Logarithmically-growing counting patterns

For discussion of other cellular automata.
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muzik
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Joined: January 28th, 2016, 2:47 pm
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Logarithmically-growing counting patterns

Post by muzik » May 5th, 2021, 2:39 am

An offshoot of the original "counting patterns" thread from an hour ago, this one specifically focuses on patterns that as a whole grow logarithmically as they count, as opposed to for example counting from an infinitely puffed stream of objects from a separate pattern.

Examples:

Base 1
toroidalet wrote:
September 5th, 2017, 10:50 am
What would this be called?

Code: Select all

x = 13, y = 5, rule = B3-y4q5a/S23-e
5bo4b2o$5bobobo2bo$b2o2b2o3b2o$o2bo$b2o!
Would it be called some arcane term like "Empty space unary counting shuttle™" or is there a simpler term for it?

Code: Select all

x = 34, y = 12, rule = Snowflakes
9b2o$obo6bo4bobo$9b2o!
Base 2
toroidalet wrote:
November 3rd, 2017, 11:06 am
p22 fourfold binary counter with a 2-cell predecessor:

Code: Select all

x = 41, y = 3, rule = B2ci3aer4eiqrz5i6cik8/S01c2cn3ek4nqtw5aekry6ekn78
39bo$obo35bobo$39bo!
Variant:

Code: Select all

x = 41, y = 3, rule = B2ci3aer4eiqr5i6cik8/S01c2cn3ek4nqtw5aekry6ekn78
39bo$obo35bobo$39bo!
toroidalet wrote:
October 13th, 2019, 8:56 pm
Here's a mediocre rule with a p330 binary counter:

Code: Select all

x = 3, y = 4, rule = B2-ak3ai4n5/S2i3-i4-q5iq8
obo3$obo!
Naszvadi wrote:
October 2nd, 2020, 6:56 am
Binary counter stream generator - coolest "sawtooth-rake" ever?

Code: Select all

x = 8, y = 24, rule = B3-ck4jqz5c/S2aek3ijnqr4ciy5ce6e7c
3b2o$4bo$2b3o16$b2o2bo$o3bob2o$bo5bo$3bo3bo$4b3o$4bo!
AforAmpere wrote:
April 27th, 2021, 7:01 pm
Binary and ternary counters, from 2 cells:

Code: Select all

x = 3, y = 1, rule = B2aei3e4ijkqrtz5cekn6ai8/S01e2en3-acei4-nq5-anry6a7e8
obo!
AforAmpere wrote:
April 28th, 2021, 12:21 pm
Crazy looking binary counter:

Code: Select all

x = 3, y = 1, rule = B2aei3ekn4eijqr5cy6ci/S01e2ek3-einq4acijnrt5eir6e7e8
obo!

Code: Select all

x = 3, y = 1, rule = B2-ck3ce4inrty5ejkqy6ai/S01e2kn3acry4-ntyz5-ck6ac7e8
obo!

Code: Select all

x = 16, y = 16, rule = B2e3aeijk4cejwz5cjkqr6an7c/S1c2-c3-aen4-eqr5aknr6ack7c8
o2bobob2obobo2bo$b4o3bo2bob2o$5b4ob3obo$b3o2b6obobo$b2obob3o2b2obo$b3o
b4o3bo2bo$2bo4b2o$bobob2o2b3obo$o3bo2b2o3b2o$2bo2bo2bobo2b3o$o4b7o2bo$
ob4ob2o2bo3bo$b2ob3o2bob3o$6bo2bobob3o$2bobob3o2b3obo$2bob2obo3b3obo!
Base 3
AforAmpere wrote:
April 27th, 2021, 7:01 pm
Binary and ternary counters, from 2 cells:

Code: Select all

x = 3, y = 1, rule = B2aei3cek4-acenz5-ikqr6-n8/S01e2e3cjqry4-cn5-kry6ae7e8
obo!
Base 4
AforAmpere wrote:
April 28th, 2021, 12:21 pm
Appears to count in base 4

Code: Select all

x = 3, y = 59, rule = B2aei3ekn4eijnqr5jny6aci8/S01e2ekn3cjnry4-aeqw5-aqy6ac7e8
obo!

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