The floor in my bathroom is tiled, unlike that of the kitchen (old plastic carpeting) and the living room and bed room (brown wall-to-wall carpeting). The tiles are perhaps an inch squared, and come in four colours: light grey, medium grey, light yellow, and medium brown. There are no repeatable sequences anywhere, and I thus assume that they have been placed randomly. Here are some interesting statistics (colours in parenthesis):
Largest rectangular one-colour area:
6×2 = 12 tiles (medium brown), located near wash basin.
Largest quadratic one-colour area:
3×3 = 9 tiles (light grey), located near bathtub.
Largest one-colour area entirely enclosed by tiles of another colour, including diagonally:
One (light grey), near the door, entirely enclosed by medium brown tiles.
Largest multiple-colour area entirely enclosed by tiles of another colour, including diagonally:
Same as previous.
Largest one-colour area entirely enclosed by tiles of another colour, excluding diagonally:
Three (light grey), enclosed by yellow on all sides but only on one diagonal. The other diagonals are either medium brown (2) or light grey (1).
Longest one colour row:
6 (medium brown), same as largest rectangular area above.
Longest diagonal one-colour row without reusing the same tile twice:
13 (light yellow), near toilet seat.
One-colour digital numbers that are written using the following parametres: the long side has to be exactly five tiles; the short side has to be exactly three tiles:
1 (several times), 7 (medium brown, near toilet seat), 9 (medium brown, near door).
Please write in about your experiences with symmetry or patterns arising from random placement of tiles.