[Community Puzzle] circular automation, the period of chaos

Puzzles
#1

Coding Games and Programming Challenges to Code Better

Send your feedback or ask for help here!

Created by @igolus,validated by @pluieciel,@Didelabedeli and @TeddyS.
If you have any issues, feel free to ping them.

#2

Why I can’t validate rule 110 ?
The rule table I got seems good but I got repeat block directly on 1364 line and pattern is a 28 block but result says 2730. Is there something special with 110 rule ?

#3

Could you list out the first 50 patterns so that we may take a look and see where things might have gone wrong?

#4

May somebody explain me the goal of that game. I can’t get the purpose and figure out the kind of output needed.

#5

First, you have to understand what “Elementary Cellular Automaton” is. You may read the links in the statement, or search the term on YouTube for a relevant video to get a better idea.

The required task here is to determine the length of the cycle with the input parameters, i.e. at which step you’ll see one of the previously seen states again.

#6

Correct me if i’m wrong:

  • It’s all about the development of an array of cells from a state to a final one led by the rule number building a tree from array 1. It’s nothing about deciphering any message or random code.

  • We get to know for each rule-number the fastest it gets to its original state by its own and output the length of the corresponding development.

I assume the development of the array given by the rule numb is not random and results as a repetition in a kind of way, therefore it can converge to the initial array.

Thx

#7

Correct.

Not necessarily the original state. In the “rule 254” example shown in the statement, the cycle consists of one state only (11111), which is not the initial state. However, in the “rule 1” example, the cycle does include the initial state.

As mentioned above, the cycle may not necessarily start from the initial state. Also, for this puzzle, you’re required to check up to the given maximum number of iterations only, while the cycle length may or may not exceed that.

#8

This is my first 50 patterns :

.............................................1.............................................
............................................11.............................................
...........................................111.............................................
..........................................11.1.............................................
.........................................11111.............................................
........................................11...1.............................................
.......................................111..11.............................................
......................................11.1.111.............................................
.....................................1111111.1.............................................
....................................11.....111.............................................
...................................111....11.1.............................................
..................................11.1...11111.............................................
.................................11111..11...1.............................................
................................11...1.111..11.............................................
...............................111..1111.1.111.............................................
..............................11.1.11..11111.1.............................................
.............................11111111.11...111.............................................
............................11......1111..11.1.............................................
...........................111.....11..1.11111.............................................
..........................11.1....111.1111...1.............................................
.........................11111...11.111..1..11.............................................
........................11...1..11111.1.11.111.............................................
.......................111..11.11...11111111.1.............................................
......................11.1.111111..11......111.............................................
.....................1111111....1.111.....11.1.............................................
....................11.....1...1111.1....11111.............................................
...................111....11..11..111...11...1.............................................
..................11.1...111.111.11.1..111..11.............................................
.................11111..11.111.111111.11.1.111.............................................
................11...1.11111.111....11111111.1.............................................
...............111..1111...111.1...11......111.............................................
..............11.1.11..1..11.111..111.....11.1.............................................
.............11111111.11.11111.1.11.1....11111.............................................
............11......111111...11111111...11...1.............................................
...........111.....11....1..11......1..111..11.............................................
..........11.1....111...11.111.....11.11.1.111.............................................
.........11111...11.1..11111.1....1111111111.1.............................................
........11...1..11111.11...111...11........111.............................................
.......111..11.11...1111..11.1..111.......11.1.............................................
......11.1.111111..11..1.11111.11.1......11111.............................................
.....1111111....1.111.1111...111111.....11...1.............................................
....11.....1...1111.111..1..11....1....111..11.............................................
...111....11..11..111.1.11.111...11...11.1.111.............................................
..11.1...111.111.11.11111111.1..111..1111111.1.............................................
.11111..11.111.111111......111.11.1.11.....111.............................................
11...1.11111.111....1.....11.111111111....11.1.............................................
.1..1111...111.1...11....11111.......1...11111............................................1
11.11..1..11.111..111...11...1......11..11...1...........................................11
.1111.11.11111.1.11.1..111..11.....111.111..11..........................................11.
#9

The last three lines are different from mine:

(This line is the same)
11...1.11111.111....1.....11.111111111....11.1.............................................

(These three are different)
11..1111...111.1...11....11111.......1...11111............................................1
.1.11..1..11.111..111...11...1......11..11...1...........................................11
11111.11.11111.1.11.1..111..11.....111.111..11..........................................111
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