ConwayLife.com

Posted: **February 11th, 2018, 7:32 pm**

Saka wrote:I thought that this thread was unsinkable

It has only been 6 days.

Posted: **February 12th, 2018, 10:09 am**

I have a function.
f(1) = 1
f(2) = 1
f(3) = 1
f(4 + 5) = 4
f(f(4) + f(5)) = 2
What is the function and what are
f(25)
f(23 - 11)
f(f(50) + f(21))

Posted: **February 12th, 2018, 10:31 am**

Saka wrote:I have a function.
f(1) = 1
f(2) = 1
f(3) = 1
f(4 + 5) = 4
f(f(4) + f(5)) = 2
What is the function and what are
f(25)
f(23 - 11)
f(f(50) + f(21))

f(1) = 1
f(2) = 1
f(3) = 1
f(4) = 2
f(5) = 4
f(6) = 2
f(9) = 4

Posted: **February 12th, 2018, 4:12 pm**

PHPBB12345 wrote:f(1) = 1
f(2) = 1
f(3) = 1
f(4) = 2
f(5) = 4
f(6) = 2
f(9) = 4

f(1), f(2), f(3) and f(9) are the only ones that are actually known. Your guesses for f(4), f(5) and f(6) are just that, guesses, because we don't have enough information to determine them exactly, as "f(f(4) + f(5)) = 2" is one equation with three unknowns (f(4), f(5) and f(whatever f(4) + f(5) is)).

Because of how limited the information Saka gave about the function is, I think we are supposed to guess it as a "well-known" function.

Posted: **February 12th, 2018, 6:56 pm**

Saka wrote:I have a function.
f(1) = 1
f(2) = 1
f(3) = 1
f(4 + 5) = 4
f(f(4) + f(5)) = 2
What is the function and what are
f(25)
f(23 - 11)
f(f(50) + f(21))

There are infinitely many functions possible.

Posted: **February 12th, 2018, 7:17 pm**

Yes it is probably impossible. It's the number of "sharp edges" in the number/equation without doing the equation unless there are more of the function in the equation.

Whatever,let's carion.
bjhwxy.com

Posted: **February 12th, 2018, 9:29 pm**

Don't read this URL

This is strange, I wonder what else can be manipulated in the URL

hmm

Posted: **February 13th, 2018, 9:20 am**

: QM37VoM.png (2.01 KiB) Viewed 844 times

I couldn't resist.

Posted: **February 13th, 2018, 10:04 am**

Can't you stop what's happening?

Posted: **February 13th, 2018, 10:17 am**

Stop what? It's just a pun.

Posted: **February 14th, 2018, 8:00 am**

I have a new avatar!

Posted: **February 14th, 2018, 8:12 am**

i've not been here for half a year. are p19s discovered yet?

Posted: **February 14th, 2018, 8:16 am**

72c20e wrote:i've not been here for half a year. are p19s discovered yet?

Nope.

Posted: **February 15th, 2018, 8:59 am**

Copperhead minimum rule:

Code: Select all

x = 8, y = 12, rule = B3-ceky/S23-ci
 b2o2b2o$3b2o$3b2o$obo2bobo$o6bo2$o6bo$b2o2b2o$2b4o2$3b2o$3b2o!

(Yes, copperhead requires ALL s2 transitions.)

Posted: **February 15th, 2018, 9:53 am**

Gamedziner wrote:Copperhead minimum rule:
Code: Select all
x = 8, y = 12, rule = B3-ceky/S23-ci
 b2o2b2o$3b2o$3b2o$obo2bobo$o6bo2$o6bo$b2o2b2o$2b4o2$3b2o$3b2o!
(Yes, copperhead requires ALL s2 transitions.)

Should you post that in Miscellaneous Discoveries?

Posted: **February 15th, 2018, 9:54 am**

KittyTac wrote: Should you post that in Miscellaneous Discoveries?

The minimal rule for any given pattern in any NT or totalistic rule can be easily found using the script.

Posted: **February 15th, 2018, 6:17 pm**

Saka wrote: The minimal rule for any given pattern in any NT or totalistic rule can be easily found using the script.

Script?

Posted: **February 16th, 2018, 7:40 pm**

Gamedziner wrote:
Saka wrote: The minimal rule for any given pattern in any NT or totalistic rule can be easily found using the script.
Script?

Code: Select all


import golly as g
from glife import validint
from string import replace

Hensel = [
    ['0'],
    ['1c', '1e'],
    ['2a', '2c', '2e', '2i', '2k', '2n'],
    ['3a', '3c', '3e', '3i', '3j', '3k', '3n', '3q', '3r', '3y'],
    ['4a', '4c', '4e', '4i', '4j', '4k', '4n', '4q', '4r', '4t', '4w', '4y', '4z'],
    ['5a', '5c', '5e', '5i', '5j', '5k', '5n', '5q', '5r', '5y'],
    ['6a', '6c', '6e', '6i', '6k', '6n'],
    ['7c', '7e'],
    ['8']
]

# Python versions < 2.4 don't have "sorted" built-in
try:
    sorted
except NameError:
    def sorted(inlist):
        outlist = list(inlist)
        outlist.sort()
        return outlist

# --------------------------------------------------------------------

def chunks(l, n):
    for i in range(0, len(l), n):
        yield l[i:i+n]

# --------------------------------------------------------------------

def rulestringopt(a):
    result = ''
    context = ''
    lastnum = ''
    lastcontext = ''
    for i in a:
        if i in 'BS':
            context = i
            result += i
        elif i in '012345678':
            if (i == lastnum) and (lastcontext == context):
                pass
            else:
                lastcontext = context
                lastnum = i
                result += i
        else:
            result += i
    result = replace(result, '4aceijknqrtwyz', '4')
    result = replace(result, '3aceijknqry', '3')
    result = replace(result, '5aceijknqry', '5')
    result = replace(result, '2aceikn', '2')
    result = replace(result, '6aceikn', '6')
    result = replace(result, '1ce', '1')
    result = replace(result, '7ce', '7')
    return result

clist = []
rule = g.getrule().split(':')[0]

fuzzer = rule + '9'
oldrule = rule
rule = ''
context = ''
deletefrom = []
for i in fuzzer:
    if i == '-':
        deletefrom = [x[1] for x in Hensel[int(context)]]
    elif i in '0123456789/S':
        if deletefrom:
            rule += ''.join(deletefrom)
            deletefrom = []
        context = i
    if len(deletefrom) == 0:
        rule += i
    elif i in deletefrom:
        deletefrom.remove(i)
rule = rule.strip('9')

if not (rule[0] == 'B' and '/S' in rule):
    g.exit('Please set Golly to a Life-like rule.')

if g.empty():
    g.exit('The pattern is empty.')

s = g.getstring('Enter the period:', '', 'Rules calculator')
if not validint(s):
    g.exit('Bad number: %s' % s)

numsteps = int(s)
if numsteps < 1:
    g.exit('Period must be at least 1.')

g.select(g.getrect())
g.copy()
s = int(s)

for i in range(0,s):
    g.run(1)
    clist.append(list(chunks(g.getcells(g.getrect()), 2)))
    mcc = min(clist[i])
    clist[i] = [[x[0] - mcc[0], x[1] - mcc[1]] for x in clist[i]]

g.show('Processing...')

ruleArr = rule.split('/')
ruleArr[0] = ruleArr[0].lstrip('B')
ruleArr[1] = ruleArr[1].lstrip('S')

b_need = []
b_OK = []
s_need = []
s_OK = []

context = ''
fuzzed = ruleArr[0] + '9'
for i in fuzzed:
    if i in '0123456789':
        if len(context) == 1:
            b_need += Hensel[int(context)]
            b_OK += Hensel[int(context)]
        context = i
    elif context != '':
        b_need.append(context[0] + i)
        b_OK.append(context[0] + i)
        context += context[0]
context = ''
fuzzed = ruleArr[1] + '9'
for i in fuzzed:
    if i in '0123456789':
        if len(context) == 1:
            s_need += Hensel[int(context)]
            s_OK += Hensel[int(context)]
        context = i
    elif context != '':
        s_need.append(context[0] + i)
        s_OK.append(context[0] + i)
        context += context[0]

for i in [iter2 for iter1 in Hensel for iter2 in iter1]:
    if not i in b_OK:
        b_OK.append(i)
        execfor = 1
        # B0 and nontotalistic rulestrings are mutually exclusive
        try:
            g.setrule(rulestringopt('B' + ''.join(b_OK) + '/S' + ruleArr[1]))
        except:
            b_OK.remove(i)
            execfor = 0
        for j in range(0, s * execfor):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    b_OK.remove(i)
                    break
            except:
                b_OK.remove(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        b_OK.sort()

    if not i in s_OK:
        s_OK.append(i)
        execfor = 1
        # B0 and nontotalistic rulestrings are mutually exclusive
        try:
            g.setrule(rulestringopt('B' + ruleArr[0] + '/S' + ''.join(s_OK)))
        except:
            s_OK.remove(i)
            execfor = 0
        for j in range(0, s * execfor):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    s_OK.remove(i)
                    break
            except:
                s_OK.remove(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        s_OK.sort()

    if i in b_need:
        b_need.remove(i)
        g.setrule(rulestringopt('B' + ''.join(b_need) + '/S' + ruleArr[1]))
        for j in range(0, s):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    b_need.append(i)
                    break
            except:
                b_need.append(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        b_need.sort()

    if i in s_need:
        s_need.remove(i)
        g.setrule(rulestringopt('B' + ruleArr[0] + '/S' + ''.join(s_need)))
        for j in range(0, s):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    s_need.append(i)
                    break
            except:
                s_need.append(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        s_need.sort()

g.setrule(oldrule)
ruleres = 'B' + ''.join(sorted(b_need)) + '/S' + ''.join(sorted(s_need))
ruleres = rulestringopt(ruleres)
g.setrule(ruleres)

Posted: **February 17th, 2018, 8:40 am**

Rhombic wrote:

Gamedziner wrote:
Saka wrote: The minimal rule for any given pattern in any NT or totalistic rule can be easily found using the script.
Script?

Code: Select all


import golly as g
from glife import validint
from string import replace

Hensel = [
    ['0'],
    ['1c', '1e'],
    ['2a', '2c', '2e', '2i', '2k', '2n'],
    ['3a', '3c', '3e', '3i', '3j', '3k', '3n', '3q', '3r', '3y'],
    ['4a', '4c', '4e', '4i', '4j', '4k', '4n', '4q', '4r', '4t', '4w', '4y', '4z'],
    ['5a', '5c', '5e', '5i', '5j', '5k', '5n', '5q', '5r', '5y'],
    ['6a', '6c', '6e', '6i', '6k', '6n'],
    ['7c', '7e'],
    ['8']
]

# Python versions < 2.4 don't have "sorted" built-in
try:
    sorted
except NameError:
    def sorted(inlist):
        outlist = list(inlist)
        outlist.sort()
        return outlist

# --------------------------------------------------------------------

def chunks(l, n):
    for i in range(0, len(l), n):
        yield l[i:i+n]

# --------------------------------------------------------------------

def rulestringopt(a):
    result = ''
    context = ''
    lastnum = ''
    lastcontext = ''
    for i in a:
        if i in 'BS':
            context = i
            result += i
        elif i in '012345678':
            if (i == lastnum) and (lastcontext == context):
                pass
            else:
                lastcontext = context
                lastnum = i
                result += i
        else:
            result += i
    result = replace(result, '4aceijknqrtwyz', '4')
    result = replace(result, '3aceijknqry', '3')
    result = replace(result, '5aceijknqry', '5')
    result = replace(result, '2aceikn', '2')
    result = replace(result, '6aceikn', '6')
    result = replace(result, '1ce', '1')
    result = replace(result, '7ce', '7')
    return result

clist = []
rule = g.getrule().split(':')[0]

fuzzer = rule + '9'
oldrule = rule
rule = ''
context = ''
deletefrom = []
for i in fuzzer:
    if i == '-':
        deletefrom = [x[1] for x in Hensel[int(context)]]
    elif i in '0123456789/S':
        if deletefrom:
            rule += ''.join(deletefrom)
            deletefrom = []
        context = i
    if len(deletefrom) == 0:
        rule += i
    elif i in deletefrom:
        deletefrom.remove(i)
rule = rule.strip('9')

if not (rule[0] == 'B' and '/S' in rule):
    g.exit('Please set Golly to a Life-like rule.')

if g.empty():
    g.exit('The pattern is empty.')

s = g.getstring('Enter the period:', '', 'Rules calculator')
if not validint(s):
    g.exit('Bad number: %s' % s)

numsteps = int(s)
if numsteps < 1:
    g.exit('Period must be at least 1.')

g.select(g.getrect())
g.copy()
s = int(s)

for i in range(0,s):
    g.run(1)
    clist.append(list(chunks(g.getcells(g.getrect()), 2)))
    mcc = min(clist[i])
    clist[i] = [[x[0] - mcc[0], x[1] - mcc[1]] for x in clist[i]]

g.show('Processing...')

ruleArr = rule.split('/')
ruleArr[0] = ruleArr[0].lstrip('B')
ruleArr[1] = ruleArr[1].lstrip('S')

b_need = []
b_OK = []
s_need = []
s_OK = []

context = ''
fuzzed = ruleArr[0] + '9'
for i in fuzzed:
    if i in '0123456789':
        if len(context) == 1:
            b_need += Hensel[int(context)]
            b_OK += Hensel[int(context)]
        context = i
    elif context != '':
        b_need.append(context[0] + i)
        b_OK.append(context[0] + i)
        context += context[0]
context = ''
fuzzed = ruleArr[1] + '9'
for i in fuzzed:
    if i in '0123456789':
        if len(context) == 1:
            s_need += Hensel[int(context)]
            s_OK += Hensel[int(context)]
        context = i
    elif context != '':
        s_need.append(context[0] + i)
        s_OK.append(context[0] + i)
        context += context[0]

for i in [iter2 for iter1 in Hensel for iter2 in iter1]:
    if not i in b_OK:
        b_OK.append(i)
        execfor = 1
        # B0 and nontotalistic rulestrings are mutually exclusive
        try:
            g.setrule(rulestringopt('B' + ''.join(b_OK) + '/S' + ruleArr[1]))
        except:
            b_OK.remove(i)
            execfor = 0
        for j in range(0, s * execfor):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    b_OK.remove(i)
                    break
            except:
                b_OK.remove(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        b_OK.sort()

    if not i in s_OK:
        s_OK.append(i)
        execfor = 1
        # B0 and nontotalistic rulestrings are mutually exclusive
        try:
            g.setrule(rulestringopt('B' + ruleArr[0] + '/S' + ''.join(s_OK)))
        except:
            s_OK.remove(i)
            execfor = 0
        for j in range(0, s * execfor):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    s_OK.remove(i)
                    break
            except:
                s_OK.remove(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        s_OK.sort()

    if i in b_need:
        b_need.remove(i)
        g.setrule(rulestringopt('B' + ''.join(b_need) + '/S' + ruleArr[1]))
        for j in range(0, s):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    b_need.append(i)
                    break
            except:
                b_need.append(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        b_need.sort()

    if i in s_need:
        s_need.remove(i)
        g.setrule(rulestringopt('B' + ruleArr[0] + '/S' + ''.join(s_need)))
        for j in range(0, s):
            g.run(1)
            try:
                dlist = list(chunks(g.getcells(g.getrect()), 2))
                mcc = min(dlist)
                dlist = [[x[0] - mcc[0], x[1] - mcc[1]] for x in dlist]
                if not(clist[j] == dlist):
                    s_need.append(i)
                    break
            except:
                s_need.append(i)
                break
        g.new('')
        g.paste(0, 0, 'or')
        g.select(g.getrect())
        s_need.sort()

g.setrule(oldrule)
ruleres = 'B' + ''.join(sorted(b_need)) + '/S' + ''.join(sorted(s_need))
ruleres = rulestringopt(ruleres)
g.setrule(ruleres)

Is there one for a maximum rule?

Posted: **February 17th, 2018, 8:42 am**

KittyTac wrote:

Is thare one for a maximum rule?

Doesn't that also give a max rule?

Posted: **February 17th, 2018, 8:51 am**

Saka wrote:
KittyTac wrote:

Is thare one for a maximum rule?
Doesn't that also give a max rule?

Either way, I couldn't find the max rule.

Posted: **February 17th, 2018, 8:53 am**

KittyTac wrote: Either way, I couldn't find the max rule.

Post the output here

Posted: **February 17th, 2018, 9:03 am**

Saka wrote:
KittyTac wrote: Either way, I couldn't find the max rule.
Post the output here

It just automatically opens the minimum rule, no output file or anything.

Posted: **February 17th, 2018, 10:23 am**

Gamedziner wrote:
Saka wrote: The minimal rule for any given pattern in any NT or totalistic rule can be easily found using the script.
Script?

Both the totalistic and isotropic version of this script can be found in this post on the Golly scripts thread. There's lots of good stuff there, it's a shame it tends to be hard to find things if you don't know that they're there.

P.S. See my post two posts down for a copy/paste friendly output format

Posted: **February 18th, 2018, 2:21 am**

Code: Select all

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