Storing and comparing grid patterns

I have a 2 dimensional array that stores pattern information. The data may look something like this:

var testGrid = [["blank", "red", "blank"],
/* row 2 */ ["blank", "yellow", "green"],
/* row 3 */ ["blank", "blue", "blank"]];

The max pattern size is a 3 by 3 grid, however, not all spaces have to be used. Since blanks basically mean that there is no information there, I regularly encounter scenarios where two patterns are structured differently, but are functionally the same. Like this:

[["red", "red" "blank"],
["red", "red", "blank"], 
["blank", "blank", "blank"]

[["blank", "blank", "blank"],
["blank", "red", "red"],
["blank", "red", "red"]]

All patterns would have 4 possible representations due to orientation. However, some patterns like this one below:

[["blank", "blank", "blank"],
["blank", "yellow", "green"],
["blank", "blue", "blank"]]

would have 8 possible representations in a 3 by 3 grid.

So I have a few questions:

1. What would be the best way to store this data? I was thinking I could store the more simple patterns as a 2 by 2 grid, which would reduce the amount of checks I would have to do on those to the normal 4.

2. What is the best way to check against patterns already in the database? Just loop through a function that compares the newly created pattern to every other entry in the database? (I'm using a mongoDB by the way).