dominoEs
The Domino
The word Domino usually pops in two contexts. First off, there are many games which use Domino pieces, which contain two sets of dots. Second we often here the term "Domino effect". This refers simply to any type of chain reaction in which a sequence of events inevitably occurs, much like a row of dominoes falling in succession.
But what exactly is a Domino? A Domino is simply a 2nd order Polyomino, that is, it is merely 2 squares joined at a common side. The word Domino is formed by combining Du- with -mino ( we change the vowels to make the sounds "fit" better).
Basically what we get is a rectangle where one of the sides is twice the length of the other. A moments thought makes it quite clear that their can be only ONE kind of Domino. We can simply call this the "Domino" or simply the "Doon" for short.
( We can get the word Doon from Domino by removing "mi" and switching the "n" with the "o" on the right. The word is part of my Polyomino petnames)
The Doon, Just like the Nod, is it's own reflection. Unlike the Nod however the Doon is not completely identical under rotation. Basically the Doon has 2 disguishable orientations. Normally we can think of a doon has being vertical, but when tilted at 90 or 270 degrees it becomes horizontal.
Below is a Picture of the Doon in both it's vertical and horizontal orientation.
Norm,180 90,270
Domino No. 1: The Doon
A Doon has XY-symmetry, but it lacks any slant symmetries.
THE GAME OF DOMIS
The game of "Domis" plays much like Monis. We can use a 5x10 board this time. Although Domis allows for more variety of moves than Monis, it is virtually no more difficult for a human than Monis is. A simple periodic solution would be to stack a row of 5 vertical doons at a time ( getting 2 rows every time ! ) . It is also possible to have 1 vertical doon, and stack a 2x2 set of horizontal Doons to once again create a double row.
Assuming a 5x10 board there are EXACTLY 9 distinct moves one could make on any given turn(Not including "slide-ins"). Admittedly a machine programmed to excute random moves in Domis would have a higher probability of losing than a random move machine playing Monis. The Horizontal Doons seem to pose greater risk to unwanted stacking than do the verticals. In any case this game is still far to simple to even entertain a human child for long.
Poly(2)
Well once again we return to the Poly(n) function. Poly(2) is the number of distinct dominoes. Of coarse we know that Poly(2) = 1 because the Doon is the only Domino. So far we have not been confronted with much variety at all. The Poly function also seems to be stable at the moment. What happens if we move to 3rd order Polyominoes ?
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