idea for cool reversible 1d oca

[tommyaweosme]

for my 200th post, i will show you this

three states. black, blue, and pink.

groups are in two, and move left every generation

Screenshot 2024-04-27 12.16.47 PM.png (5.95 KiB) Viewed 4083 times

like margolus, but for 1D.

anyway, here is an explanation of what my idea is.

0 = black
1 = blue
2 = pink

00 > 00
01 > 12
02 > 10
10 > 01
11 > 20
12 > 21
20 > 02
21 > 11
22 > 22

here is an example:
0 0|0 2|
0|0 1|0
0 1|2 0|
1|2 0|2

if there was a way to make it in lifeviewer, i would like it.

[pipsqueek]

1D Margolus rules do sound interesting, I made an emulation ruletable of this one, which is the 1D equivalent of the billiard balls rule.

Code: Select all

x = 26, y = 1, rule = 1dmargolus
DCDCDCBCDCDCDCDCDCDADCDCDC!
@RULE 1dmargolus

0 = nothing
1 = alive (even parity)
2 = alive (odd parity)
3 = dead (even parity)
4 = dead (odd parity)

red = left
blue = right

@TABLE
n_states:5
neighborhood:oneDimensional
symmetries:none

#switch parity
3,0,0,4
4,0,0,3

3,4,4,4
4,3,3,3

3,4,0,4
4,3,0,3

3,0,4,4
4,0,3,3
#rule specific transitions

#red move left
4,3,1,1
1,4,4,4
4,1,3,3

#blue move right
3,4,2,4
3,2,4,2
2,3,3,3

#bounce off eachother
2,3,1,1
1,2,4,2
1,4,2,4
2,1,3,3

#grow emulation agar
0,3,0,3
0,0,3,3
0,4,0,4
0,0,4,4
@COLORS
1 255 128 128
2 128 128 255
3 128 0 0
4 0 0 128

In fact, I wrote python implementation to simulate 1D Margolus rules. A lot of them are boring, but some of them have interesting dynamics, for example, most elementary 1D rules form down-facing triangles, however, this Margolus rule forms sideways triangles!

sidewaystriangles.png (632.08 KiB) Viewed 4015 times

Which follows this rule
00 -> 10
01 -> 01
10 -> 00
11 -> 11

As for the rule you described, it shouldn't be too hard to make, however, I don't think you specified enough transitions to make into a rule. But if someone were to try, I would be curious to see the results.

EDIT: I made a mistake, you actually did specify enough transitions to complete the rule. I put it into the python implementation and ran it on a random torus of size 512. Here is the result:

1dmargolus.png (1.15 MiB) Viewed 4008 times

[tommyaweosme]

could you provide the code needed for this implement?

edit: there are only 24 2-state (edit: reversible) 1d margolus rules

edit: there are actually 4^4 (edit: 256) 2-state 1d margolus rules

[pipsqueek]

Here is the code, currently configured to run the described rule. Press E to randomize the pattern, space to pause, and R to randomize the rule. Other parameters can be changed in the code.

Code: Select all

from random import randint

#parameters

cellnum = 512
cellwidth = 1024/cellnum
cellheight = 1024/cellnum
height = 320/cellheight #number of generations to show at once
states = 3 #number of cell states

rule = {}

def randomrule():
    global rule
    rule = {}
    for a in range(states):
        for b in range(states):
            rule[(a,b)] = (randint(0,states-1),randint(0,states-1))

#set the rule
rule[(0,0)] = (0,0)
rule[(0,1)] = (1,2)
rule[(0,2)] = (1,0)
rule[(1,0)] = (0,1)
rule[(1,1)] = (2,0)
rule[(1,2)] = (2,1)
rule[(2,0)] = (0,2)
rule[(2,1)] = (1,1)
rule[(2,2)] = (2,2)

cells = [randint(0,states-1) for c in range(cellnum)]
def step():
    global cells
    previous.append(cells)
    newcells = cells[:]
    for c in range(0,cellnum,2):
        partion = (cells[(c+parity)%cellnum],cells[(c+parity+1)%cellnum])
        newpartion = rule[(partion[0],partion[1])]
        newcells[(c+parity)%cellnum] = newpartion[0]
        newcells[(c+parity+1)%cellnum] = newpartion[1]
    cells = newcells

#store previous generations
previous = []

def draw():
    for p in range(len(previous)):
        for c in range(cellnum):
            '''if previous[p][c] == 0:
                color = (0,0,0)
            else:
                color = (255/previous[p][c],
                         255/previous[p][c],
                         255/previous[p][c])'''
            if previous[p][c] == 0:
                color = (0,0,0)
            if previous[p][c] == 1:
                color = (0,128,255)
            if previous[p][c] == 2:
                color = (255,0,255)
            pygame.draw.rect(window,color,
                             (c*cellwidth,p*cellheight,cellwidth,cellheight))
    if len(previous)>height:
        previous.pop(0)
    pygame.display.flip()
            
            
    


import pygame
window = pygame.display.set_mode((1024,320))
pygame.display.set_caption("1D Partioning Automata")

from time import sleep

#what cell to start partioning at (0 or 1)
parity = 0

running = True
paused = False
while running:
    parity = 1-parity
    if not paused:
        step()
        draw()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_r:
                #change the rule to a random one
                window.fill((0,0,0))
                randomrule()
                previous = []
                cells = [randint(0,states-1) for c in range(cellnum)]
            elif event.key == pygame.K_e:
                window.fill((0,0,0))
                previous = []
                cells = [randint(0,states-1) for c in range(cellnum)]
            elif event.key == pygame.K_SPACE:
                #paused the simulation
                paused = not paused
            
pygame.quit()

[iddi01]

I made some minor improvements to pipsqueek's code:

1. The program now prompts you for the torus size and the rule. Note: when it prompts you about "(x,x) becomes:", you should give two numbers without separators, like "02" (without the quotes)
2. Then, it prompts about whether or not to use a random starting condition. Type "yes" to start randomly, or "no" to start with an ordered pattern.
3. The colors now looks better.

Code: Select all

from random import randint

#parameters

cellnum = int(input("torus size: "))
cellwidth = 1024/cellnum
cellheight = 1024/cellnum
height = 320/cellheight #number of generations to show at once
states = 3 #number of cell states

rule = {}

def randomrule():
    global rule
    rule = {}
    for a in range(states):
        for b in range(states):
            rule[(a,b)] = (randint(0,states-1),randint(0,states-1))

#set the rule
rule[(0,0)] = [int(n) for n in tuple(input("(0,0) becomes: "))]
rule[(0,1)] = [int(n) for n in tuple(input("(0,1) becomes: "))]
rule[(0,2)] = [int(n) for n in tuple(input("(0,2) becomes: "))]
rule[(1,0)] = [int(n) for n in tuple(input("(1,0) becomes: "))]
rule[(1,1)] = [int(n) for n in tuple(input("(1,1) becomes: "))]
rule[(1,2)] = [int(n) for n in tuple(input("(1,2) becomes: "))]
rule[(2,0)] = [int(n) for n in tuple(input("(2,0) becomes: "))]
rule[(2,1)] = [int(n) for n in tuple(input("(2,1) becomes: "))]
rule[(2,2)] = [int(n) for n in tuple(input("(2,2) becomes: "))]

if input("randomize pattern? ").lower() == 'yes':
    cells = [randint(0,states-1) for c in range(cellnum)]
else:
    cells = [0] * (cellnum // 2) + [1] * (cellnum // 2) 
    
def step():
    global cells
    previous.append(cells)
    newcells = cells[:]
    for c in range(0,cellnum,2):
        partion = (cells[(c+parity)%cellnum],cells[(c+parity+1)%cellnum])
        newpartion = rule[(partion[0],partion[1])]
        newcells[(c+parity)%cellnum] = newpartion[0]
        newcells[(c+parity+1)%cellnum] = newpartion[1]
    cells = newcells

#store previous generations
previous = []

def draw():
    for p in range(len(previous)):
        for c in range(cellnum):
            '''if previous[p][c] == 0:
                color = (0,0,0)
            else:
                color = (255/previous[p][c],
                         255/previous[p][c],
                         255/previous[p][c])'''
            if previous[p][c] == 0:
                color = (0,0,0)
            if previous[p][c] == 1:
                color = (255,255,255)
            if previous[p][c] == 2:
                color = (0,255,0)
            pygame.draw.rect(window,color,
                             (c*cellwidth,p*cellheight,cellwidth,cellheight))
    if len(previous)>height:
        previous.pop(0)
    pygame.display.flip()
            
            
    


import pygame
window = pygame.display.set_mode((1024,320))
pygame.display.set_caption("1D Partioning Automata")

from time import sleep

#what cell to start partioning at (0 or 1)
parity = 0

running = True
paused = False
while running:
    parity = 1-parity
    if not paused:
        step()
        draw()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_r:
                #change the rule to a random one
                window.fill((0,0,0))
                randomrule()
                previous = []
                cells = [randint(0,states-1) for c in range(cellnum)]
            elif event.key == pygame.K_e:
                window.fill((0,0,0))
                previous = []
                cells = [randint(0,states-1) for c in range(cellnum)]
            elif event.key == pygame.K_SPACE:
                #paused the simulation
                paused = not paused
            
pygame.quit()

@tommyaweosme: According to Wolfram's classification (the classification for 1D rules), your rule is class 3.
@pipsqueek: Why does the script generate slower and slower over time?

The 3-state 1D margolus rulespace is really quite interesting, here are some rules i discovered:
Strobing, symmetrical, probably class 4:

Example class 4 3-state 1D margolus

1dmarg1.png (45.98 KiB) Viewed 3945 times

Strobing, class 3:

Example class 3 3-state 1D margolus

1dmarg2.png (28.53 KiB) Viewed 3945 times

Class 2 (uninteresting, just an example of class 2 rules):

[pipsqueek]

Why does the script generate slower and slower over time?

Each row on screen is 1 generation of the pattern. These generations are stored in one big array and displayed on the screen. When the program first starts, it doesn't have many rows in the array, so it draws it quickly. But when the entire screen is filled, it gets slow (it shouldn't get any slower, as the top row is removed when it's out of view). It could be made faster by storing the generations as pixels on the screen. Make the following modifications to the code to do so:

Code: Select all

cells = [randint(0,states-1) for c in range(cellnum)]
def step():
    global cells
    newcells = cells[:]
    for c in range(0,cellnum,2):
        partion = (cells[(c+parity)%cellnum],cells[(c+parity+1)%cellnum])
        newpartion = rule[(partion[0],partion[1])]
        newcells[(c+parity)%cellnum] = newpartion[0]
        newcells[(c+parity+1)%cellnum] = newpartion[1]
    cells = newcells

def draw():
    window.scroll(dy=-int(cellheight))
    #for p in range(len(previous)):
    for c in range(cellnum):
        if cells[c] == 0:
            color = (0,0,0)
        else:
            color = (255/cells[c],
                     255/cells[c],
                     255/cells[c])
        pygame.draw.rect(window,color,
                         (c*cellwidth,320-int(cellheight),cellwidth,cellheight))

    pygame.display.flip()

Also, I propose we dedicate this thread to 1D Margolus rules in general, rather than the one that it was originally suppose to be about. And that we change the thread's name to "1D Margolus rules".

[tommyaweosme]

the code has random end of line markers. can you fix that please?

[pipsqueek]

the code has random end of line markers. can you fix that please?

Do you mean the newline character? Those are just for readability. The code runs fine with or without them. Without them it would be this:

Code: Select all

cells = [randint(0,states-1) for c in range(cellnum)]
def step():
    global cells
    newcells = cells[:]
    for c in range(0,cellnum,2):
        partion = (cells[(c+parity)%cellnum],cells[(c+parity+1)%cellnum])
        newpartion = rule[(partion[0],partion[1])]
        newcells[(c+parity)%cellnum] = newpartion[0]
        newcells[(c+parity+1)%cellnum] = newpartion[1]
    cells = newcells
def draw():
    window.scroll(dy=-int(cellheight))
    for c in range(cellnum):
        if cells[c] == 0:
            color = (0,0,0)
        else:
            color = (255/cells[c],255/cells[c],255/cells[c])
        pygame.draw.rect(window,color,(c*cellwidth,320-int(cellheight),cellwidth,cellheight))
    pygame.display.flip()

Just plug that in where the previous step() and draw() functions were and it should work.

[tommyaweosme]

i meant the first two scripts posted here
edit: i mean end of file
edit: it was a problem with the compiler i was using

[b-engine]

When I run the script in Python 3.11 it gives this error:

Code: Select all

Traceback (most recent call last):
 File "wxpython.cpp", line 3, in <module>
 File "C:\Users\User\AppData\Roaming\Golly\golly_clip.py", line 5, in <module>
  cellnum = int(input("torus size: "))
            ^^^^^^^^^^^^^^^^^^^^^
RuntimeError: input(): lost sys.stdin

Can someone update the script for Python 3?

[wildmyron]

When I run the script in Python 3.11 it gives this error:

Code: Select all

Traceback (most recent call last):
 File "wxpython.cpp", line 3, in <module>
 File "C:\Users\User\AppData\Roaming\Golly\golly_clip.py", line 5, in <module>
  cellnum = int(input("torus size: "))
            ^^^^^^^^^^^^^^^^^^^^^
RuntimeError: input(): lost sys.stdin

Can someone update the script for Python 3?

The script should run fine in python 3, but it's not intended to be run in Golly. Instead, you should run the script with Python from a command line or using IDLE, or whichever IDE you have/use for Python. You will also need the pygame module installed.

[pipsqueek]

I made a small error in the code, the parity switches when it is paused. Which means the evolution of a pattern changes when you pause. To prevent this, just replace this:

Code: Select all

parity = 1-parity
    if not paused:
        step()
        draw()

with this:

Code: Select all

if not paused:
    parity = 1-parity
    step()
    draw()

[tommyaweosme]

thats ok. im not planning to pause on a m-

-OPEN, CL-

that was weird

anyway, im not planning to pause on a margolus 1d oca, so that doesnt matter

any script for 2-state 1d margolus oca?

[unname4798]

thats ok. im not planning to pause on a m-

-OPEN, CL-

that was weird

anyway, im not planning to pause on a margolus 1d oca, so that doesnt matter

any script for 2-state 1d margolus oca?

Too complex for me.

[tommyaweosme]

thats ok. im not planning to pause on a m-

-OPEN, CL-

that was weird

anyway, im not planning to pause on a margolus 1d oca, so that doesnt matter

any script for 2-state 1d margolus oca?

Too complex for me.

IM JUST ASKING YOU TO REMOVE A STATE. AND I AM ASKING THE ENTIRE POPULATION OF CONWAYLIFE.COM, NOT JUST YOU!

sorry for snaping. im just really tired of this.

tommyaweosme, you should probably move this to a sandbox thread

ok, i will move the tommyaweosme lore clues to a sandbox thread. unless january 16 tommyaweosme comes back...

back on topic, it seems like someone already made it, so if someone could please post it please do! :D

[pipsqueek]

back on topic, it seems like someone already made it, so if someone could please post it please do! :D

You didn't notice this part of the code?

Code: Select all

states = 3 #number of cell states

Just change it to 2 and the code should work. I designed it to work with any number of states. Also, if you're using iddi01's version, you might have to change these parts too:

Code: Select all

#old coloring
if cells[c] == 0:
            color = (0,0,0)
        else:
            color = (255/cells[c],
                     255/cells[c],
                     255/cells[c])

Code: Select all

#same thing, but for 2 states
rule[(0,0)] = [int(n) for n in tuple(input("(0,0) becomes: "))]
rule[(0,1)] = [int(n) for n in tuple(input("(0,1) becomes: "))]
rule[(1,0)] = [int(n) for n in tuple(input("(1,0) becomes: "))]
rule[(1,1)] = [int(n) for n in tuple(input("(1,1) becomes: "))]

EDIT: Actually, for that last code snippet, use this instead, it works with any number of states (don't use parenthesis when inputting)

Code: Select all

for a in range(states):
    for b in range(states):
        i = input(f"({a},{b}) becomes:")
        c,d = i.split(',')
        c,d = int(c),int(d)
        rule[(a,b)] = (c,d) 

[iddi01]

I made 2 scripts which would allow the exploration of 3-state 1D margolus rules in Golly:

1. This script generates a ruletable like this one, It can be run in shell or Golly.
Type a rulestring using a simple notation: For each 2-cell configuration, type what it becomes using 2 numbers without separators, type a comma, then type what the next configuration becomes in the same way. The order for initial configurations are 00,01,02,10,11,12,20,21,22.
Example: tommyaweosme's rule would be encoded as "00,12,10,01,20,21,02,11,22".
You can choose to generate a true 1D rule or a 2D emulation.

Code: Select all

def gen1dmargtable(rulestring):
    transitions = [[0,0],[0,0],[0,0],[0,0],[0,0],[0,0],[0,0],[0,0],[0,0]]
    x = 0
    y = 0
    for char in rulestring:
        if char == ' ':
            pass
        elif char == ',':
            x = 0
            y += 1
        else:
            transitions[y][x] = int(char)
            x += 1

    if __name__ == '__main__':
        emulation = input("True 1D or emulation by 2D (1D/2D)? ").upper() == "2D"
    else:
        emulation = golly.getstring("True 1D or emulation by 2D (1D/2D)? ", "1D").upper() == "2D"

    if emulation:
        temp = "0,%s,%s,0,0,0,0,0,%s,%s\n"
    else:
        temp = "%s,%s,%s,%s\n"
    table = """@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:%s
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

""" % ("Moore" if emulation else "oneDimensional")

    for n in range(9):
        table += temp % (n // 3, 'a', n % 3 + 3, transitions[n][0] + 3)
        if n % 3 == 2:
            table += temp % (n // 3, 'a', 'b', transitions[n-2][0] + 3)
            if n == 2:
                table += temp % ('0','b','a',transitions[0][0] + 3)
    for n in range(9):
        table += temp % (n % 3 + 3, n // 3, 'a', transitions[n][1])
        if n >= 6:
            table += temp % (n % 3 + 3, 'b', 'a', transitions[n-6][1])
    table += """
@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
"""
    return table

if __name__ == '__main__':
    rulestring = input('Type a rulestring, in the format "xx,xx,xx,xx,xx,xx,xx,xx,xx": ')
    print(gen1dmargtable(rulestring))
else:
    import golly
    rulestring = golly.getstring('Type a rulestring, in the format "xx,xx,xx,xx,xx,xx,xx,xx,xx": ','00,01,02,10,11,12,20,21,22')
    try:
        f = open(golly.getdir('rules') + "1dmargtest.rule", 'r')
        golly.warn("""1dmargtest.rule already exists.
Please rename the file and try again.""")
        golly.exit()
    except FileNotFoundError:
        f = open(golly.getdir('rules') + "1dmargtest.rule", 'w')
        f.write(gen1dmargtable(rulestring))
        f.close()
        golly.setrule('1dmargtest')

2. This script generates a 512x1 3-state margolus soup. It can be run in shell or Golly.

Code: Select all

import random

def gen1dmargsoup():
    char = ['.', 'A', 'B', 'C', 'D', 'E']
    rle = "x = 512, y = 1, rule = 1dmargtest\n"
    for n in range(512):
        rle += char[n % 2 * 3 + random.randrange(3)]
    return rle

if __name__ == '__main__':
    print(gen1dmargsoup())
else:
    import golly
    golly.setclipstr(gen1dmargsoup())
    golly.paste(0,0,"or")

This rulespace turned out to be more interesting than i thought. I've discovered a bunch of interesting rules, which are likely all class 4:
(Note that the ruletables below are all 2D emulation.)

00,21,02,20,00,21,10,12,22 generates adjustable-speed spaceships that interact in complex ways:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!

@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,3
0,0,a,0,0,0,0,0,4,5
0,0,a,0,0,0,0,0,5,3
0,0,a,0,0,0,0,0,b,3
0,0,b,0,0,0,0,0,a,3
0,1,a,0,0,0,0,0,3,5
0,1,a,0,0,0,0,0,4,3
0,1,a,0,0,0,0,0,5,5
0,1,a,0,0,0,0,0,b,5
0,2,a,0,0,0,0,0,3,4
0,2,a,0,0,0,0,0,4,4
0,2,a,0,0,0,0,0,5,5
0,2,a,0,0,0,0,0,b,4
0,3,0,0,0,0,0,0,a,0
0,4,0,0,0,0,0,0,a,1
0,5,0,0,0,0,0,0,a,2
0,3,1,0,0,0,0,0,a,0
0,4,1,0,0,0,0,0,a,0
0,5,1,0,0,0,0,0,a,1
0,3,2,0,0,0,0,0,a,0
0,3,b,0,0,0,0,0,a,0
0,4,2,0,0,0,0,0,a,2
0,4,b,0,0,0,0,0,a,1
0,5,2,0,0,0,0,0,a,2
0,5,b,0,0,0,0,0,a,2

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

00,20,01,02,11,12,10,21,11 has small reflectors and overall complex behavior:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!
@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,3
0,0,a,0,0,0,0,0,4,5
0,0,a,0,0,0,0,0,5,3
0,0,a,0,0,0,0,0,b,3
0,0,b,0,0,0,0,0,a,3
0,1,a,0,0,0,0,0,3,3
0,1,a,0,0,0,0,0,4,4
0,1,a,0,0,0,0,0,5,4
0,1,a,0,0,0,0,0,b,3
0,2,a,0,0,0,0,0,3,4
0,2,a,0,0,0,0,0,4,5
0,2,a,0,0,0,0,0,5,4
0,2,a,0,0,0,0,0,b,4
0,3,0,0,0,0,0,0,a,0
0,4,0,0,0,0,0,0,a,0
0,5,0,0,0,0,0,0,a,1
0,3,1,0,0,0,0,0,a,2
0,4,1,0,0,0,0,0,a,1
0,5,1,0,0,0,0,0,a,2
0,3,2,0,0,0,0,0,a,0
0,3,b,0,0,0,0,0,a,0
0,4,2,0,0,0,0,0,a,1
0,4,b,0,0,0,0,0,a,0
0,5,2,0,0,0,0,0,a,1
0,5,b,0,0,0,0,0,a,1

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

Even though nothing changes every generation except same-color blocks in 11,01,02,10,22,12,20,21,00, it still has complex behavior:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!
@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,4
0,0,a,0,0,0,0,0,4,3
0,0,a,0,0,0,0,0,5,3
0,0,a,0,0,0,0,0,b,4
0,0,b,0,0,0,0,0,a,4
0,1,a,0,0,0,0,0,3,4
0,1,a,0,0,0,0,0,4,5
0,1,a,0,0,0,0,0,5,4
0,1,a,0,0,0,0,0,b,4
0,2,a,0,0,0,0,0,3,5
0,2,a,0,0,0,0,0,4,5
0,2,a,0,0,0,0,0,5,3
0,2,a,0,0,0,0,0,b,5
0,3,0,0,0,0,0,0,a,1
0,4,0,0,0,0,0,0,a,1
0,5,0,0,0,0,0,0,a,2
0,3,1,0,0,0,0,0,a,0
0,4,1,0,0,0,0,0,a,2
0,5,1,0,0,0,0,0,a,2
0,3,2,0,0,0,0,0,a,0
0,3,b,0,0,0,0,0,a,1
0,4,2,0,0,0,0,0,a,1
0,4,b,0,0,0,0,0,a,1
0,5,2,0,0,0,0,0,a,0
0,5,b,0,0,0,0,0,a,2

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

00,12,10,21,02,12,01,21,00 may look explosive at first, but it's still class 4:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!
@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,3
0,0,a,0,0,0,0,0,4,4
0,0,a,0,0,0,0,0,5,4
0,0,a,0,0,0,0,0,b,3
0,0,b,0,0,0,0,0,a,3
0,1,a,0,0,0,0,0,3,5
0,1,a,0,0,0,0,0,4,3
0,1,a,0,0,0,0,0,5,4
0,1,a,0,0,0,0,0,b,5
0,2,a,0,0,0,0,0,3,3
0,2,a,0,0,0,0,0,4,5
0,2,a,0,0,0,0,0,5,3
0,2,a,0,0,0,0,0,b,3
0,3,0,0,0,0,0,0,a,0
0,4,0,0,0,0,0,0,a,2
0,5,0,0,0,0,0,0,a,0
0,3,1,0,0,0,0,0,a,1
0,4,1,0,0,0,0,0,a,2
0,5,1,0,0,0,0,0,a,2
0,3,2,0,0,0,0,0,a,1
0,3,b,0,0,0,0,0,a,0
0,4,2,0,0,0,0,0,a,1
0,4,b,0,0,0,0,0,a,2
0,5,2,0,0,0,0,0,a,0
0,5,b,0,0,0,0,0,a,0

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

00,10,02,01,22,12,20,21,11 is population-conserving, but the behavior seems to be more complex than the aforementioned rules:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!
@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,3
0,0,a,0,0,0,0,0,4,4
0,0,a,0,0,0,0,0,5,3
0,0,a,0,0,0,0,0,b,3
0,0,b,0,0,0,0,0,a,3
0,1,a,0,0,0,0,0,3,3
0,1,a,0,0,0,0,0,4,5
0,1,a,0,0,0,0,0,5,4
0,1,a,0,0,0,0,0,b,3
0,2,a,0,0,0,0,0,3,5
0,2,a,0,0,0,0,0,4,5
0,2,a,0,0,0,0,0,5,4
0,2,a,0,0,0,0,0,b,5
0,3,0,0,0,0,0,0,a,0
0,4,0,0,0,0,0,0,a,0
0,5,0,0,0,0,0,0,a,2
0,3,1,0,0,0,0,0,a,1
0,4,1,0,0,0,0,0,a,2
0,5,1,0,0,0,0,0,a,2
0,3,2,0,0,0,0,0,a,0
0,3,b,0,0,0,0,0,a,0
0,4,2,0,0,0,0,0,a,1
0,4,b,0,0,0,0,0,a,0
0,5,2,0,0,0,0,0,a,1
0,5,b,0,0,0,0,0,a,2

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

00,11,12,10,12,21,22,21,02 is one of the sideways triangles rules, and not explosive:

Code: Select all

x = 513, y = 1, rule = 1dmargtest
BDBC.EADADBEBDBDACBEAEBC.EAC.DACBDADAEBDADBEACBEADADBEAEACADAEADAEAD.
DBEBDBDAEBDBDBCBEAEBEBCACBCACACACBE.E.DBEACBDBEACBE.EACBCBCAEACAEBCBC
BDACAE.EBCBDADACBCACADAEBEBCBDAEBC.EBDADBEBEBEBEAC.CBEBDADBEACADBEAC.
DBEBCBEACACADBCACBDACBEACAEAEAEACACBCBDAD.EAEAEAEAEACAEACBD.EACBEBCBC
BE.EBDAEACBDBDBEBDBDBEAEAEBEBCADACBCADBEACAC.CACACBCBDACBDAEBDBCBDBEB
DAEBE.CBCBDBC.D.DAEADADBCBEBCBDAEBDBEBDBCBEACBCADBC.DBDAEBDACAEACADBE
AEADBCBCADAEBCBCBCADBDADBDBDBCBCAEBCBEBCBD.DAEADBEBEADBEADADAE.EBCBEA
EBDBDACBEAE.E.EBD.EADBEBEBCAD!
@RULE 1dmargtest

@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5}
var b = {1,2,3,4,5}

0,0,a,0,0,0,0,0,3,3
0,0,a,0,0,0,0,0,4,4
0,0,a,0,0,0,0,0,5,4
0,0,a,0,0,0,0,0,b,3
0,0,b,0,0,0,0,0,a,3
0,1,a,0,0,0,0,0,3,4
0,1,a,0,0,0,0,0,4,4
0,1,a,0,0,0,0,0,5,5
0,1,a,0,0,0,0,0,b,4
0,2,a,0,0,0,0,0,3,5
0,2,a,0,0,0,0,0,4,5
0,2,a,0,0,0,0,0,5,3
0,2,a,0,0,0,0,0,b,5
0,3,0,0,0,0,0,0,a,0
0,4,0,0,0,0,0,0,a,1
0,5,0,0,0,0,0,0,a,2
0,3,1,0,0,0,0,0,a,0
0,4,1,0,0,0,0,0,a,2
0,5,1,0,0,0,0,0,a,1
0,3,2,0,0,0,0,0,a,2
0,3,b,0,0,0,0,0,a,0
0,4,2,0,0,0,0,0,a,1
0,4,b,0,0,0,0,0,a,1
0,5,2,0,0,0,0,0,a,2
0,5,b,0,0,0,0,0,a,2

@COLORS
0 62 62 62
1 220 220 220
2 0 220 0
3 90 90 90
4 255 255 255
5 0 255 0
#C [[ ZOOM 1 ]]

Also, I propose we dedicate this thread to 1D Margolus rules in general, rather than the one that it was originally suppose to be about. And that we change the thread's name to "1D Margolus rules".

I totally agree. If you look at my last post in here (and this post), you'll see that it says "Re: 1D margolus rules".

[unname4798]

Code: Select all

#R 2PCA3_01254637:T100,0
2E98A!
@RULE 2PCA3_01254637
@TABLE
n_states:8
neighborhood:Moore
symmetries:none
var a0={0,1,4,5}
var a1={2,3,6,7}
var b0={0,1,2,3}
var b1={4,5,6,7}
var c0={0,2,4,6}
var c1={1,3,5,7}
0,a0,b0,0,0,0,0,0,c0,0
0,a0,b0,0,0,0,0,0,c1,1
0,a1,b0,0,0,0,0,0,c0,2
0,a1,b0,0,0,0,0,0,c1,5
0,a0,b1,0,0,0,0,0,c0,4
0,a0,b1,0,0,0,0,0,c1,6
0,a1,b1,0,0,0,0,0,c0,3
0,a1,b1,0,0,0,0,0,c1,7
@COLORS
0 000 000 000
1 255 000 000
2 000 255 000
3 255 255 000
4 000 000 255
5 255 000 255
6 000 255 255
7 255 255 255
@NAMES
0 empty
1 L
2 C
3 LC
4 R
5 LR
6 CR
7 LCR

1D PCA. (2PCA3,01254637 in this case)
2PCA3 = 2-state, 3-neighbor PCA.
There are 40320 reversible rules and 16777216 total.

...

Also, I propose we dedicate this thread to 1D Margolus rules in general, rather than the one that it was originally suppose to be about. And that we change the thread's name to "1D Margolus rules".

I totally agree. If you look at my last post in here (and this post), you'll see that it says "Re: 1D margolus rules".

The original thread title also includes PCA.

Edit: 3PCA3:

Code: Select all

#R 3PCA3
!
@RULE 3PCA3
@TABLE
n_states:27
neighborhood:Moore
symmetries:none
var a0={0,1,2,9,10,11,18,19,20}
var a1={3,4,5,12,13,14,21,22,23}
var a2={6,7,8,15,16,17,24,25,26}
var b0={0,1,2,3,4,5,6,7,8}
var b1={9,10,11,12,13,14,15,16,17}
var b2={18,19,20,21,22,23,24,25,26}
var c0={0,3,6,9,12,15,18,21,24}
var c1={1,4,7,10,13,16,19,22,25}
var c2={2,5,8,11,14,17,20,23,26}
0,a0,b0,0,0,0,0,0,c0,0
0,a0,b0,0,0,0,0,0,c1,25
0,a0,b0,0,0,0,0,0,c2,2
0,a1,b0,0,0,0,0,0,c0,23
0,a1,b0,0,0,0,0,0,c1,22
0,a1,b0,0,0,0,0,0,c2,21
0,a2,b0,0,0,0,0,0,c0,6
0,a2,b0,0,0,0,0,0,c1,19
0,a2,b0,0,0,0,0,0,c2,8
0,a0,b1,0,0,0,0,0,c0,17
0,a0,b1,0,0,0,0,0,c1,16
0,a0,b1,0,0,0,0,0,c2,15
0,a1,b1,0,0,0,0,0,c0,14
0,a1,b1,0,0,0,0,0,c1,13
0,a1,b1,0,0,0,0,0,c2,12
0,a2,b1,0,0,0,0,0,c0,11
0,a2,b1,0,0,0,0,0,c1,10
0,a2,b1,0,0,0,0,0,c2,9
0,a0,b2,0,0,0,0,0,c0,18
0,a0,b2,0,0,0,0,0,c1,7
0,a0,b2,0,0,0,0,0,c2,20
0,a1,b2,0,0,0,0,0,c0,5
0,a1,b2,0,0,0,0,0,c1,4
0,a1,b2,0,0,0,0,0,c2,3
0,a2,b2,0,0,0,0,0,c0,24
0,a2,b2,0,0,0,0,0,c1,1
0,a2,b2,0,0,0,0,0,c2,26
@COLORS
0  000 000 000
1  128 000 000
2  255 000 000
3  000 128 000
4  128 128 000
5  255 128 000
6  000 255 000
7  128 255 000
8  255 255 000
9  000 000 128
10 128 000 128
11 255 000 128
12 000 128 128
13 128 128 128
14 255 128 128
15 000 255 128
16 128 255 128
17 255 255 128
18 000 000 255
19 128 000 255
20 255 000 255
21 000 128 255
22 128 128 255
23 255 128 255
24 000 255 255
25 128 255 255
26 255 255 255
@NAMES
0 000
1 100
2 200
3 010
4 110
5 210
6 020
7 120
8 220
9 001
10 101
11 201
12 011
13 111
14 211
15 021
16 121
17 221
18 002
19 102
20 102
21 012
22 112
23 212
24 022
25 122
26 222

1e28 reversible and 4e38 total.