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Sebastien Palcoux
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A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets: 
$$ \substack{ \displaystyle{◻◻◻◻} \cr \displaystyle{◻◼◻◻} \cr \displaystyle{◻◼◼◻} \cr \displaystyle{◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◼◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◼◼◻◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◼◻◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◻◻◻◻} } $$

Aenter image description here
A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻} } \quad \quad \quad \quad \quad \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻} } $$

enter image description here
Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} }$$enter image description here

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets: $$ \substack{ \displaystyle{◻◻◻◻} \cr \displaystyle{◻◼◻◻} \cr \displaystyle{◻◼◼◻} \cr \displaystyle{◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◼◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◼◼◻◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◼◻◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◻◻◻◻} } $$

A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻} } \quad \quad \quad \quad \quad \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻} } $$

Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} }$$

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets: 
enter image description here
A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
enter image description here
Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
enter image description here

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

Nicer CA grid formatting
Source Link
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets:
  enter image description here$$ \substack{ \displaystyle{◻◻◻◻} \cr \displaystyle{◻◼◻◻} \cr \displaystyle{◻◼◼◻} \cr \displaystyle{◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◼◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◼◼◻◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◼◻◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◻◻◻◻} } $$

A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
enter image description here$$ \substack{ \displaystyle{◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻} } \quad \quad \quad \quad \quad \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻} } $$

Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
enter image description here$$ \substack{ \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} }$$

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets:
  enter image description here

A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
enter image description here

Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
enter image description here

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets: $$ \substack{ \displaystyle{◻◻◻◻} \cr \displaystyle{◻◼◻◻} \cr \displaystyle{◻◼◼◻} \cr \displaystyle{◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◼◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◼◼◻◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◼◻◼◻} \cr \displaystyle{◻◻◻◻◻} } \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻} \cr \displaystyle{◻◼◻◻◻} \cr \displaystyle{◻◻◼◻◻} \cr \displaystyle{◻◻◻◼◻} \cr \displaystyle{◻◻◻◻◻} } $$

A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻} } \quad \quad \quad \quad \quad \quad \quad \quad \substack{ \displaystyle{◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◼◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻} } $$

Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
$$ \substack{ \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻◻◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻} \cr \displaystyle{◻◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◼◻◻◻◻} \cr \displaystyle{◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻◻} }$$

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

Source Link
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186

The 1-step vanishing polyplets on Conway's game of life

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets:
enter image description here

A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
enter image description here

Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
enter image description here

Bonus question: Are there $1$-step vanishing polyplets of an other kind?