Thread for basic questions

[Chris857]

Some past discussion on similar questions.

viewtopic.php?f=7&t=2036&p=162560&hilit ... le#p162558
viewtopic.php?f=2&t=5296

[tommyaweosme]

you might be looking for state 6 in lifehistory

Code: Select all

x = 6, y = 13, rule = LifeHistory
5.F$5.F$5.F$.A3.F$2.A2.F$3A2.F$5.F$5.F$5.F$5.F$5.F$5.F$5.F!

i will guide you, newcomer, on the journey from being a ca newcomer to master

[squareroot12621]

you might be looking for state 6 in lifehistory

Code: Select all

x = 6, y = 13, rule = LifeHistory
5.F$5.F$5.F$.A3.F$2.A2.F$3A2.F$5.F$5.F$5.F$5.F$5.F$5.F$5.F!

i will guide you, newcomer, on the journey from being a ca newcomer to master

I think they meant Life, not LifeHistory.

[Vort]

Dieter and Peter's glider gun collection wiki page mentions two methods for managing gun patterns: Git and Catagolue.
Git is decentralized version control system, which means many copies of data exist on computers of various users.
If GitHub fails, data can be moved to GitLab, from GitLab it can be moved somewhere else and so on.
But such method have disadvantage - it requires manual work for checking and updating patterns.

Catagolue database solves maintenance problem by automation of verification tasks.
But it makes storage mostly centralized.
Of course, some users will have copies of some patterns, but not all of them.

I think gun collection is valuable enough to have some storage redundancy.
It is possible to write script which will download and parse HTML pages from Catagolue and upload new found patterns to Git, but maybe someone knows smarter solution?

[confocaloid]

[...]
I think gun collection is valuable enough to have some storage redundancy.
It is possible to write script which will download and parse HTML pages from Catagolue and upload new found patterns to Git, but maybe someone knows smarter solution?

Well, redundancy is relatively easy (indeed, it would suffice to periodically run a script that fetches the current guns and stores them somewhere).

What would be very useful is a filterable collection of all known guns. Some kind of repository with multiple different p64 glider guns, multiple different p120 guns, multiple different p690 guns, and so on. More details: viewtopic.php?p=173768#p173768

Note: consider fetching a plain-text page instead of decoding an HTML page. (For example, instead of gun_2024 you can use /textsamples/gun_2024/b3s23/synthesis.)

[vilc]

It is possible to write script which will download and parse HTML pages from Catagolue and upload new found patterns to Git, but maybe someone knows smarter solution?

As confocaloid said, you can access the rle of pXXX gun using the following URLs :

Code: Select all

https://catagolue.hatsya.com/textsamples/gun_XXX/b3s23/synthesis
https://catagolue.hatsya.com/textsamples/guntrue_XXX/b3s23/synthesis

I suggest you also keep updated a copy of the following pages

Code: Select all

https://catagolue.hatsya.com/textcensus/b3s23/synthesis-costs/gun
https://catagolue.hatsya.com/textcensus/b3s23/synthesis-costs/guntrue

and use their data to spot updates.

[Vort]

What would be very useful is a filterable collection of all known guns.

Basic level of such functionality can be achieved with processing of history for Git repository.

As confocaloid said, you can access the rle of pXXX gun using the following URLs : ...

Ok. thanks.

I made primitive tool for making backups:
https://github.com/Vort/GliderGunBackup
And pointed it to this repository:
https://github.com/Vort/glider_guns

I made almost no tests for it, so it may contain bugs.
Also I have problems with hosting of this bot, will think later what to do with it next.

[H. H. P. M. P. Cole]

Is there a one-glider seed that will produce a LWSS/MWSS/HWSS when it is hit one way and self-destructs when it is hit another way?

[confocaloid]

Is there a one-glider seed that will produce a LWSS/MWSS/HWSS when it is hit one way and self-destructs when it is hit another way?

If the glider is translated three cells up, then the pattern vanishes:

Is this one known? MWSS from 3 blocks.

Code: Select all

x = 9, y = 9, rule = B3/S23
6bo$2o4bobo$2o4b2o5$b2o4b2o$b2o4b2o!

Found with gencols [...]

If the glider is translated five cells down, then the pattern vanishes (the 1G seed for the LWSS is from the octo3obj database):

Code: Select all

x = 8, y = 11, rule = B3/S23
5b2o$4bo2bo$5b2o$2o$2o$4b2o$4b2o2$6bo$5b2o$5bobo!

If the glider is translated ten cells down, then the pattern vanishes (the 1G seed for the HWSS is from the octo3obj database):

Code: Select all

x = 14, y = 7, rule = B3/S23
7b2o$6bo2bo$7b2o2b3o$2o9bo$2o10bo$4b2ob2o$4b2ob2o!

In general, many compact stationary patterns have an one-glider destruction. (For example many small still lives.)

[AlbertArmStain]

Does this script prove that anything that has a glider synthesis also can be constructed by slow salvos?

Oh, I thought that I'd already published gnf2seed.py but I can't seem to find it on the forums, so here it is:

Code: Select all

import lifelib
from functools import reduce

sess = lifelib.load_rules('b3s23')
lt = sess.lifetree(n_layers=1)


raw_splitters = ['9bo$8bobo$8bo2bo$9b2o3$2o$obo$bo3$6b3o$6bo$7bo!',
 '7b2o$6bo2bo$7b2o3$2bo$bobo$o2bo$b2o4$9b3o$9bo$10bo!',
 '3bo$2bobo$2b2o3$2o$obo$bobo$2bo2$9b3o$9bo$10bo!',
 '2bo$2b3o$5bo$4b2o5$b2o$o2bo$o2bo$b2o3$11b3o$11bo$12bo!',
 '2o$obo$bo2$9b2o$8bo2bo$8bobo$9bo7$11b3o$11bo$12bo!',
 '5b2o$5bobo$6bobo$7bo3$2o$obo$bo6$3b3o$3bo$4bo!',
 '2bo6bo$bobo4bobo$obo5bobo$2o7bo6$9b3o$9bo$10bo!',
 '2b2o$2bobo$3bobo$4bo3$b2o$o2bo$b2o$7b3o$7bo$8bo!',
 '2b2o$bobo$obo$bo3$7b2o$6bobo$7bo5$9b3o$9bo$10bo!',
 '8b2o$b2o4bo2bo$o2bo3bobo$o2bo4bo$b2o3$11b3o$11bo$12bo!',
 '8b2o$7bo2bo$7bo2bo$8b2o$bo$obo$obo$bo2$7b3o$7bo$8bo!']

raw_180 = ['10b2o$10bobo$11bobo$12b2o5$3o$2bo$bo!',
 '5b2o$5bobo$6bobo$7bo8$3o$2bo$bo!',
 '11bo$10bobo$11bobo$12b2o4$3o$2bo$bo!',
 '6b2o$6bobo$7bobo$8b2o8$3o$2bo$bo!']

raw_90 = ['53bo$52bobo$53b2o52$3o$2bo$bo!',
 '47b2o$48bo$48bobo$49b2o52$b2o$obo$2bo!',
 '52b2o$51bobo$50bobo$51bo53$2o$b2o$o!',
 '52b2o$52b2o3$57b2o$57b2o49$2o$b2o$o!',
 '53bo$52bobo$53bobo$54b2o$59b2o$58bo2bo$58bo2bo$59b2o54$b2o$obo$2bo!',
 '39bo$38bobo$39b2o$43b2o$42bobo$42b2o46$3o$2bo$bo!',
 '46bo$44bobo$45bobo$45bo3$48b2o$48b2o49$3o$2bo$bo!',
 '26bo$25bobo$26b2o4$33b2o$32bobo$31bobo$32bo5$28b2o$27bo2bo$28bo2bo$29b2o9$bo$b2o$obo!',
 '22bo$20bobo$21bobo$21bo4$28bo$28b3o$31bo$30b2o$20bo$19bobo11b2o$18bobo12b2o$18b2o2$28b2o$16b2o10bobo$16bobo10bo$17bobo$18bo23$2o$b2o$o!']


def centre_by(x, y):

    bbox = y.bounding_box
    return x(-(bbox[0] + (bbox[2] // 2)), -(bbox[1] + (bbox[3] // 2)))


def normalise_inserter(p):

    p = lt.pattern(p)
    g = (p - p[8])
    p = (p - g) + g(-128, 128)
    p = centre_by(p, p[1024])(256, 256)
    return p


inserters = [normalise_inserter(p) for p in raw_90]


def try_build_salvo(s, ins):

    gc = lt.pattern('bo$2bo$3o!').centre()

    v = s.components()
    v.sort(key=(lambda x : x.bounding_box[0] - x.bounding_box[1]))

    for g in v:
        for i in range(4):
            h = g[-i]
            if h.centre() == gc:
                dx, dy = h.bounding_box[:2]
                dx += 1
                dy += 1
                assert(gc(dx, dy)[i] == g)
                ii = ins(dx, dy)[i]
                if (s - g + ii)[1024] == s[1024]:
                    return (s - g, ii)
                break
        else:
            raise RuntimeError('Unexpected object in salvo')


def build_salvo_1G(s, direction='left'):

    orients = ['identity', 'transpose'][::{'left': 1, 'right': -1}[direction]]

    for (i, ins) in enumerate(inserters):
        for o in orients:
            res = try_build_salvo(s(o), ins)
            if res:
                return tuple([r(o) for r in res]) + (i, o)

    raise RuntimeError('Failed to construct glider')


def analyse_turner(x):

    tg = x - x[8]
    sl = x & x[8]
    assert(tg.population == 5)
    og = lt.pattern('2o$obo$o!')('flip_x')

    for t in range(4):
        m = tg.match(og[t])
        if m.nonempty():
            x, y = m.bounding_box[:2]
            return [x + y, t - 4*y, sl]


def build_salvo(s, direction='left'):

    comps = []
    dirs = []

    while s.nonempty():
        s, c, i, o = build_salvo_1G(s, direction)
        direction = {'identity': 'right', 'transpose': 'left'}[o]
        comps.append(c)
        dirs.append(o)

    fds = [(sum((r - r[8]).bounding_box) + 48 * i) >> 1 for (i, r) in enumerate(comps)]
    m = max(fds)
    fds = [m - f for f in fds]
    comps = [(((r & r[8]) + (r - r[8])[-4*f])(d)(f, f), d) for (f, r, d) in zip(fds, comps, dirs)]
    comps = [[d] + analyse_turner(c) for (c, d) in comps]
    return comps


def make_adj_splitter(a, b):

    a = lt.pattern(a)
    b = lt.pattern(b)
    a160 = a[160]
    c = lt.pattern('', 'b3s23')
    gnw = lt.pattern('3o$o$bo!', 'b3s23')

    for _ in range(4):
        c += a160.match(b - b[8]).convolve(b & b[8])
        b = b[1]

    while True:
        gg = (a + c(-5, 5))[256] ^ (a + c)[256]
        if (gg.population != 10):
            break
        if (gg[4] != gg(-1, 1)):
            break
        c = c(-1, 1)

    a = a + c(8, -8)
    a = gnw.replace(a.match(gnw).convolve(gnw), a)
    return a


def analyse_splitter(x):

    g = x - x[8]
    assert(g.bounding_box == [0, 0, 3, 3])
    assert(g.population == 5)

    res = []

    for s in [-1, 1]:
        for t in range(256, 260):
            a = x[t].match(g)
            if (a.nonempty()):
                a = a.bounding_box[:2] + [t]
                a[2] += 4 * a[1]
                a[0] += s * a[1]
                res.append(a[::2])
                break

        g = g('flip_x')

    solid = x & x[8]

    res += [solid[:,:8], solid[:,8:]]
    print([(p if isinstance(p, list) else p.apgcode) for p in res])
    return res


def make_best_splitters():

    v = [make_adj_splitter(a, b) for a in raw_splitters for b in raw_180]
    v.sort(key=(lambda x : x.population))
    d = {}
    g = lt.pattern('bo$o$3o!', 'b3s23')

    for w in v[::-1]:
        w256 = w[256]
        for i in range(4):
            m = w256.match(g[i])
            if m.nonempty():
                k = i + ((m.bounding_box[0] & 1) << 2) + ((sum(m.bounding_box) & 1) << 3)
                d[k] = w

    d = [analyse_splitter(d[k]('transpose')) for k in range(16)]

    return d


adj_splitters = make_best_splitters()

# print(reduce((lambda x, y : x + y), [l(i*100, 0) for (i, l) in enumerate(adj_splitters)]).rle_string())


def split_synth(x):

    g = lt.pattern("bo$2bo$3o", "b3s23")
    gsets = []
    for i in range(4):
        gsets.append(lt.pattern('', 'b3s23'))
        for j in range(4):
            gsets[-1] += x.match(g, halo="3o$3o$3o").convolve(g)
            g = g[1]
        g = g('rot90')
    y = x - (gsets[0] + gsets[1] + gsets[2] + gsets[3])
    return y, gsets


def load_seed():

    runtime = 4096
    seed = '''x = 389, y = 389, rule = B3/S23
185bo$184bobo$185bo3$179bo$179b3o$182bo$181b2o91$278b2o$278b2o3$278b2o
$278b2o3$108b2o$108b2o167b2ob2o$99b2o2b2o172b2ob2o$99b2o2b2o3b2o$108b
2o65$202bo$201bobo$201b2o$382b2o$382bo$380bobo$380b2o2$195b2o190bo$
194bo2bo188bobo$195b2o190bo5$185bo31b2o72bo$184bobo30b2o70bo3bo$184bob
o37b2o3b2o57bo$185bo17bo20b2o2bo2bo56bo4bo$202bobo24b2o57b5o$202bobo$
194b2o7bo$194b2o21b2o$217b2o3$bo190b2o$obo188bo2bo$bo190b2o2$7b2o$6bob
o$6bo$5b2o68$279b2o$279b2o3b2o2b2o$107b2ob2o172b2o2b2o$107b2ob2o167b2o
$279b2o3$109b2o$109b2o3$109b2o$109b2o91$206b2o$206bo$207b3o$209bo3$
203bo$202bobo$203bo!'''

    seed = lt.pattern(seed).centre()

    mwss = (seed - seed[32])
    seed -= mwss
    seed += mwss(1024, 0)

    # check D8_1 symmetry of glider outputs:
    gliders = seed[runtime]
    assert(gliders('rot90') == gliders)
    assert(gliders('flip_x') == gliders)

    bbox = gliders.match(lt.pattern('2o$obo$o!')).bounding_box
    dx = bbox[0] - bbox[1]
    dt = runtime + 4 * bbox[1]

    return seed, dx, dt


class Octopus(object):

    def __init__(self):

        self.seed, dx, dt = load_seed()
        self.arms = [[dx, dt] for _ in range(8)]
        self.starts = ['left', 'left', 'left', 'left']
        print(self.arms)

    def add_stage(self, salvos):

        reverse_transforms = ['identity', 'rot270', 'rot180', 'rot90']
        forward_transforms = ['identity', 'rot90', 'rot180', 'rot270']

        rotated_salvos = [s(t) for (s, t) in zip(salvos, reverse_transforms)]
        rotated_seeds = []

        for (i, s) in enumerate(rotated_salvos):

            seedpart = []
            if s.nonempty():
                comps = build_salvo(s, self.starts[i])
                for (tfm, ol, ot, sl) in comps:
                    aidx = 2*i+len(tfm)-8
                    il, it = self.arms[aidx]
                    for (j, aspl) in enumerate(adj_splitters):
                        disp, delay = aspl[1]
                        if (((disp + il - ol) & 1) == 0) and (((delay + it + ot) & 7) == 0):
                            self.arms[aidx][0] += aspl[0][0]
                            self.arms[aidx][1] += aspl[0][1]
                            x = (il + ol - disp) >> 1
                            y = x - il
                            z = (-ot - it - delay) >> 3
                            seedpart.append([z, x, y, j, sl, tfm])
                            break
                    self.starts[i] = {'transpose': 'left', 'identity': 'right'}[tfm]

                minz = min([a[0] for a in seedpart])
                for a in seedpart:
                    for jdx in range(3):
                        a[jdx] -= minz
                    a[4] = a[4](-minz, -minz)

            seedpart = [[tfm, sl + adj_splitters[j][2](x, y), adj_splitters[j][3](x - z, y + z)] for z, x, y, j, sl, tfm in seedpart]
            rotated_seeds.append(seedpart)

        flat_seeds = []

        for s in rotated_seeds:

            subseed = lt.pattern('')
            for tfm, sl1, sl2 in s:
                subseed += (sl1 + sl2)(tfm)
            flat_seeds.append(subseed)

        lb = 0
        ub = 65536

        halo = lt.pattern('4bo$2b5o$b7o$b7o$9o$b7o$b7o$2b5o$4bo!').centre()
        forbidden = self.seed.convolve(halo)

        def try_dist(d):

            s = self.seed
            for fs, tfm in zip(flat_seeds, forward_transforms):
                fs = fs(-d, -d)(tfm)
                if (fs & forbidden):
                    return None
                s = s + fs

            t = 65536 + 8 * d
            st = s[t]
            og = lt.pattern('2o$obo$o!')

            for (i, (x, dt)) in enumerate(self.arms):
                g = og[t - dt](x, 0)
                g = g(['identity', 'transpose'][i & 1])
                g = g(forward_transforms[i >> 1])
                if ((st & g) != g):
                    return None
                st -= g
            return s, st

        s, desired = try_dist(ub)

        while (ub - lb > 1):
            mb = (ub + lb) >> 1
            x = try_dist(mb)
            if (x is not None) and (x[1] == desired):
                s = x[0]
                ub = mb
            else:
                lb = mb

        print(ub)
        for seedpart in rotated_seeds:
            for s in seedpart:
                for i in [1, 2]:
                    s[i] = s[i](-ub, -ub)

        self.binary_search(rotated_seeds)

    def binary_search(self, rotated_seeds, strategy='binary'):

        halo = lt.pattern('4bo$2b5o$b7o$b7o$9o$b7o$b7o$2b5o$4bo!').centre()
        forbidden = self.seed.convolve(halo)
        forward_transforms = ['identity', 'rot90', 'rot180', 'rot270']

        collapsed = lt.pattern('')
        for (tfm, seedpart) in zip(forward_transforms, rotated_seeds):
            for s in seedpart:
                collapsed += (s[1] + s[2])(s[0])(tfm)

        res = (self.seed + collapsed)[65536]
        for (tfm, seedpart) in zip(forward_transforms, rotated_seeds):
            for s in seedpart:
                lb = sum(s[1].bounding_box[:2]) >> 1
                ub = 0
                while (ub - lb > 1):
                    if (strategy == 'linear') and (ub - lb > 8):
                        mb = ub - 8
                    elif (strategy == 'raenil') and (ub - lb > 8):
                        mb = lb + 8
                    else:
                        mb = (ub + lb) >> 1
                    newp = (s[1] + s[2](mb, -mb))(s[0])(-mb,-mb)(tfm)
                    if (newp & forbidden).nonempty():
                        lb = mb
                        continue
                    cprime = collapsed - (s[1] + s[2](ub, -ub))(s[0])(-ub,-ub)(tfm)
                    cprime = cprime    + newp
                    if (self.seed + cprime)[65536] == res:
                        ub = mb
                        collapsed = cprime
                    else:
                        lb = mb
                print(ub)
                comp = (s[1] + s[2](ub, -ub))(s[0])(-ub,-ub)(tfm)
                self.seed += comp
                forbidden += comp.convolve(halo)

    def finalise(self):

        rotated_seeds = []
        for j in range(4):
            rotated_seeds.append([])
            for (k, tfm) in enumerate(['identity', 'transpose']):
                rotated_seeds[-1].append([tfm,
                    lt.pattern('oo$oo!')(-8000 + self.arms[2*j+k][0], -8000),
                    lt.pattern()])

        self.binary_search(rotated_seeds, 'linear')


def load_stages(filename='gnf.rle'):

    gnf = lt.load(filename)
    bbox = gnf.bounding_box
    gnf = centre_by(gnf, gnf[bbox[0] + bbox[2] - 128:,:])

    stages = []
    while gnf.nonempty():
        x = gnf[-80:, :]
        if x.empty():
            raise ValueError('Malformed GNF')
        # print(x.bounding_box)
        stages.append(x)
        gnf = (gnf - x)(160, 0)

    print('%d stages collected.' % len(stages))

    stages = [split_synth(x) + (x[4096],) for x in stages[::-1]]
    for i in range(len(stages)):
        des = (stages[i-1][2] if (i > 0) else lt.pattern())
        if (stages[i][0] != des):
            print(stages[i][0].rle_string())
            print(des.rle_string())
            assert(False)

    gcount = sum([y.population for x in stages for y in x[1]]) // 5
    print('%d gliders involved.' % gcount)

    return stages


def to_cts(stages):

    orig = lt.pattern()

    for _, g, t in stages:
        lb = 0
        ub = 65536
        while (ub - lb >= 4):
            mb = (ub + lb) >> 1
            g4 = g[0][-mb] + g[1][-mb] + g[2][-mb] + g[3][-mb]
            if (orig + g4)[mb + 4096] == t:
                ub = mb
            else:
                lb = mb
        print(ub)
        g4 = g[0][-ub] + g[1][-ub] + g[2][-ub] + g[3][-ub]
        orig = orig + g4

    return orig


def main():

    octo = Octopus()

    stages = load_stages()
    # print(to_cts(stages).rle_string())

    for (i, s) in enumerate(stages):
        octo.add_stage(s[1])

    print('Finalising...')
    octo.finalise()

    print(octo.seed.rle_string())


if __name__ == '__main__':

    main()

[dvgrn]

Does this script prove that anything that has a glider synthesis also can be constructed by slow salvos?

Seems like the script doesn't _entirely_ constitute an actual proof, since it doesn't do anything to show for certain that there are no edge cases for which the script doesn't work.

If you ran the script on all possible relevant inputs and checked that it worked in every case, that might constitute some kind of case-bash proof ... once you proved that you had in fact enumerated all possible relevant inputs!

It seems to me that Nathaniel's Appendix B.1 in the Life textbook is probably the place to point to for an actual proof of that statement. Appendix B.1 adds some key technical points to the discussion in section 5.7, about how an arrangement of well-separated blocks into a "seed" pattern can create any possible configuration of synchronized gliders, and how a slow salvo can be found to set up any arrangement of well-separated blocks.

[AlbertArmStain]

Seems like the script doesn't _entirely_ constitute an actual proof, since it doesn't do anything to show for certain that there are no edge cases for which the script doesn't work.

If you ran the script on all possible relevant inputs and checked that it worked in every case, that might constitute some kind of case-bash proof ... once you proved that you had in fact enumerated all possible relevant inputs!

Maybe finding a seed for this Borg will further the proof

I've written a script along these lines. Applied to Dave's Borg salvo, it produces the following:

Code: Select all

# [[ MAXGRIDSIZE 14 ]]
x = 15598, y = 15646, rule = B3/S23
1311bo1581bo48bo45bo9457bo383bo46bo432bo48bo2062bo$1067bobo239b2o1581b
o47b2o46bobo9453b2o383bo46bo382bobo46b2o47b2o2062bo$923bo143b2o241b2o
1580b3o46b2o45b2o9455b2o382b3o44b3o380b2o48b2o47b2o2061b3o$922bo145bo
12191bo$922b3o92bo$1016bo1774bobo9599bo$1016b3o1772b2o9598b2o$2792bo
9599b2o6$480bo$480bobo2539bobo$480b2o2540b2o$3023bo3$8058bo4847bo$
2394bo5662bo4847bo$952bo1440bo430bo5232b3o4413bo431b3o44bo2256bo$951bo
1441b3o428bobo9645bo478bo2256bo$951b3o1870b2o8204bo1441b3o476b3o2254b
3o$374bo10654bo$373bo7629bo96bobo2926b3o$373b3o2061bo5565bobo94b2o
4415bo$2435b2o5566b2o96bo4413b2o$1570bo865b2o10078b2o1531bo$560bo1008b
o12479bobo$559bo96bo912b3o12477b2o$559b3o93bo958bo910bobo$655b3o955bo
432bo478b2o5422bo$1613b3o429bo480bo5422bobo3115bobo$699bobo1343b3o
5901b2o236bobo2877b2o2303bo$699b2o7486b2o2879bo1676bobo623bo767bo$700b
o7487bo4556b2o624b3o764bo$2137bo6189bobo4416bo1391b3o$1654bo481bo6190b
2o$741bo912bobo479b3o6189bo$741bobo45bo864b2o1389bo4847bobo3310bo1486b
o$741b2o46bobo2252bo4848b2o476bobo2831bo1487bobo957bo286bo$789b2o1051b
o1201b3o4847bo476b2o2832b3o1485b2o956b2o287bobo44bobo$1747bo94bobo
4700bo1826bo46bo5232b2o286b2o45b2o$1746bo95b2o4701bobo1870bo4559bo
1009bo$1746b3o475bo4320b2o1871b3o4556bo$2224bobo10316bo433b3o907bobo$
2224b2o43bobo1629bobo7342bobo862bo430bo1344b2o$2269b2o1630b2o2685bo
4657b2o861b2o431b3o1343bo1675bo$2270bo1631bo2685bobo4656bo862b2o3452bo
bo$3180bo814bo143bo2448b2o8974b2o$3178b2o814bo47bo96bobo4076bobo$3179b
2o188bo624b3o44bo97b2o91bo2401bo1583b2o$3369bobo669b3o188bobo2398bo
287bo1297bo2877bo3166bo$3369b2o43bobo815b2o2399b3o284bo4175bo1053bo
2112bo$3414b2o47bo3456b3o4173b3o1051bobo2110b3o$3415bo46bo8687b2o$
3462b3o42bo49bo$3507bobo45b2o3120bo284bobo3886bo$3507b2o47b2o763bo
2353b2o285b2o3887bobo$4321bobo46bo239bo2065b2o285bo3887b2o1340bobo$
3647bobo671b2o45b2o239bo7583b2o$3647b2o720b2o238b3o7582bo$3648bo1004bo
$2637bobo1053bo959bobo286bo93bobo1967bo$2637b2o1054bobo44bo912b2o285b
2o94b2o1967bo7343bo$2638bo1054b2o44bo767bo383bo49b2o94bo1967b3o1435bo
5903b2o$3739b3o764bo383bo1585bo1965bo5905b2o$4506b3o189bo191b3o236bobo
1342b2o1966b3o3595bobo$4697bo431b2o1344b2o5563b2o$4697b3o430bo3453bo
3456bo$1864bo6718bo2686bo$1862b2o3884bo2834b3o2684bobo3115bo$1863b2o
2875bo1007bobo1100bo4418b2o3116bobo45bo$4740bobo1005b2o1101bobo7534b2o
45bo$4740b2o2109b2o2156bo5425b3o$3107bo5901bobo$3105b2o5902b2o2350bo$
3106b2o8252bo3118bo$5215bo6144b3o3116bobo$5214bo9264b2o$4827bo386b3o
1483bobo2445bobo$4827bobo1870b2o2446b2o$4827b2o525bo481bo864bo2447bo
3070bo$5354bobo139bobo335b2o3645bo2736b2o$5354b2o140b2o45bo291b2o3643b
o2738b2o$5497bo45bobo3837bobo94b3o$5543b2o381bo3456b2o$5589bo336bobo
1099bobo2353bo$5588bo337b2o284bo815b2o2542bo$5588b3o620bo817bo2541bo$
6211b3o3357b3o$5635bo333bobo1245bobo$5633b2o334b2o142bo1103b2o2542bo$
5634b2o334bo140b2o142bo962bo2541bo$6112b2o141bobo3502b3o$6255b2o1147bo
$6012bo1391bobo$6012bobo1389b2o$6012b2o332bobo1197bo7153bo$6346b2o
1198bobo7149b2o$6347bo1198b2o7151b2o$10136bo$10135bo240bo189bo$10135b
3o92bo93bo49b2o189bo$10228b2o94bobo48b2o188b3o4269bo$10229b2o93b2o
4509b2o$10419bo4416b2o$9937bo480bo96bo95bo$9936bo481b3o92b2o94b2o$
9936b3o575b2o94b2o2$10029bo623bo$10029bobo620bo3072bo1726bobo$10029b2o
621b3o46bo3021b2o1727b2o141bo$10699b2o3023b2o1727bo141bobo$10700b2o
4893b2o4$14582bo$14580b2o$14581b2o3$14720bo$14720bobo$14720b2o9$13412b
obo1581bo$13412b2o1582bobo$13413bo1582b2o66$193bo$192bobo$193b2o10$
228bo$227bobo$228b2o15$251bo$250bobo$251bobo$252b2o3$255b2o$254bo2bo$
254bo2bo$255b2o33$256bo$255bobo$256bobo$257b2o$262b2o$261bo2bo$261bo2b
o$262b2o22$284bo$283bobo$284b2o12$311b2o$312bo$312bobo$313b2o21$335bo$
335b3o$338bo$337b2o20$359bo$359b3o$362bo$361b2o34$377bo$376bobo$377b2o
7$34b2o$33bobo$35bo10$405bo$404bobo$405b2o12$420bo$418bobo$419bobo$
419bo4$426bo$426b3o$429bo$428b2o$418bo$417bobo11b2o$416bobo12b2o$416b
2o47bo$464bobo$426b2o37bobo$414b2o10bobo37b2o$414bobo10bo$415bobo$416b
o52b2o$468bo2bo$468bo2bo$469b2o12$489bo$488bobo$489b2o2$492b2o$491bobo
$491b2o19$515bo$514bobo$515bobo$516b2o3$519b2o$518bo2bo$518bo2bo$519b
2o11$542bo$541bobo$542bobo$543b2o3$546b2o$545bo2bo$545bo2bo$546b2o12$
2b3o$4bo$3bo8$560b2o$561bo$561bobo$562b2o19$595bo$594bobo$595b2o23$
609b2o$610bo$610bobo$611b2o19$21bo622bo$21b2o620bobo$20bobo621b2o13$
669bo$668bobo$669bobo$670b2o3$673b2o$672bo2bo$672bo2bo$673b2o20$688b2o
$689bo$689bobo$690b2o30$702b2o$703bo$703bobo$704b2o17$730b2o$731bo$
731bobo$732b2o16$758b2o$759bo$759bobo$760b2o24$787bo$786bobo$787b2o4$
794b2o$793bobo$792bobo$793bo5$789b2o$788bo2bo$789bo2bo$790b2o9$803bo$
803b3o$806bo$805b2o24$823bo$823b3o$826bo$825b2o20$42bo$42b2o$41bobo9$
844bo$843bobo$844b2o17$874bo$873bobo$874b2o4$881b2o$880bobo$879bobo$
880bo5$876b2o$875bo2bo$876bo2bo$877b2o16$882bo$882b3o$885bo$884b2o14$
912b2o$913bo$913bobo$914b2o21$935bo$935b3o$938bo$937b2o26$964bo$963bob
o$964b2o12bo$977bobo$977bo2bo18b2o$978bobo19bo$971bo7bo20bobo$970bobo
28b2o$969bobo$969b2o24$1018b2o$1019bo$1019bobo$1020b2o19$1045bo$1045b
3o$1048bo$1047b2o22$1066b2o$1067bo$1067bobo$1068b2o20$1093bo$1093b3o$
1096bo$1095b2o10$32bo$32b2o$31bobo8$1116b2o$1117bo$1117bobo$1118b2o35$
1135bo$32b2o1100bobo$31bobo1101b2o$33bo13$1158bo$1158b3o$1161bo$1160b
2o21$1191bo$1190bobo$1191b2o2$36b2o$37b2o$36bo1161b2o$1197bobo$1196bob
o22bo$1197bo22bobo$1221b2o2$1224b2o$1223bobo$1193b2o28b2o$1192bo2bo$
1193bo2bo$1194b2o14$1246bo$1245bobo$1246b2o2$1249b2o$1248bobo$1248b2o
14$38bo$38b2o$37bobo6$1269b2o$1270bo$1270bobo$1271b2o23$1289bo$1289b3o
$1292bo$1291b2o22$1313b2o$1314bo$1314bobo$1315b2o22$1337b2o$1338bo$
1338bobo$1339b2o7$40b2o$39bobo$41bo4$1367b2o$1367bobo$1363b2o3bobo$
1362bobo4bo$1351bo9bobo$1352b2o8bo$1350b2o$1352bo5$1357b2o7b2o$1358bo
7bobo$1358bobo6bo$1359b2o2$1362b2o$1362b2o26$37b2o1380bo$38b2o1378bobo
$37bo1320bo60bobo$1359b2o59b2o$1357b2o$1359bo$1423b2o$1422bo2bo$1422bo
2bo$1365bo57b2o$1365b3o$1368bo$1367b2o$1357bo$1356bobo11b2o$1355bobo
12b2o$1355b2o2$1365b2o$1353b2o10bobo$1353bobo10bo$1354bobo$1355bo2$
1441bo$1440bobo$1441b2o2$1444b2o$1443bobo$1443b2o14$41bo$41b2o$40bobo
3$1467bo$1466bobo$1467bobo$1468b2o3$1471b2o$1470bo2bo$1470bo2bo$1471b
2o11$1495bo$1494bobo$1495bobo$1496b2o3$1499b2o$1498bo2bo$1498bo2bo$
1499b2o10$44b2o$45b2o$44bo1476bo$1520bobo$1521bobo$1522b2o3$1525b2o$
1524bo2bo$1524bo2bo$1525b2o8$73b3o$75bo$74bo16$1541b2o$1541b2o4$1545b
2o$1545b2o6$1570b2o$1570bobo$1566b2o3bobo$1565bobo4bo$1555bo8bobo$
1553bobo9bo$1554bobo$1554bo5$1560b2o7b2o$1561bo7bobo$1561bobo6bo$1562b
2o2$1565b2o$1565b2o39$1549bo$1550b2o$1548b2o$1550bo4$1556bo$1556b3o$
1559bo$1558b2o$1548bo$1547bobo11b2o$1546bobo12b2o$1546b2o2$1556b2o$
1544b2o10bobo$1544bobo10bo$1545bobo$1546bo14$1585bo$1584bobo$1585b2o
12bo$1598bobo$1598bo2bo$1599bobo$1592bo7bo$1591bobo$1590bobo$1590b2o
23$1600bo$1599bobo$1600b2o24$1614bo$1613bobo$1614bobo$1615b2o$1620b2o$
1619bo2bo$1619bo2bo$1620b2o9$71bo$71b2o$70bobo3$1640bo$1639bobo$1640bo
bo$1641b2o$1646b2o$1645bo2bo$1645bo2bo$1646b2o22$1661bo$1660bobo$1661b
obo$1662b2o$1667b2o$1666bo2bo$1666bo2bo$1667b2o10$1691bo$1691b3o$1694b
o$1693b2o19$1716bo$1716b3o$1719bo$1718b2o34$1737bo$1736bobo$1737b2o13$
1760bo$1760b3o$1763bo$1762b2o5$34b2o$33bobo$35bo14$1793bo$1792bobo$
1793b2o17$1822bo$1821bobo$1822b2o4$1829b2o$1828bobo$1827bobo$1828bo5$
1824b2o$1823bo2bo$1824bo2bo$1825b2o15$1837bo$1836bobo$1837b2o26$1858bo
$1857bobo$1858b2o14$1882bo$1882b3o$1885bo$1884b2o12$52b3o$54bo$53bo5$
1915bo$1914bobo$1915b2o4$1922b2o$1921bobo$1920bobo$1921bo5$1917b2o$
1916bo2bo20b2o$1917bo2bo20bo$1918b2o21bobo$1942b2o16$1969bo$1969b3o$
1972bo$1971b2o7$49bo$49b2o$48bobo14$1993b2o$1994bo$1994bobo$1995b2o18$
2019bo$2019b3o$2022bo$2021b2o19$2045bo$2045b3o$2048bo$2047b2o3$2087b2o
$2088bo$2088bobo$2089b2o22$54b2o$55b2o$54bo9$2099bo$2099b3o$2102bo$
2101b2o11$2132b2o$2133bo$2133bobo$2134b2o34$2143bo$2143b3o$2146bo$
2145b2o17$2173b2o$2174bo$2174bobo$2175b2o3$62b2o$63b2o$62bo19$2192bo$
2192b3o$2195bo$2194b2o31$2215bo$2214bobo$2215b2o19$2231bo$2230bobo$
2231b2o$2235b2o$2234bobo$2234b2o26$2251b2o$2252bo$2252bobo$2253b2o9$
88b2o$89b2o$88bo14$2271bo$2271b3o$2274bo$2273b2o11$2304b2o$2305bo$
2305bobo$2306b2o22$2329bo$2329b3o$2332bo$2331b2o24$2348bo$2348b3o$
2351bo$2350b2o26$2369bo$2369b3o$2372bo$2371b2o21$2392bo$2392b3o$2395bo
$2394b2o19$2418b2o$2419bo$2419bobo$2420b2o11$62bo$62b2o$61bobo10$2439b
o$2439b3o$2442bo$2441b2o16$2469bo$2469b3o$2472bo$2471b2o17$2497bo$
2497b3o$2500bo$2499b2o24$2517b2o$2518bo$2518bobo$2519b2o11$65b3o$67bo
2482bo$66bo2483b3o$2553bo$2552b2o31$2564b2o$2565bo$2565bobo$2566b2o7$
69bo$69b2o$68bobo7$2594bo$2594b3o$2597bo$2596b2o23$2616b2o$2617bo$
2617bobo$2618b2o25$2637bo$2637b3o$2640bo$2639b2o14$2675bo$2674bobo$
2675b2o24$2689b2o$2690bo$2690bobo$2691b2o4$52b2o$51bobo$53bo17$2711bo$
2711b3o$2714bo$2713b2o15$2748bo$2747bobo$2748b2o27$2769bo$2768bobo$
2769b2o4$2776b2o$2775bobo$2774bobo$2775bo5$2771b2o$2770bo2bo$2771bo2bo
$2772b2o14$2776bo$2776b3o$2779bo$2778b2o18$2803bo$2803b3o$2806bo$2805b
2o25$2824bo$2824b3o$2827bo$2826b2o21$2849bo$2849b3o$2852bo$2851b2o22$
2879bo$2878bobo$2879b2o32bo$2912bobo$2913b2o2$2886b2o28b2o$2885bobo27b
obo$2884bobo28b2o$2885bo5$2881b2o$2880bo2bo$2881bo2bo$2882b2o15$2943bo
$2942bobo$2943b2o25$2957bo$2957b3o$2960bo$2959b2o27$2973b2o$2974bo$
2974bobo$2975b2o19$3000bo$3000b3o$3003bo$3002b2o23$3022bo$3022b3o$
3025bo$3024b2o24$3043bo$3043b3o$3046bo$3045b2o12$3076b2o$3077bo$3077bo
bo$3078b2o3$55b2o$54bobo$56bo20$3096bo$3096b3o$3099bo$3098b2o14$3128b
2o$3129bo$3129bobo$3130b2o23$3149bo$3149b3o$3152bo$3151b2o22$3172bo$
3172b3o$3175bo$3174b2o27$3191b2o$3192bo$3192bobo$3193b2o18$3217bo$
3217b3o$3220bo$3219b2o18$3232bo$3230bobo$3231bobo$3231bo4$3238bo$3238b
3o$3241bo$3240b2o$3230bo$3229bobo11b2o$3228bobo12b2o32bo$3228b2o46bobo
$3277b2o$3238b2o$3226b2o10bobo39b2o$3226bobo10bo39bobo$3227bobo49b2o$
3228bo9$8b3o$10bo$9bo4$3304bo$3304b3o$3307bo$3306b2o21$3328bo$3328b3o$
3331bo$3330b2o21$b2o$2b2o$bo3350bo$3352b3o$3355bo$3354b2o24$3373bo$
3373b3o$3376bo$3375b2o9$3407b2o$3407bobo$3403b2o3bobo$3402bobo4bo$
3391bo9bobo$3392b2o8bo$3390b2o$3392bo$2b2o$bobo$3bo2$3397b2o7b2o$3398b
o7bobo$3398bobo6bo$3399b2o2$3402b2o$3402b2o45$3399b2o$3399b2o3$3404b2o
$3404b2o9$3415bo$3416b2o$3414b2o$3416bo$3467bo$3466bobo$3467b2o$3422bo
$3422b3o45b2o$3425bo43bobo$3424b2o43b2o$3414bo$3413bobo11b2o$3412bobo
12b2o$3412b2o2$3422b2o$3410b2o10bobo$3410bobo10bo$3411bobo$3412bo6$
3498bo$3498b3o$3501bo$3500b2o25$3523b2o$3523b2o4$3527b2o$3527b2o18$
3542bo$3542b3o$3545bo$3544b2o11$3573b2o$3573bobo$3569b2o3bobo$3568bobo
4bo$3557bo9bobo$3558b2o8bo$3556b2o$3558bo5$3563b2o7b2o$3564bo7bobo$
3564bobo6bo$3565b2o2$3568b2o$3568b2o44$66b3o$68bo$67bo2$3553bo$3552bob
o$3553b2o$3557b2o$3556bobo$3556b2o21$3586b2o$3586b2o3$3591b2o$3591b2o
76b2o$3669bobo$3665b2o3bobo$3664bobo4bo$3653bo9bobo$3654b2o8bo$3652b2o
$3654bo2$3601bo$3602b2o$3600b2o$3602bo56b2o7b2o$3660bo7bobo$3660bobo6b
o$3661b2o$3608bo$3608b3o53b2o$3611bo52b2o$3610b2o$3600bo$3599bobo11b2o
$3598bobo12b2o$3598b2o2$3608b2o$3596b2o10bobo$3596bobo10bo$3597bobo$
3598bo29$3656bo$3655bobo$3656b2o$3660b2o$3659bobo$3659b2o25$3676bo$
3675bobo$3676b2o$3680b2o$3679bobo$3679b2o3$3764b2o$3764bobo$3760b2o3bo
bo$3759bobo4bo$3749bo8bobo$3701bo45bobo9bo$3699bobo46bobo$3700bobo45bo
$3700bo4$3707bo46b2o7b2o$3707b3o45bo7bobo$3710bo44bobo6bo$3709b2o45b2o
$3699bo$3698bobo11b2o45b2o$3697bobo12b2o45b2o$3697b2o2$3707b2o$3695b2o
10bobo$3695bobo10bo$3696bobo$3697bo34$3756b2o$66b3o3688bo$68bo3688bobo
$67bo3690b2o10$3837b2o$3837bobo$3833b2o3bobo$3774bo57bobo4bo$3775b2o
45bo8bobo$3773b2o45bobo9bo$3775bo45bobo$3821bo3$3781bo$3781b3o$3784bo
42b2o7b2o$3783b2o43bo7bobo$3773bo54bobo6bo$3772bobo11b2o41b2o$3771bobo
12b2o$3771b2o59b2o$3832b2o$3781b2o$3769b2o10bobo$3769bobo10bo$3770bobo
$3771bo36$43b2o$44b2o$43bo5$3818bo$3817bobo$3818b2o$3822b2o$3821bobo$
3821b2o20$3841bo$3840bobo$3841b2o$3845b2o$3844bobo$3844b2o21$3866bo$
3865bobo$3866bobo$3867b2o$3872b2o$3871bo2bo$3871bo2bo$3872b2o16$3898b
2o83bo$3898b2o82bobo$3983b2o2$3903b2o81b2o$3903b2o80bobo$3985b2o5$49bo
$49b2o$48bobo3861bo$3913b2o$3911b2o$3913bo4$3919bo91bo$3919b3o88bobo$
3922bo88b2o$3921b2o$3911bo102b2o$3910bobo11b2o87bobo$3909bobo12b2o87b
2o$3909b2o2$3919b2o$3907b2o10bobo$3907bobo10bo$3908bobo$3909bo8$4037bo
$4036bobo$4037b2o2$4040b2o$4039bobo$4039b2o16$4064bo$4063bobo$4064b2o
2$4067b2o$4066bobo$4066b2o18$4088bo$4087bobo$4088b2o2$4091b2o$4090bobo
$4090b2o28$4114bo$4113bobo$4114b2o4$4121b2o$4120bobo$4119bobo$4120bo5$
68b3o4045b2o$70bo4044bo2bo$69bo4046bo2bo$4117b2o13$4130b2o$4130b2o4$
4134b2o29b2o$4134b2o29bobo$4161b2o3bobo$4160bobo4bo$4149bo9bobo$4150b
2o8bo$4148b2o$4150bo5$4155b2o7b2o$4156bo7bobo$4156bobo6bo$4157b2o2$
4160b2o$4160b2o42$4201bo$4201b3o$4204bo$4203b2o7$4131bo$4129bobo$4130b
obo$69b3o4058bo$71bo$70bo2$4137bo$4137b3o$4140bo$4139b2o$4129bo$4128bo
bo11b2o$4127bobo12b2o$4127b2o2$4137b2o$4125b2o10bobo$4125bobo10bo82bo$
4126bobo92b3o$4127bo96bo$4223b2o21$4247bo$4247b3o$4250bo$4249b2o10$
4280b2o$4280bobo$4276b2o3bobo$4275bobo4bo$4265bo8bobo$4263bobo9bo$
4264bobo$4264bo5$4270b2o7b2o$4271bo7bobo$4271bobo6bo$4272b2o2$4275b2o$
4275b2o23$74b2o$73bobo$75bo26$4260b2o$4261bo$4261bobo$4262b2o$4352b2o$
4352bobo$4348b2o3bobo$4347bobo4bo$4337bo8bobo$4335bobo9bo$4336bobo$
4336bo5$4342b2o7b2o$4280bo62bo7bobo$4278bobo62bobo6bo$4279bobo62b2o$
4279bo$4347b2o$4347b2o2$4286bo$4286b3o$4289bo$4288b2o$4278bo$4277bobo
11b2o$4276bobo12b2o$4276b2o2$4286b2o$4274b2o10bobo$4274bobo10bo$4275bo
bo$4276bo46$4318bo$4317bobo$4318b2o$4322b2o$4321bobo$4321b2o23$4341bo$
4340bobo$4341bobo$4342b2o$4347b2o$4346bo2bo$4346bo2bo$4347b2o6$65b2o$
64bobo$66bo8$4367bo$4366bobo$4367bobo$4368b2o$4373b2o$4372bo2bo$4372bo
2bo$4373b2o15$4388bo$4387bobo$4388b2o$4392b2o$4391bobo$4391b2o23$4412b
o$4411bobo$4412bobo$4413b2o$4418b2o$4417bo2bo$4417bo2bo$46b3o4369b2o$
48bo$47bo17$4433bo$4432bobo$4433bobo$4434b2o$4439b2o$4438bo2bo$4438bo
2bo$4439b2o3$4566b2o$4566bobo$4562b2o3bobo$4561bobo4bo$4551bo8bobo$
4549bobo9bo$4550bobo$4550bo5$4556b2o7b2o$4457bo99bo7bobo$4456bobo98bob
o6bo$4457b2o99b2o$4461b2o$4460bobo98b2o$4460b2o99b2o9$4482bo$4480bobo$
4481bobo$4481bo4$4488bo$4488b3o$4491bo$4490b2o$4480bo$4479bobo11b2o$
4478bobo12b2o$4478b2o2$4488b2o$4476b2o10bobo$4476bobo10bo$4477bobo$
4478bo12$53b3o$55bo$54bo14$4636b2o$4636bobo$4632b2o3bobo$4534bo96bobo
4bo$4533bobo84bo9bobo$4534b2o85b2o8bo$4538b2o79b2o$4537bobo81bo$4537b
2o4$4626b2o7b2o$4627bo7bobo$4627bobo6bo$4628b2o2$4631b2o$4631b2o4$
4555bo$4553bobo$4554bobo$4554bo4$4561bo$4561b3o$4564bo$4563b2o$4553bo$
4552bobo11b2o$4551bobo12b2o$4551b2o2$4561b2o$4549b2o10bobo$4549bobo10b
o$4550bobo$4551bo34$4607bo$4606bobo$4607b2o$4611b2o$4610bobo$4610b2o
21$4629bo$4628bobo$4629b2o$4633b2o$4632bobo$4632b2o16$4753b2o$4656b2o
95bobo$4657bo91b2o3bobo$4657bobo88bobo4bo$4658b2o77bo9bobo$4738b2o8bo$
4736b2o$4738bo5$4743b2o7b2o$4744bo7bobo$4744bobo6bo$4745b2o2$4748b2o$
4748b2o$4675bo$4673bobo$4674bobo$4674bo4$4681bo$4681b3o$4684bo$4683b2o
$4673bo$4672bobo11b2o$4671bobo12b2o$4671b2o2$4681b2o$4669b2o10bobo$
4669bobo10bo$4670bobo$4671bo6$4804b2o$4804bobo$4800b2o3bobo$4799bobo4b
o$4789bo8bobo$4787bobo9bo$4788bobo$4788bo5$4794b2o7b2o$4795bo7bobo$
4795bobo6bo$4796b2o2$4799b2o$4799b2o2$4725bo$4723bobo$4724bobo$4724bo
4$4731bo$4731b3o$4734bo$4733b2o$4723bo$4722bobo11b2o$4721bobo12b2o$
4721b2o2$4731b2o$4719b2o10bobo$4719bobo10bo$4720bobo$4721bo11$59b3o
4787b2o$61bo4787bobo$60bo4784b2o3bobo$4844bobo4bo$4834bo8bobo$4832bobo
9bo$4833bobo$4833bo5$4839b2o7b2o$4840bo7bobo$4840bobo6bo$4841b2o$4774b
o$4772bobo69b2o$4773bobo68b2o$4773bo4$4780bo$4780b3o$4783bo$4782b2o$
4772bo$4771bobo11b2o$4770bobo12b2o$4770b2o2$4780b2o$4768b2o10bobo$
4768bobo10bo$4769bobo$4770bo32$4828bo$4827bobo$4828b2o$4832b2o$4831bob
o$4831b2o21$4849bo$4848bobo$4849b2o$4853b2o90b2o$4852bobo90bobo$4852b
2o87b2o3bobo$4940bobo4bo$4930bo8bobo$4928bobo9bo$4929bobo$4929bo5$
4871bo63b2o7b2o$4872b2o62bo7bobo$4870b2o64bobo6bo$4872bo64b2o2$4940b2o
$4940b2o$4878bo$4878b3o$4881bo$4880b2o$4870bo$4869bobo11b2o$4868bobo
12b2o$4868b2o2$4878b2o$4866b2o10bobo$4866bobo10bo$4867bobo$4868bo7$
4954b2o$4955bo$4955bobo$4956b2o17$4982b2o$4983bo$4983bobo$4984b2o22$
5004b2o$5005bo$5005bobo$5006b2o4$62b3o$64bo$63bo8$5035b2o$5035bobo$
5031b2o3bobo$5030bobo4bo$5020bo8bobo$5018bobo9bo$5019bobo$5019bo5$
5025b2o7b2o$5026bo7bobo$5026bobo6bo$5027b2o2$5030b2o$5030b2o23$5050bo$
5049bobo$5050b2o4$5057b2o$5056bobo24b2o$5055bobo25bobo$5056bo22b2o3bob
o$5078bobo4bo$5068bo8bobo$5066bobo9bo$5067bobo$5052b2o13bo$5051bo2bo$
5052bo2bo$5053b2o2$5073b2o7b2o$5074bo7bobo$5074bobo6bo$5075b2o2$5078b
2o$5078b2o17$65b3o$67bo$66bo19$5075b2o$5076bo$5076bobo$5077b2o27$5095b
o$5095b3o$5098bo$5097b2o14$5125b2o$5126bo$5126bobo$5127b2o22$69b2o$70b
2o$69bo2$5144bo$5144b3o$5147bo$5146b2o22$5175bo$5174bobo$5175b2o4$
5182b2o$5181bobo$5180bobo$5181bo5$5177b2o$5176bo2bo$5177bo2bo$5178b2o
3$5202bo$5201bobo$5202b2o20$5222bo$5222b3o$5225bo$5224b2o15$76b2o$75bo
bo$77bo$5249bo$5249b3o$5252bo$5251b2o25$5265bo$5264bobo$5265b2o$5269b
2o$5268bobo$5268b2o12$76bo$76b2o$75bobo7$5291bo$5291b3o$5294bo$5293b2o
8$5327bo$5327b3o$5330bo$5329b2o25$5348bo$5348b3o$5351bo$5350b2o24$
5368bo$5368b3o$5371bo$5370b2o10$83b2o$84b2o$83bo11$5485b2o$5485bobo$
5481b2o3bobo$5480bobo4bo$5470bo8bobo$5468bobo9bo$5469bobo$5469bo$5391b
o$5390bobo$110b2o5279b2o$109bobo$111bo5363b2o7b2o$5476bo7bobo$5476bobo
6bo$5477b2o2$5480b2o$5480b2o2$5404bo$5405b2o$5403b2o$5405bo4$5411bo$
5411b3o$5414bo$5413b2o$5403bo$5402bobo11b2o$5401bobo12b2o$5401b2o2$
5411b2o$5399b2o10bobo$5399bobo10bo$5400bobo$5401bo43$5554b2o$5554b2o$
5450b2o$5451bo$5451bobo$5452b2o104b2o$5558b2o7$5578bo$5577bobo$5578b2o
2$5581b2o$5580bobo$5580b2o$5466bo$5467b2o$5465b2o$5467bo4$5473bo$5473b
3o$5476bo$5475b2o$5465bo$5464bobo11b2o$5463bobo12b2o$5463b2o144b2o$
5609bobo$5473b2o130b2o3bobo$5461b2o10bobo128bobo4bo$5461bobo10bo119bo
8bobo$5462bobo127bobo9bo$5463bo129bobo$5593bo5$5599b2o7b2o$5600bo7bobo
$5600bobo6bo$5601b2o2$5604b2o$5604b2o48$5647b2o$5647b2o4$5651b2o$5651b
2o7$5566bo$5564bobo$5565bobo$5565bo4$5572bo$5572b3o91bo$5575bo90b3o$
5574b2o93bo$5564bo103b2o$5563bobo11b2o$5562bobo12b2o$5562b2o2$5572b2o$
5560b2o10bobo$5560bobo10bo$5561bobo$5562bo3$5698b2o$5698bobo$5694b2o3b
obo$5693bobo4bo$5683bo8bobo$5681bobo9bo$5682bobo$5682bo5$5688b2o7b2o$
5689bo7bobo$5689bobo6bo$5690b2o2$5693b2o$5693b2o18$104b3o$106bo$105bo
13$5744b2o$5744bobo$5740b2o3bobo$5739bobo4bo$5729bo8bobo$5727bobo9bo$
5728bobo$5728bo5$5734b2o7b2o$5735bo7bobo$5735bobo6bo$5736b2o2$5739b2o$
5739b2o2$5663bo$5664b2o$5662b2o$5664bo4$5670bo$5670b3o$5673bo$5672b2o$
5662bo$5661bobo11b2o$5660bobo12b2o$5660b2o2$5670b2o$5658b2o10bobo$
5658bobo10bo$5659bobo$5660bo43$5705bo$5704bobo$5705b2o$5709b2o$5708bob
o$5708b2o8$89b2o$90b2o$89bo12$5727bo$5726bobo$5727b2o$5731b2o$5730bobo
$5730b2o19$5750bo$5749bobo$5750b2o$5754b2o$5753bobo$5753b2o19$5775bo$
5774bobo$5775b2o$5779b2o$5778bobo$5778b2o20$5799bo$5798bobo$5799b2o$
5803b2o$5802bobo$5802b2o13$79b2o$80b2o$79bo5$5820bo$5819bobo$5820b2o$
5824b2o$5823bobo$5823b2o21$5843bo$5842bobo$5843b2o$5847b2o$5846bobo$
5846b2o23$5866bo$5865bobo$5866bobo$5867b2o$5872b2o$5871bo2bo$5871bo2bo
$5872b2o15$5892bo$5891bobo$5892bobo$5893b2o$5898b2o$5897bo2bo$5897bo2b
o$5898b2o17$5913bo$5912bobo$5913b2o$5917b2o$5916bobo$5916b2o21$5937bo$
5936bobo$5937bobo$5938b2o$5943b2o$5942bo2bo$5942bo2bo$5943b2o12$6069b
2o$6069b2o3$5959bo$5958bobo112b2o$5959b2o112b2o$5963b2o$5962bobo$5962b
2o6$6103b2o$6103b2o3$5984bo$5982bobo122b2o$5983bobo121b2o$5983bo4$
5990bo$5990b3o$5993bo$91b2o5899b2o$92b2o5888bo$91bo5889bobo11b2o$5980b
obo12b2o$5980b2o2$5990b2o$5978b2o10bobo129bo$5978bobo10bo130b3o$5979bo
bo143bo$5980bo143b2o24$6144bo$6144b3o$6147bo$6146b2o12$6177b2o$6177bob
o$6173b2o3bobo$6172bobo4bo$6161bo9bobo$6162b2o8bo$6160b2o$6162bo5$
6167b2o7b2o$6168bo7bobo$6168bobo6bo$6169b2o2$6172b2o$6172b2o24$6231bo$
6230bobo$95b2o6134bobo$94bobo6135b2o$96bo2$6235b2o$6234bo2bo$6234bo2bo
$6235b2o16$6254bo$6253bobo$6254bobo$6255b2o3$6258b2o$6257bo2bo$6257bo
2bo$6258b2o6$6131bo$6129bobo$6130bobo$6130bo4$6137bo140bo$6137b3o137bo
bo$6140bo137b2o$6139b2o$6129bo151b2o$6128bobo11b2o136bobo$6127bobo12b
2o136b2o$6127b2o2$6137b2o$6125b2o10bobo$6125bobo10bo$6126bobo$6127bo
10$6303bo$6302bobo$6303b2o2$6306b2o$6305bobo$6305b2o13$6333b2o$6333bob
o$6329b2o3bobo$6328bobo4bo$6318bo8bobo$6316bobo9bo$6317bobo$6317bo5$
6323b2o7b2o$6324bo7bobo$6324bobo6bo$6325b2o2$6328b2o$6328b2o43$91b2o$
90bobo$92bo17$6395bo$6394bobo$6395b2o2$6398b2o$6397bobo$6397b2o13$
6279bo$6278bobo141bo$6279b2o140bobo$6283b2o137b2o$6282bobo$6282b2o141b
2o$6424bobo$6424b2o12$6301bo$6299bobo$6300bobo$6300bo4$6307bo$6307b3o
139bo$6310bo137bobo$6309b2o138bobo$6299bo150b2o$6298bobo11b2o$6297bobo
12b2o$6297b2o154b2o$6452bo2bo$6307b2o143bo2bo$112b2o6181b2o10bobo143b
2o$113b2o6180bobo10bo$112bo6183bobo$6297bo9$6475bo$6474bobo$6475bobo$
6476b2o3$6479b2o$6478bo2bo$6478bo2bo$6479b2o13$6498bo$6497bobo$6498b2o
2$6501b2o$6500bobo$6500b2o24$6519bo$6519b3o$6522bo$6521b2o11$6553b2o$
6553bobo$6549b2o3bobo$6548bobo4bo$6538bo8bobo$6536bobo9bo$6537bobo$
6537bo5$6543b2o7b2o$6544bo7bobo$6544bobo6bo$6545b2o2$6548b2o$6548b2o
97$6486bo$6485bobo$6486bobo$6487b2o$6492b2o$6491bo2bo$6491bo2bo$6492b
2o$6669bo$6668bobo$6669bobo$6670b2o3$6673b2o$6672bo2bo$6672bo2bo$6673b
2o9$6508bo$6507bobo$6508bobo$6509b2o186bo$6514b2o180bobo$6513bo2bo180b
obo$6513bo2bo181b2o$6514b2o2$6701b2o$6700bo2bo$6700bo2bo$6701b2o10$
6534bo$6533bobo$6534bobo$6535b2o187bo$6540b2o181bobo$6539bo2bo181bobo$
6539bo2bo182b2o$6540b2o2$6728b2o$6727bo2bo$6727bo2bo$6728b2o2$6556bo$
6557b2o$6555b2o$6557bo4$6563bo$6563b3o$6566bo184b2o$6565b2o184bobo$
6555bo191b2o3bobo$6554bobo11b2o176bobo4bo$6553bobo12b2o166bo8bobo$
6553b2o179bobo9bo$6735bobo$6563b2o170bo$6551b2o10bobo$6551bobo10bo$
6552bobo$6553bo$6741b2o7b2o$6742bo7bobo$6742bobo6bo$6743b2o2$6746b2o$
6746b2o102$6686b2o$6686b2o3$6691b2o$6691b2o14$6708b2o$6709bo$6709bobo$
6710b2o2$39b2o$40b2o$39bo6852b2o$6892bobo$6888b2o3bobo$6887bobo4bo$
6876bo9bobo$6877b2o8bo$6875b2o$6877bo5$6882b2o7b2o$6883bo7bobo$6883bob
o6bo$6884b2o2$6887b2o$6887b2o$6737bo$6736bobo$6737b2o12bo$65b2o6683bob
o$64bobo6683bo2bo$66bo6684bobo$6744bo7bo$6743bobo$6742bobo$6742b2o7$
6759bo$6758bobo$6759b2o$6763b2o$6762bobo$6762b2o13$6779bo$6780b2o$
6778b2o$6780bo4$6786bo$6786b3o$6789bo$6788b2o$6778bo$6777bobo11b2o$
6776bobo12b2o$6776b2o2$6786b2o$6774b2o10bobo$6774bobo10bo$6775bobo$
6776bo27$6849b2o$6849b2o3$6854b2o$6854b2o25$6859b2o$6860bo$6860bobo$
6861b2o3$6994bo$6993bobo$6994b2o2$6997b2o$6996bobo$6996b2o14$6889bo$
6888bobo130bo$6889b2o129bobo$7021b2o2$7024b2o$7023bobo$7023b2o6$6903bo
$6904b2o$6902b2o$6904bo4$6910bo$6910b3o$6913bo$6912b2o$6902bo$6901bobo
11b2o$6900bobo12b2o$6900b2o2$6910b2o$6898b2o10bobo$6898bobo10bo$6899bo
bo$6900bo3$7044b2o$7044b2o4$7048b2o$7048b2o8$7071bo$7071b3o$7074bo$
7073b2o22$7101bo$7100bobo$7101b2o15$7123bo$7122bobo$7123b2o2$7126b2o$
7125bobo$7125b2o18$7158bo$7157bobo$7158b2o23$7172b2o$7173bo$7173bobo$
7174b2o13$7203b2o$7203bobo$7199b2o3bobo$7198bobo4bo$7188bo8bobo$7186bo
bo9bo$7187bobo$7187bo5$7193b2o7b2o$7194bo7bobo$7194bobo6bo$7195b2o2$
7198b2o$7198b2o16$26b3o$28bo$27bo13$7204b2o$7205bo$7205bobo$7206b2o23$
7225bo$7225b3o$7228bo$7227b2o6$25b2o$26b2o$25bo22$50b2o$49bobo7194bo$
51bo7193bobo$7246b2o19$7266bo$7266b3o$7269bo$7268b2o22$7289bo$7289b3o$
7292bo$7291b2o22$7311b2o$7312bo$7312bobo$7313b2o13$56b2o$57b2o$56bo8$
7334b2o$7335bo$7335bobo$7336b2o24$7411bo$7410bobo$7411b2o3$7358bo$
7357bobo58b2o$7358b2o12bo44bobo$7371bobo42bobo$7371bo2bo42bo$7372bobo$
7365bo7bo$7364bobo$7363bobo$7363b2o48b2o$7412bo2bo$7413bo2bo$7414b2o6$
46b2o$45bobo$47bo24$67b2o$68b2o$67bo3$7398bo$7398b3o$7401bo$7400b2o22$
7428bo$7427bobo$7428b2o12bo$7441bobo$7441bo2bo$7442bobo$7435bo7bo$
7434bobo$7433bobo$7433b2o26$7441bo$7440bobo$7441b2o4$7448b2o$7447bobo$
7446bobo$7447bo5$7443b2o$7442bo2bo$7443bo2bo18bo$7444b2o19b3o$7468bo$
7467b2o23$7486b2o$7487bo$7487bobo$54b2o7432b2o$53bobo$55bo16$7514b2o$
7515bo$7515bobo$7516b2o3$77b3o$79bo$78bo12$7543b2o$7544bo$7544bobo$
7545b2o22$7659bo$7658bobo$7659b2o2$7662b2o$7661bobo$7566bo94b2o$7565bo
bo$7566b2o12bo$7579bobo$7579bo2bo$7580bobo$7573bo7bo$7572bobo$7571bobo
$7571b2o33$7562bo$7561bobo$7562b2o$7566b2o$7565bobo$7565b2o41$7760bo$
40b2o7717bobo$39bobo7718bobo$41bo7719b2o3$7764b2o$7763bo2bo$7763bo2bo$
7764b2o19$7587bo$7586bobo$7587bobo$7588b2o$7593b2o$7592bo2bo$7592bo2bo
$7593b2o9$45bo$45b2o$44bobo9$7609bo$7608bobo$7609bobo$7610b2o$7615b2o$
7614bo2bo$7614bo2bo$7615b2o17$7631bo$7630bobo$7631bobo$7632b2o$7637b2o
$7636bo2bo$7636bo2bo$7637b2o33$7831bo$7831b3o$7834bo$7833b2o2$7883bo$
7882bobo$7689b2o192b2o$7689b2o3$7694b2o$7694b2o4$2b2o$bobo$3bo4$44b2o$
43bobo$45bo11$7701bo$7700bobo$7701bobo$7702b2o$7707b2o$7706bo2bo$7706b
o2bo$7707b2o3$68b3o$70bo$69bo4$7733bo$7733b3o$7736bo$7735b2o19$7911bo$
7910bobo$7911b2o60$7801bo$7800bobo$7801b2o160$105b2o$104bobo$106bo172$
73b2o$74b2o$73bo249$63b2o$62bobo$64bo23$87bo$87b2o$86bobo157$23b2o$24b
2o$23bo64$5b2o$6b2o$5bo51$bo$b2o$obo19$26b2o$27b2o$26bo73$3o$2bo$bo43$
2b3o$4bo$3bo32$18b2o$17bobo$19bo25$39bo$39b2o$38bobo97$34b2o$35b2o$34b
o37$44b2o$45b2o$44bo99$40bo$40b2o$39bobo51$35b2o$34bobo$36bo44$35b3o$
37bo$36bo24$58bo$58b2o$57bobo89$63bo$63b2o$62bobo90$67b2o$68b2o$67bo
96$66b2o$65bobo$67bo52$59b2o$60b2o$59bo26$78b3o$80bo$79bo73$100b3o$
102bo$101bo42$104bo$104b2o$103bobo44$105b3o$107bo$106bo70$129b2o$130b
2o$129bo154$69b3o$71bo$70bo90$74b2o$75b2o$74bo68$100b2o$99bobo$101bo
203$87b2o$86bobo$88bo272$100b3o$102bo$101bo145$51bo$51b2o$50bobo24$72b
2o$71bobo$73bo184$78b2o$79b2o$78bo184$84b3o$86bo$85bo132$45b3o$47bo$
46bo68$24b3o$26bo$25bo41$28b2o$29b2o$28bo39$36b2o$35bobo$37bo42$41bo$
41b2o$40bobo56$29b3o$31bo$30bo43$33b2o$34b2o$33bo72$7b3o$9bo$8bo51$2b
2o$3b2o$2bo23$25b2o$24bobo$26bo68$2b2o$3b2o$2bo21$27b3o$29bo$28bo26$
48bo$48b2o$47bobo281$53b2o$54b2o$53bo292$46b3o$48bo$47bo35$59bo$59b2o$
58bobo435$5b2o$4bobo$6bo43$8b2o$9b2o$8bo53$b2o$2b2o$bo6$42b2o$41bobo$
43bo253$26bo$26b2o$25bobo40$32b3o$34bo$33bo76$50b3o$52bo$51bo34$62b3o$
64bo$63bo90$67b2o$66bobo$68bo63$49b3o$51bo$50bo71$72b3o$74bo$73bo199$
110b2o$111b2o$110bo93$113bo$113b2o$112bobo45$113b2o$114b2o$113bo97$
111bo$111b2o$110bobo237$110b2o$111b2o$110bo44$113bo$113b2o$112bobo69$
138b3o$140bo$139bo155$125b3o$127bo$126bo114$104b3o$106bo$105bo43$108b
3o$110bo$109bo42$113b2o$112bobo$114bo128$78b2o$77bobo$79bo168$4bo$4b2o
$3bobo45$6b2o$5bobo$7bo49$b3o$3bo$2bo80$17bo$17b2o$16bobo61$b3o$3bo$2b
o31$112b3o$114bo$113bo92$114b2o$113bobo$115bo!

Note that at this stage there isn't any tightening: this just keeps the input gliders at intervals of approximately 48hd. Tightening can only really be done after the adjustable splitters have been wired up, and this part hasn't been implemented yet.

[dvgrn]

Maybe finding a seed for this Borg will further the proof...

Not really. The proof is already complete, as I said.

A seed for the Borg salvo would be more like "yet another data point that fails to provide any evidence that the proof is faulty".

[Vort]

After reading sentence from confocaloid "I wonder what would be consequences to the gun collection if all recent discoveries are accounted for", I started to wonder - how is it possible to visualize gun collection as a whole to see how particular events affected it?
First and simple idea is to make plot of averaged area versus gun period (this is what is displayed in attached image - min/avg/max area of guns divided into 100 blocks).
What other useful visualizations are possible? Did anyone made them?

[wwei47]

In what ways, if any, can a 2-engine cordership reflect a glider?

[Vort]

Did anyone created gun, which can be turned on (and later off) by glider (or other) signal?
Similar effect can be achieved by filtering output of always-on gun, but this is not what I'm asking about.
I'm thinking about creating high-delay reflector with such signal controlled gun and for it to work delay from "on" signal to first glider appearing at output should be constant.

[confocaloid]

Did anyone created gun, which can be turned on (and later off) [...]

Related discussion: viewtopic.php?p=156801#p156801
Related discussion: viewtopic.php?p=152794#p152794
An alien delay device: viewtopic.php?p=151812#p151812

[tommyaweosme]

maybe possibly we could use the fact that glider gun without blocks makes one glider and dies, and then we can use a specific regenerating structure to turn the ash back into a glider gun when another glider is put

edit:

i want to know how to make rule trees

manually

[Tawal]

It's about Golly.
My version : 4.2

How to save a pattern (that I constructed, pasted …) with some comments ?
Do I edit the rle file ?
If yes, is there a script to save a rle which ask for comments ?

If not, perhaps I can make it with python3.
But I'm not sure to right handle the files names (with high security).
I'm aware of that in Bash not in Python …


Edit: second question
Is there a way always in Golly to read/see the comments of a loaded rle file ?

[wirehead]

Edit: second question
Is there a way always in Golly to read/see the comments of a loaded rle file ?

View->Pattern Info will display the comments.

Not sure about your first question, I never do anything with comments…

[b-engine]

How to save a pattern (that I constructed, pasted …) with some comments ?
Do I edit the rle file ?
If yes, is there a script to save a rle which ask for comments ?

You can open the RLE file in a text editor, then manually append comments into it.

[dvgrn]

You can open the RLE file in a text editor, then manually append comments into it.

Yup. File > Preferences in Golly lets you pick your favorite text editor, and a right-click on a saved RLE file in Golly's file picker will then open the file in that editor. It never seemed like a high priority to unnecessarily duplicate text-editor functionality inside Golly.

There are some slightly awkward areas, for sure, like the hoops you need to jump through to edit comments in an .mc.gz or .rle.gz file -- but you can get them in there by renaming a commented .rle or .mc text file to .rle.gz or .mc.gz, opening the file in Golly (it auto-detects the type, ignoring the file extension) ... and then just re-saving.

[wwei47]

Do we have another sparker that can fit here? I've been trying to reduce the switch engine conga line extruder using new technology.

Code: Select all

x = 221, y = 256, rule = B3/S23
91bo$89b3o$88bo$88b2o2$84bo$74bo8bobo$74bo3bo3bo2bo$70b2ob2ob3o4b2o12b
2o5b2o$69bo5bo21b2o5b2o$70bo4bo$66bo4bo3bo21bo7bo$65bobo28bobo5bobo$
64bo2bo2b5o20b2ob2o3b2ob2o$65b2o2b2o25bo2bo3bo2bo$67b3o27bo7bo$67bobo
27b3o3b3o$68bo$65b3o$65bo$152b2o$79b2o16b2o5b2o46b2o$79b2o16b2o5b2o34b
2o3bo$76bo62bob4o2bo$76b5o14b4o40bobob4o$81bo13bo2bo13bo11b2o12b2obobo
$66bo11b3o12bobo15bobo10b2o11bo4b2obo$66bobo8bo15b2o4bo3bo3b2o2bobo24b
3o3b3o7b3o$66b2o9b4o16b3o2bobo2bo2b2ob2o24bob2o4bo6b3o$75b2o3bo3b2o10b
o5bobo3bobo30bobob2o7bob3o$74bo2b3o4b2o10b2o5bob4o2bob2o23b4obobo11bob
o$74b2obo27bo3bobob2o22bo2b4obo3bo4bo2b3o$77bo26bo3bobo28bo3b2o3bobo3b
2o$77b2o24bo3bobo38bo2b2obo$66b2o35b2o3bo38b4o2b2o$66bobo77b3ob2ob2o
15b2o$68bo4b2o10b2o59b2o4b3o15bobo$40b2o22b4ob2o2bo2bo9bo66bo18bo$41bo
22bo2bobobobob2o6b3o30b2o35bo18b2o$41bobo23bobobobo9bo32b2o16b2o18bo4b
o$42b2o24b2obobo57b2o2bo22bobo$72bo57bo2b2o23bobo$131bo25b2ob2o$46b2o
10b2o24b2o46b3o17b2o3bo4bo$45bo2bo10bo7b2o15b2o49bo12b2obo2bo2b4o2bo$
46bobo10bobo5b2o65b2o12b2o2b2o4bo2b2o$39bo7bo12b2o58b2o33bo4bo2b3o$39b
3o78bo34bo2b5o3bo$42bo62b2o14bo8b2o9bo16bo3bo2bobo$41b2o23bo38bobo12b
2o8bobo7bobo13bobob3o3b2o2bo$47b2o17b2o39bo22bo9bobo5b2o4b3ob2o4bo3b3o
$44b2ob2o16bobo39b2o32bo5bo2bo2bo3bo3b7o$42bobo103bobo2b2o2bob2obo5bo$
41bobo26b2o74b2obo8bobo4b3o$41bo28bo75b3o11bo2bo4b3o$40b2o29b3o62bob2o
6b2o12bob2o2b2o2bo$73bo60b2ob2o18b2obo2bo3bo$137b2o19bobob2ob2o$29bo
127bo2b2obo$19b2o8b3o126b2o4b5o$19b2o11bo4b2o2b2o91b2ob2o21b4o2bo2bo$
29b2o2bo3bo3bo2b2o89bob2o2b2o17bo2bo4b2o$29bob2obo4bobo3bo84b2obobo6bo
$34b5obo4bobo82bob2ob7o$30b2obo4bo7b2o86bo$30b2obobo3bo94bob4o$34bobo
3bo94b2o2bo$35bo3b2o$56bo68b3o$55bobo67b4o$56bo64b4o3b2o4b2o$121b3ob2o
2b2o3b2o$27b2o96b4o$27b2o$12b2o24b2o$11bo2bo23b3o26b2o4b2o$10bob2o24bo
4b2o11b2obo7bo5bobo49b4o$10bo29b2o2bo11b2ob3o3bobo7b3o43b3ob2o2b2o3b2o
$9b2o31b2o18bob3o7bo3bo42b4o3b2o4b2o$24b2o16bo18bob2o9b2o2bo46b4o$3b2o
19bo36bo2bo14b2o44b3o$4bo20b3o28b2o12bo9bo$2bo24bo10b2o16b2o11bobo7bo$
2b5o14b2o14bobo22bo2bo2bo2bo7b2o$7bo13bo15bo25b2o4b2o$4b3o12bobo14b2o$
3bo15b2o$3b4o$b2o3bo3b2o46b2o$o2b3o4b2o41b2obo2bo$2obo21bo24bobobob2o
29b2o$3bo21b3o21bob2obobo30bo$3b2o23bo6bo13bo3bo2bo32bo$27b2o4b2o13b2o
3bobo13b2o14b5o$34b2o18bo15bo13bo$11b2o57bobo12b3o$12bo58b2o15bo$9b3o
73b4o$9bo70b2o3bo3b2o$80b2o4b3o2bo42bo$37b2o49bob2o43b2o47b2o$30b2o5bo
bo13bobo32bo38bo6b2o39bo9bo7bo$30b2o7bo13b2o32b2o39b2o45b3o7bobo3b3o$
39bobo12bo72b2o49bo7b3obo$40b2o135b2o9b2obo$26bo52b2o107bo2bo$25bobob
2o48bo65bo36bo34bo$25bobobobo12b2o34b3o61b2o35bobo24b2ob2o3bobo$22b2ob
obobobo2bo8bo2bo35bo61bobo34bo2bo2bo2bo16bobobobo2b2o$22bo2bo2b2ob4o9b
obo135b2o4b2o16bo2bobob3o$24b2o4bo6bo7bo160bobo7b4o$30bobo4b3o165b2obo
bob2o2bo2bo$31b2o7bo70b2o92bo2bobobob2obo$39bo71b2o93b2o4bo2bob2o$39bo
2bo2b2o83b2o12bo63b2ob2o6bo$42bo2b2o61b2o10bobo6bobo13b2o61bobo6b2o$
40bobo65bobo10b2o8bo11b2o64b3obobo$39bobo67bo11bo23bo42bobo22bob2o$36b
o2bo149b2o18b2o2b4o$24b2o10b4o149bo19bo4bo2bo$25bo97b2o80b2o3bo3bo2bo$
23bo7b2o3b2o6bo77b2o81bo2bobo2bo3bo$21b4o6b2o3b2o5bobo78bo82b2obob2o$
20bo23bo163bobob5o2b2o$19bo2b3o88b2o88b2obo3bo4bo4bo$20b2o2bo87bobo89b
ob4obobobob3o$22b2o90bo89bo4bo2bo5bo$22bo98b2o82b3o3b2obo3bo$23bo96b2o
85bobo4bo2b2o$20b3o99bo86b5ob2o$20bo187bo8b3o$49b2o157b2o3bo3b3o$49bo
165b2obo$50b3o126bo7b2o26bo$52bo65bo60b3o5b2o31bo$117b3o62bo35bobo$53b
o63b3o61b2o13b2o20b2o$51b3o63b3o76bo$10bo35b2o2bo65b3o75bobo$10b3o17b
2o14bobo2bo63bo78b2o18b2o$13bo17bo17b2obo61bobobob2o67b2o22bo2bo$12b2o
14b3o19bob3o59bob2ob3o67b2o22bobo$28bo18bo2bo4bo59bo4b2o27b2o30b2o31bo
$46bobobo3b2o60bo31bobo31b2o$4b2o41bo2b2o2bo58b3o34bo30bo$4bo43b2o2bob
o58bo79bo$b2obo46bobo138bobo18b2o$bo2b3o4b2o35b2obo141bo19bo$2b2o3bo3b
2o35b2o2bo160bo$4b4o43b2o157b3o$4bo15b2o162b2o22bo4b3o$5b3o12bobo8b2o
11b2o109bo28b2o22bo4bo$8bo13bo9bo11bob2o106b2o52bo$3b5o14b2o8bobo11b2o
106bobo51bobo2bo$3bo29b2o11b2o46bo89bo22b2o2bobo$5bo35bo51bo2bo87b3o
18b3o4bo$4b2o24bo11b3o4b2o39b2o5bo89bo16bobo$28b3o12b2o5b2o37bo8bo3b2o
82b2o15bob2ob2o$27bo21bo39bo8bo3b2o99bo3bo2bo$27b2o11b2o48bob2ob3o104b
2o3bobo$94b2o101b2o9bo$189bo8bo$49bo44b2o92bobo5bo$48b3o3b2o7b2o25bob
2ob3o89bo3bo4b2o$38bo8bobobo2bo2bob2obo2bo23bo8bo3b2o83bo3bo6bo$37bobo
5b3o3b3o2b2obo3bobo23bo8bo3b2o83bo3bo4b2obo$17b2o18bobo4bo4b2o3b2o3bob
2obo25b2o5bo90bobo4bobo2bo$16bobo5b2o12bo5b2ob2ob2obo2bob3obo30bo2bo
92bo6bo2b2o$16bo7b2o9b3o10bobo2bob2o5bo31bo83b2o$15b2o18bo12bobobo4b3o
2b2o114bo2bo$47b2obob4obo2bobo116b3o9b2o$29bo21bo4bo2bo2bo121bo6bo$25b
2obobo21b3o5b2o119b4o7b3o$24bobobobo23b2o125bo12bo$21bo2bobobobob2o
148b3o$21b4ob2o2bo2bo150bo$25bo4b2o$23bobo$23b2o$30bo$20b2o8b3o$20bo
12bo4b2o2b2o123b2o$30b2o2bo3bo3bo2b2o120bobo$30bob2obo4bobo3bo122b3o$
21bobo11b5obo4bobo119bo3bo$31b2obo4bo7b2o112bo6b2o2bo29b2o5b2o$19bo3bo
2bo4b2obobo3bo119bobo10b2o26bo2bo3bo2bo$20bo4bobo7bobo3bo119bo13bo25bo
9bo$26b3o7bo3b2o133bo28bo3bo$28b2o27bo108b2o8b2o22bo3bo3bo3bo$23bo3b2o
27bobo107b2o9bo21bo5bobo5bo$24bo32bo42b2o30b2o39b2o2bobo24b2ob2o$23b2o
74bobo31b2o38b2o3b2o20bo3bo3bo3bo$23bo77bo30bo68bo2bo3bo2bo$156b2o44b
2o5b2o$13b2o51b2o88b2o$12bo2bo51bo66b2o$11bob2o42b2o6bo7b2o3b2o6bo48bo
35b2o$11bo45b2o4b4o6b2o3b2o5bobo45bo7b2o3b2o6bo16bobo28b2o5b2o$10b2o
50bo23bo44b4o6b2o3b2o5bobo17bo28b2o5b2o$25b2o34bo2b3o63bo23bo18b2o$4b
2o19bo36b2o2bo62bo2b3o$5bo20b3o28b2o5b2o64b2o2bo$3bo24bo10b2o16b2o5bo
67b2o11b3o$3b5o14b2o14bobo24bo66bo11bo3bo$8bo13bo15bo23b3o68bo10b2o2bo
$5b3o12bobo14b2o23bo67b3o14b2o$4bo15b2o69b2o37bo$4b4o83bo53b2o12b2o53b
2o$2b2o3bo3b2o79b3o49bo2bo11bo54bo$bo2b3o4b2o41b2obo36bo49b2o14b3o53bo
$b2obo21bo24bobobob3o102bo18bo14b2o14b5o$4bo21b3o18bo2bob2obo4bo34bo
85b2o14bo13bo$4b2o23bo17b4o3bo2b3o33b3o67bo16bobo14bobo12b3o$28b2o21b
2o2b3o8bo21b2o2bo68b3o34b2o15bo$49bo2b3o10bo6b2o14bobo2bo26bo35b2o2bo
51b4o$12b2o35b2o4bo9b3o5bo17b2obo25b3o17b2o14bobo2bo45b2o3bo3b2o$13bo
40b2o14b3o19bob3o26bo17bo17b2obo38b2o4b2o4b3o2bo$10b3o57bo18bo2bo4bo
24b2o14b3o19bob3o37b2o11bob2o$10bo77bobobo3b2o40bo14bo3bo2bo4bo35bo13b
o$46b2o41bo2b2o2bo54bobo2bobobo3b2o48b2o$38b2o6bo43b2o2bobo17b2o36b2o
3bo2b2o2bo$31b2o5bobo2b2obo46bobo18bo43b2o2bobo$31b2o7bo2bo2b3o4b2o35b
2obo17b2obo46bobo42b2o$40b2obobo3bo3b2o35b2o2bo16bo2b3o4b2o35b2obo44bo
$43bo2b4o43b2o17b2o3bo3b2o35b2o2bo44b3o$27bo15b2obo15b2o50b4o43b2o38b
2o6bo$26bobob2o12bo2b3o12bobo8b2o11bo27bo15b2o18b2o48bobo$26bobobobo
11bo5bo13bo9bo10bobo27b3o12bobo8b2o7b2o48bo$23b2obobobobo2bo9b5o14b2o
8bobo11bo29bo13bo9bo45b2o9b2obo2bo$23bo2bo2b2ob4o11bo27b2o8bo2bo24b5o
14b2o8bobo43b2o2b2o5bo2b4o$25b2o4bo51bobo27bo29b2o47bobo6bo$31bobo38bo
9b2o2b3obo24bo32b3o42bo5bo2b4o$32b2o36b3o9b2o2b2o3bo22b2o24bo9bo48b2ob
o3bo$69bo13b3o5b2o45b3o8bo40b2o8bo2b3obo$69b2o12bo3bo2b2o45bo53bo8bob
2obobo$83bo2b2o2b2o45b2o49b3o7b2obo3bob2o$84b4o100bo9bo2bo3bo2bo$159bo
40bob2o2bo$82b3o11b2o7b2o52bo39b2o3b2o$80bo8b2ob2o2bo2bob2obo2bo56b2o
7b2o27bobo$79bob2o4b3o3b3o2b2obo3bobo40bo8bo3bo2bo2bob2obo2bo23b2obo3b
o$59b2o18bo6bo4bo4b2o5b2obo40bobo5b3obob3o2b2obo3bobo23bo2bob2obo$58bo
bo5b2o12bo5b2ob2ob2obo2bob3obo22b2o18bobo4bo4bo4b2o5b2obo26bo5bo$58bo
7b2o9b3o10bobob2o2bo5bo21bobo5b2o12bo5b2ob2ob3o4b4obo26bob6o$57b2o18bo
12bobobo4b2obob2o20bo7b2o9b3o10bobo3b2o4bobo25bobo3bo$89b2obob4obo2bob
o20b2o18bo12bobobo4b4ob2o24bo2bo$71bo21bo4bo2bo2bo52b2obob4obo2bobo26b
2o$67b2obobo21b3o5b2o35bo21bo4bo2bo2bo$66bobobobo23b2o37b2obobo21b3o5b
2o$63bo2bobobobob2o58bobobobo23b2o$63b4ob2o2bo2bo55bo2bobobobob2o$67bo
4b2o57b4ob2o2bo2bo$65bobo67bo4b2o$65b2o66bobo$133b2o!

[Mathemagician314]

Is there any stable lifelike rule with a minimum speed limit?

[tommyaweosme]

rules without birth condition have a both minimum and maximum limit of c/0