a glider perpendicular to both input gliders) fails, I can use that - especially since the clock is more common in this rule and should be easier to synthesise.

The repeat time is, sadly, >420, so we cannot use my small glider gun to create a gun for this, but I will adjust it to p540 and use that as the basis for the T tagalong gun.

Awesome work! For some reason, the pattern tag of the tagalong didn't work, but I added a space before the start of the RLE and it works now.
Can we give this spaceship a name? Perhaps Honeybee, In respect to its small size and weak spark (stinger) at the back?

[mmmmmmmmm]

Why call the spaceship honeybee? Why not just bee? It's much simpler. It really does resemble a bee though, that was a good point.
Also, we seem to have everything we need to make a turing machine, can someone start piecing together the turing machine?

[PK22]

Why call the spaceship honeybee? Why not just bee? It's much simpler. It really does resemble a bee though, that was a good point.
Also, we seem to have everything we need to make a turing machine, can someone start piecing together the turing machine?

I do not know what the ideal name would be, but I agree that something bee-related would be good. Just be careful not to create confusion with existing bee-related terminology in Life.

Here is a 3G clock synthesis:

Code: Select all

x = 19, y = 19, rule = B3/S23-a5
3$4bobo$5b2o$5bo2$12bo$12bobo$12b2o$4bo$5b2o$4b2o!

p540 gun, which will form the basis of the xq4 gun:

Code: Select all

x = 103, y = 230, rule = B3/S23-a5
66b2o$65b3o$64bo3bo$64bobobo$63b2obo$63bob2o2$47bo$46bob2o$45b2ob2o$
47b2obo$48bo2bo2$49b2o44$55bo$2bo51b3o$2ob2o49b3o$3bobo$2bobo$4bo$2b3o
$3bo$3bo49b3o$52bob3o$51b2o$51bo3b2o$51b3o4$3b2o$2bobo$2bo$b2o35bo$36b
2obo$36b2ob2o$35bob2o$34bo2bo2$35b2o$73bo$72b3o$71bo2bo$64bo6b2obo$64b
2o7b2o$64bo6$41b2o$41bo$42b3o$44bo25$55b2o$55bobo$55bo7$45bo$45b3o$48b
o$47b2o16b2o$64b2o8b3o$66bo7bo$72b2o2bo$71b2ob2ob2o$68bobo3b2o2bo$16b
4o48bo2b3o2b3o$16bo2b2o47b2o6bobo$17bobo$17b2o2$52bo$51bo2bo23b3o$49b
2o3bo23b3o$49b4o26bo$48bo2bo$49b2o$50bo7$35b3o$34b2obo$33bo3bo$33b2o$
33b2obo$34bobo2$87bo$84b3obo$82b3o2b2o$84bobo2bo$88bo$88bo$101bo$102bo
$100b3o34$24bo$23b3o$23b3o5$41bo$39bo2bo$39bo3b2o$41b4o$42bo2bo$43b2o$
43bo4$26b2o$24b3o$23bo3bo$22b2ob3o$22b2o$24b2o!

Also, we are technically not assembling a Turing machine, only a W110 metacell, but since any Turing machine can be emulated using W110, completing the metacell should be enough to prove Travelling Ts Turing complete. I will start work on the metacell once I complete the xq4 gun.

[ThePlayzr]

I recall doing LLSSS searches for 3c/7 at fairly high symmetric width and finding only partials, but i'd have to check what width.

Can you use LLSSS to prove that the spaceship below is the smallest 2c/4?

Code: Select all

x = 15, y = 8, rule = B3/S23-a5
b3o7b3o$2ob2o5b2ob2o$2obob2ob2obob2o$6bobo$4bobobobo$6bobo$6bobo$5b2o
b2o!

Also, I found a pulling reaction that we might be able to use to make a sublinear growth pattern.

Code: Select all

x = 201, y = 341, rule = B3/S23-a5
98b2o$98b2o$98b2o23$135b2o$133b2o$133b2ob3o$67bo66bo3bo$65b2obo66b3o$65b2ob2o67b2o$64bob2o$63bo2bo2$64b2o88bo$154b2o$153bo2bo$152b4o$47b3o100bo3b2o$47bo3b2o97bo2bo$47b2o96bo6bo$48bob3o92bo$49b3o92bobo2$56b3o2$57bo$57bo7$199bo$199bo$195bobo2bo$4b2o187b3o2b2o$3b3o189b3obo$3bobobobo188bo$3b2o2b2o$4b5o136bobo$5b2o49bo87b2obo$56bo87b2o$55b3o86bo3bo$57bo87b2obo$55bobo88b3o$56bobo$53b2ob2o$55bo140b2o$196bobo$198bo$5b2o191b2o$4bobo154bo$4bo155b2o$3b2o154bo2bo$160b4o22b3o$40b3o117b2o3bo22bo$37b2o3bo119bo2bo21bo$15b2o24b2o120bo$14b2o21b3obo$16bo21b3o87b2o$128bobo48bo$127bo2b2o44b2obo$73b2o52b4o48bo$24b2o46bob3o$23b3o46bob3o$24b2o46b2o103bo$177b2o$176bobo$158b2o$24b3o132bo$24bo131b3o$25bo17b2o111bo$43bo$44b3o$46bo16$170bo$168b3o$167bo$32bo135bo$32b3o130bob2o$35bo128bo2bo$34b2o129bo$35b3o$37bo$36bobo$199b2o$197b2obo$3b2o192bo2bo$3b2o193b3o$3b3o193bo$2bo2bo155b2o$2b3o$160bo2bo$38bobo120bob2o26bo$38bob2o120b2ob2o24bo$40b2o120b2obo24bobo$37bo3bo122bo$10b3o24bob2o$37b3o$11bo$11bo3$177b3o$177bo3b2o$24bo152b2o$24bo153bob3o$20bobo2bo103bo49b3o$18b3o2b2o104bo$20b3obo103b3o$23bo50bo55bo$72b2o54bobo12bo$72b3o54bobo10b2o$71b2o27b3o23b2ob2o12bo$60bo10b2ob3o51bo$58b2o12b2ob2o24bo$60bo12b3o25bo13$175b2o2$174bo2bo$27bobo143b2obo$26b2obo141b2ob2o$26b2o144bob2o$26bo3bo142bo$27b2obo$28b3o158bob2o$189b2obo$12bo177bobobo$11bo2bo175bo3bo$9b2o3bo176b3o$9b4o179b2o$8bo2bo$9b2o$10bo$133b2o$131b2o$131b2ob3o$65bo66bo3bo$63b2obo66b3o$63b2ob2o67b2o$62bob2o$61bo2bo2$62b2o88bo$152b2o$151bo2bo$150b4o$45b3o100bo3b2o$45bo3b2o97bo2bo$45b2o96bo6bo$46bob3o92bo$47b3o92bobo2$54b3o$98b3o$55bo$55bo43bo$99bo6$197bo$197bo$193bobo2bo$2b2o187b3o2b2o$b3o189b3obo$bobobobo188bo$b2o2b2o$2b5o136bobo$3b2o49bo87b2obo$54bo87b2o$53b3o86bo3bo$55bo87b2obo$53bobo88b3o$54bobo$51b2ob2o$53bo140b2o$194bobo$196bo$3b2o191b2o$2bobo154bo$2bo155b2o$b2o154bo2bo$158b4o22b3o$38b3o117b2o3bo22bo$35b2o3bo119bo2bo21bo$13b2o24b2o120bo$12b2o21b3obo$14bo21b3o87b2o$126bobo48bo$125bo2b2o44b2obo$71b2o52b4o48bo$22b2o46bob3o$21b3o46bob3o$22b2o46b2o103bo$175b2o$174bobo$156b2o$22b3o132bo$22bo131b3o$23bo17b2o111bo$41bo$42b3o$44bo16$168bo$166b3o$165bo$30bo135bo$30b3o130bob2o$33bo128bo2bo$32b2o129bo$33b3o$35bo$34bobo$197b2o$195b2obo$b2o192bo2bo$b2o193b3o$b3o193bo$o2bo155b2o$3o$158bo2bo$36bobo120bob2o26bo$36bob2o120b2ob2o24bo$38b2o120b2obo24bobo$35bo3bo122bo$8b3o24bob2o$35b3o$9bo$9bo3$175b3o$175bo3b2o$22bo152b2o$22bo153bob3o$18bobo2bo103bo49b3o$16b3o2b2o104bo$18b3obo103b3o$21bo50bo55bo$70b2o54bobo12bo$70b3o54bobo10b2o$69b2o27b3o23b2ob2o12bo$58bo10b2ob3o51bo$56b2o12b2ob2o24bo$58bo12b3o25bo13$173b2o2$172bo2bo$25bobo143b2obo$24b2obo141b2ob2o$24b2o144bob2o$24bo3bo142bo$25b2obo$26b3o158bob2o$187b2obo$10bo177bobobo$9bo2bo175bo3bo$7b2o3bo176b3o$7b4o179b2o$6bo2bo$7b2o$8bo!

[Resu]

What is the smallest T gun?
What is the smallest glider gun?

[mmmmmmmmm]

By population, the smallest known T gun is the p348, with 285 cells:

Code: Select all

x = 80, y = 266, rule = B3/S23-a5
66b2ob2o$66bo3bo$60b2o5bobo$61bo2b4ob4o$57bo3bobo9bo$57b3obob2o3bo3b2o
$60b2o6bo$59bobo$59bo$56b2ob2o$56bob3o$60bo4bo$56bob3o3b3o$56b2ob2o3b
3o$59bo$59bobo$60b2o72$69bobo$70bo$70bo8$65bo$64b3o$64b3o2$22b2o7b2o$
23bo7bo$22bo9bo$22b4o3b4o$26bobo$22b2ob2ob2ob2o$21bo2b2o3b2o2bo$21b2o
9b2o$4b2o$3bobo$3bo47b2o$2obo46b3o$ob2obo45b2o$5bo$ob2obo$2obo$3bo$3b
obo$4b2o6$44bo$42b2o$43b2o4$9bo$8b3o$8b3o11$74b2o$74bobo$76bo$76bob2o
$74bob2obo$74bo$46bo27bob2obo$46b2o28bob2o$46bo29bo$74bobo$74b2o$32b2o
9b2o$32bo2b2o3b2o2bo$33b2ob2ob2ob2o$37bobo$33b4o3b4o$33bo9bo$34bo7bo$
33b2o7b2o12$28bo$28bo2$27b3o31$13bobo$14bo$14bo8$9bo$8b3o$8b3o28$18b2o
$18bobo$20bo$19b2ob2o$19b3obo$19bo$19b3obo$19b2ob2o$20bo$18bobo$11bo6b
2o$6b2o3bo3b2obob3o$6bo9bobo3bo$7b4ob4o2bo$10bobo5b2o$9bo3bo$9b2ob2o!

By population, the smallest known glider gun is the p420, with 198 cells:

Code: Select all

x = 75, y = 155, rule = B3/S23-a5
65bo$63b2obo$63b2ob2o$62bob2o$61bo2bo2$62b2o4$45b3o$45bo3b2o$45b2o$46b
ob3o$47b3o2$54b3o2$55bo$55bo10$2b2o$b3o$bobobobo$b2o2b2o$2b5o$3b2o49b
o$54bo$53b3o$55bo$53bobo$54bobo$51b2ob2o$53bo3$3b2o$2bobo$2bo$b2o2$38b
3o$35b2o3bo$13b2o24b2o$12b2o21b3obo$14bo21b3o3$71b2o$22b2o46bob3o$21b
3o46bob3o$22b2o46b2o4$22b3o$22bo$23bo17b2o$41bo$42b3o$44bo19$30bo$30b
3o$33bo$32b2o$33b3o$35bo$34bobo3$b2o$b2o$b3o$o2bo$3o2$36bobo$36bob2o$
38b2o$35bo3bo$8b3o24bob2o$35b3o$9bo$9bo5$22bo$22bo$18bobo2bo$16b3o2b2o
$18b3obo$21bo50bo$70b2o$70b3o$69b2o$58bo10b2ob3o$56b2o12b2ob2o$58bo12b
3o16$25bobo$24b2obo$24b2o$24bo3bo$25b2obo$26b3o2$10bo$9bo2bo$7b2o3bo$
7b4o$6bo2bo$7b2o$8bo!

Edit: I reduced the p420 glider gun to 179* cells, using 2 less eaters with one of the extra Ts being reflected towards the first glider, destroying it.

Code: Select all

x = 75, y = 155, rule = B3/S23-a5
65bo$63b2obo$63b2ob2o$62bob2o$61bo2bo2$62b2o4$45b3o$45bo3b2o$45b2o$46b
ob3o$47b3o2$54b3o2$55bo$55bo10$2b2o$b3o$bobobobo$b2o2b2o$2b5o$3b2o49b
o$54bo$53b3o$55bo$53bobo$54bobo$51b2ob2o$53bo8$43b3o$40b2o3bo$44b2o$40b
3obo$41b3o3$71b2o$22b2o46bob3o$21b3o46bob3o$22b2o46b2o4$22b3o$22bo$23b
o22$30bo$30b3o$33bo$32b2o$33b3o$35bo$34bobo3$b2o$b2o$b3o$o2bo$3o2$36b
obo$36bob2o$38b2o$35bo3bo$8b3o24bob2o$35b3o$9bo$9bo5$22bo$22bo$18bobo
2bo$16b3o2b2o$18b3obo$21bo50bo$70b2o$70b3o$69b2o$58bo10b2ob3o$56b2o12b
2ob2o$58bo12b3o16$25bobo$24b2obo$24b2o$24bo3bo$25b2obo$26b3o2$10bo$9b
o2bo$7b2o3bo$7b4o$6bo2bo$7b2o$8bo!

PK22, can you adjust the synthesis to produce this variation? This will make it cost 51G, or 52G if it turns out we need to use an insertion.

[Resu]

What parts are still needed for the W110 metacell?