The Monomino
The first order Polyominoes, or Monominoes are formed from a single unit square. It should be fairly obvious that there can only be one kind of monomino, namely, a square. We can simply call this figure the "Monomino", or we can call it the "Monad" for short, or "Nod" for really short.
(Note: The Nod is my own designation)
Below is a picture of the "Nod" ...
Monomino No.1 : Nod
The Monad is extremely simple. For one thing it is it's own reflection. Also 90,180,270 degree rotations leave it unchanged ! The Monad is the simplest Polyomino possible, and all other polyominoes are made out of combining 2 or more Monads.
The Nod possesses all 4 relevant axes of symmetry. It possesses both X & Y-symmetry and it contains both of the slant symmetries ( -45 & 45 degrees, the negative and positive slants respectively)
The Nod has only 1 "orthogonal rotation".
The Game Of MONIS
"Monis" is analogous to tetris but using only the monomino ( Nod ) as the only piece. Usually tetris is played on a board 10 units wide and 20 units high. In Monis we can use a much smaller board ( 3 wide by 5 high for example )
The Game Monis is extremely simple. In fact, even if a computer was designed to play out random moves the odds that it would lose any time soon would be slim. That's because all it would need to do to obtain a row would be place at least 1 nod in each of the 3 columns. In order to lose it would need to leave a column open long enough for the nods to pile up at least 6 units high.
A human playing such a game could potentially play forever without losing. To keep the game going simply place one nod in each of the 3 columns, and you produce a single row. Simply repeat this indefinitely.
POLY(1)
At this point I'd like to introduce the Poly(n) function. We can define it as follows ...
Poly(n) = "The maximum number of distinct nth order chiral polyominoes"
Given what we now know it should be obvious that Poly(1) = 1 because there is only 1 distinct 1st order polyomino, the Nod.
Not much more can be said for the simple Nod, except that it is fundamental. Let us now continue to higher order polyominoes starting with the Dominoes. You can return to the home page, or you can click the link to go directly to the Domino page ...