Rule with 'Memories'

[islptng]

This kind of rule has a feature: Cells can have memories.


M=1 is simply 2D Moore; M=2 means a cell can remember its previous generation; etc.
(We treat evolutionary sequences of 2D CA as 3D structures, just as how we treated 1D as 2D)
Then, when M=3, a cell and its neighborhood is:

Code: Select all

3D version=1 size=100 pos=36,51,49
x=3 y=4 z=3 rule=3D5..7/6
$3o$3o$3o/bo$3o$3o$3o/$3o$3o$3o!

Use this script for make_ruletree.py:

Code: Select all

birth = [5,9]
survival = [3,4,5,8]
memory = 2

name = "B"
for i in birth: name += str(i) + ","
name += "S"
for i in survival: name += str(i) + ","
name += "M" + str(memory)
n_states = 2 ** memory
n_neighbors = 8
def tobinary(n):
	res = []
	while n != 0:
		res.append(n % 2)
		n = n // 2
	while len(res) < memory:
		res.append(0)
	return res
def append(n, new):
	binlist = [new] + tobinary(n)[:-1]
	res = 0
	while len(binlist) != 0:
		res *= 2
		res += binlist.pop()
	return res
def onbitinbin(n):
	binlist = tobinary(n)
	cnt = 0
	for i in binlist: cnt += i
	return cnt
def transition_function(a):
	n = 0
	for i in a[:-1]:
		n += onbitinbin(i)
	if n in survival and a[8] % 2 == 1:
		return append(a[8], 1)
	if n in birth and a[8] % 2 == 0:
		return append(a[8], 1)
	return append(a[8], 0)

The rule in the script is B5,9/S3,4,5,8/M2, you can change it.

B5,9/S3,4,5,8/M2
This rule has a small P30:

Code: Select all

x = 4, y = 3, rule = B5,9,S3,4,5,8,M2
.2C$CB.C$.2C!

@RULE B5,9,S3,4,5,8,M2

@TREE

num_states=4
num_neighbors=8
num_nodes=60
1 0 2 0 2
2 0 0 0 0
1 0 3 0 3
2 0 0 0 2
2 0 2 2 2
3 1 3 3 4
1 1 3 1 3
2 2 2 2 6
3 3 4 4 7
2 2 6 6 0
3 4 7 7 9
4 5 8 8 10
2 6 0 0 0
3 7 9 9 12
4 8 10 10 13
3 9 12 12 3
4 10 13 13 15
5 11 14 14 16
1 1 2 1 2
2 0 2 2 18
3 12 3 3 19
4 13 15 15 20
5 14 16 16 21
2 2 18 18 0
3 3 19 19 23
4 15 20 20 24
5 16 21 21 25
6 17 22 22 26
2 18 0 0 0
3 19 23 23 28
4 20 24 24 29
5 21 25 25 30
6 22 26 26 31
3 23 28 28 1
4 24 29 29 33
5 25 30 30 34
6 26 31 31 35
7 27 32 32 36
3 28 1 1 1
4 29 33 33 38
5 30 34 34 39
6 31 35 35 40
7 32 36 36 41
3 1 1 1 1
4 33 38 38 43
5 34 39 39 44
6 35 40 40 45
7 36 41 41 46
8 37 42 42 47
4 38 43 43 43
5 39 44 44 49
6 40 45 45 50
7 41 46 46 51
8 42 47 47 52
4 43 43 43 43
5 44 49 49 54
6 45 50 50 55
7 46 51 51 56
8 47 52 52 57
9 48 53 53 58

and a diagonal spaceship(sorry, I didn't save it).

[LuveelVoom]

B5,9/S3,4,5,8/M2
This rule has a small P30:

Code: Select all

x = 4, y = 3, rule = B5,9,S3,4,5,8,M2
.2C$CB.C$.2C!

and a diagonal spaceship(sorry, I didn't save it).

You should probably include the ruletable in the pattern so it can be run.

[pifricted]

P224:

Code: Select all

x = 5, y = 5, rule = B4,10,S4,5,M2
3.B$B2.BA$4.A$.C.A$.ABA!

2c/4o:

Code: Select all

x = 4, y = 3, rule = B4,10,S4,5,7,M2
C2BC$.2C$.2A!

[islptng]

P224:

Code: Select all

x = 5, y = 5, rule = B4,10,S4,5,M2
3.B$B2.BA$4.A$.C.A$.ABA!

@RULE B4,10,S4,5,M2

@TREE

num_states=4
num_neighbors=8
num_nodes=60
1 0 2 0 2
2 0 0 0 0
1 1 3 1 3
2 0 0 0 2
3 1 1 1 3
1 0 3 0 3
2 0 2 2 5
3 1 3 3 6
2 2 5 5 0
3 3 6 6 8
4 4 7 7 9
2 5 0 0 0
3 6 8 8 11
4 7 9 9 12
3 8 11 11 1
4 9 12 12 14
5 10 13 13 15
3 11 1 1 1
4 12 14 14 17
5 13 15 15 18
1 1 2 1 2
2 0 0 0 20
3 1 1 1 21
4 14 17 17 22
5 15 18 18 23
6 16 19 19 24
2 0 20 20 0
3 1 21 21 26
4 17 22 22 27
5 18 23 23 28
6 19 24 24 29
2 20 0 0 0
3 21 26 26 31
4 22 27 27 32
5 23 28 28 33
6 24 29 29 34
7 25 30 30 35
3 26 31 31 1
4 27 32 32 37
5 28 33 33 38
6 29 34 34 39
7 30 35 35 40
3 31 1 1 1
4 32 37 37 42
5 33 38 38 43
6 34 39 39 44
7 35 40 40 45
8 36 41 41 46
3 1 1 1 1
4 37 42 42 48
5 38 43 43 49
6 39 44 44 50
7 40 45 45 51
8 41 46 46 52
4 42 48 48 48
5 43 49 49 54
6 44 50 50 55
7 45 51 51 56
8 46 52 52 57
9 47 53 53 58

Correct period is P244, not P224.
also a small c/3d:

Code: Select all

x = 4, y = 4, rule = B4,10,S4,5,M2
AC$C2B$.B.A$2.B!

@RULE B4,10,S4,5,M2

@TREE

num_states=4
num_neighbors=8
num_nodes=60
1 0 2 0 2
2 0 0 0 0
1 1 3 1 3
2 0 0 0 2
3 1 1 1 3
1 0 3 0 3
2 0 2 2 5
3 1 3 3 6
2 2 5 5 0
3 3 6 6 8
4 4 7 7 9
2 5 0 0 0
3 6 8 8 11
4 7 9 9 12
3 8 11 11 1
4 9 12 12 14
5 10 13 13 15
3 11 1 1 1
4 12 14 14 17
5 13 15 15 18
1 1 2 1 2
2 0 0 0 20
3 1 1 1 21
4 14 17 17 22
5 15 18 18 23
6 16 19 19 24
2 0 20 20 0
3 1 21 21 26
4 17 22 22 27
5 18 23 23 28
6 19 24 24 29
2 20 0 0 0
3 21 26 26 31
4 22 27 27 32
5 23 28 28 33
6 24 29 29 34
7 25 30 30 35
3 26 31 31 1
4 27 32 32 37
5 28 33 33 38
6 29 34 34 39
7 30 35 35 40
3 31 1 1 1
4 32 37 37 42
5 33 38 38 43
6 34 39 39 44
7 35 40 40 45
8 36 41 41 46
3 1 1 1 1
4 37 42 42 48
5 38 43 43 49
6 39 44 44 50
7 40 45 45 51
8 41 46 46 52
4 42 48 48 48
5 43 49 49 54
6 44 50 50 55
7 45 51 51 56
8 46 52 52 57
9 47 53 53 58

Most of the soup settles into this p244 and this c/3d, so far no more objects found.

[vilc]

[...]
Most of the soup settles into this p244 and this c/3d, so far no more objects found.

There are some naturally occuring p3 oscillators (on the left), one of which can be phase shifted and infinitely extended (on the right) :

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x = 55, y = 6, rule = B4,10,S4,5,M2
ABA6.2A7.B$.C7.2B7.AC24.C7.ABA$.C6.A2.A8.CA22.C8.C$.C7.2B9.B23.C8.C$
9.2A33.C8.C$44.C8.C!
@RULE B4,10,S4,5,M2

@TREE

num_states=4
num_neighbors=8
num_nodes=60
1 0 2 0 2
2 0 0 0 0
1 1 3 1 3
2 0 0 0 2
3 1 1 1 3
1 0 3 0 3
2 0 2 2 5
3 1 3 3 6
2 2 5 5 0
3 3 6 6 8
4 4 7 7 9
2 5 0 0 0
3 6 8 8 11
4 7 9 9 12
3 8 11 11 1
4 9 12 12 14
5 10 13 13 15
3 11 1 1 1
4 12 14 14 17
5 13 15 15 18
1 1 2 1 2
2 0 0 0 20
3 1 1 1 21
4 14 17 17 22
5 15 18 18 23
6 16 19 19 24
2 0 20 20 0
3 1 21 21 26
4 17 22 22 27
5 18 23 23 28
6 19 24 24 29
2 20 0 0 0
3 21 26 26 31
4 22 27 27 32
5 23 28 28 33
6 24 29 29 34
7 25 30 30 35
3 26 31 31 1
4 27 32 32 37
5 28 33 33 38
6 29 34 34 39
7 30 35 35 40
3 31 1 1 1
4 32 37 37 42
5 33 38 38 43
6 34 39 39 44
7 35 40 40 45
8 36 41 41 46
3 1 1 1 1
4 37 42 42 48
5 38 43 43 49
6 39 44 44 50
7 40 45 45 51
8 41 46 46 52
4 42 48 48 48
5 43 49 49 54
6 44 50 50 55
7 45 51 51 56
8 46 52 52 57
9 47 53 53 58

They occur with a (very) approximate frequency of 1 per megacell in large soups.

[eRroR_6o6]

So if I'm not mistaken, this is somewhat like a second-order cellular automaton but 2D, right?

[confocaloid]

So if I'm not mistaken, this is somewhat like a second-order cellular automaton but 2D, right?

As far as I can tell it's a different idea. Here, states of neighbours in the current generation and states of neighbours in the preceding generation are all added together to give a single number; then that number and the current state of the middle cell are used to compute the state of the cell in the next generation.

Second-order cellular automata are reversible, and the state of a cell in the next generation can depend on the state of that one cell in the preceding generation and the states of cells in its neighbourhood in the current generation.

[SomePersonAlt]

Use this script for make_ruletree.py:

Code: Select all

--snip--

how exactly am i supposed to run this? its not printing anything

[islptng]

how exactly am i supposed to run this? its not printing anything

Changge the rule if you want, copy it, and click Scripts/Python/Rule-Generators/make-ruletree.py in Golly. Wait a few time and you can see the rule generated.


EDIT:

I am on android, sadly. Could you make a version that just prints to the console?

Sadly not. You need the Golly library to run it.

[SomePersonAlt]

how exactly am i supposed to run this? its not printing anything

Changge the rule if you want, copy it, and click Scripts/Python/Rule-Generators/make-ruletree.py in Golly. Wait a few time and you can see the rule generated.

I am on android, sadly. Could you make a version that just prints to the console?