#Life 1.05 #D Venetian blinds #D This is a finite version of the infinite p2 oscillator in which #D rows alternate full, full, empty, empty, full, full, ... Two types #D of edges are shown, one perpendicular to the rows and one at a 45 #D degree angle. (It's easy to prove that there's no p2 edge parallel #D to the rows.) Also shown are 3 type of corners where the edges #D meet. This partly answers a question of John Conway's: What's the #D maximum average density of an infinite p2 pattern, and can it be #D obtained as a limit of finite p2 patterns? This shows that 1/2 is #D a lower bound. Hartmut Holzwart showed that 8/13 is an upper bound. #D Dean Hickerson, dean@ucdmath.ucdavis.edu 9/13/92 #N #P -31 -36 ..................*.**.**......*......**.**.* ..................**.*.*...**.*.*.**...*.*.** .....................*...*..*.*.*.*..*...* .....................*..***...*.*...***..* ....................**.*.....*.*.*.....*.** .......................*..**.*...*.**..* ....................**..***..**.**..***..** ................**.*.**...**.*****.**...**.*.** **.**...**......**.**....*...........*....**.** .*.*...*.*.........*..**.*.*.......*.*.**..* .*..*..*........**..***..**.*******.**..***..** ..*.*.*..*..**.*.**...**.*************.**...**.*.** ...*.**.**..**.**....*...................*....**.** .....**........*..**.*.*...............*.*.**..* ....*.......**..***..**.***************.**..***..** ..***.*.**.*.**...**.*********************.**...**.*.** .*...***.*.**....*...........................*....**.** .***...*...*..**.*.*.......................*.*.**..* ....**...*..***..**.***********************.**..***..** ...*..*.***...**.*****************************.**...**.*.**..** ...*.**.*....*...................................*....**.**...*..* ....**.**.**.*.*...............................*.*.**..*......*.*.* .........**..**.*******************************.**..***..**..**.*..* ....**..*.**.*************************************.**...**.*....**.* ....*..*.*...........................................*....**.**...**.** ......**.*.*.......................................*.*.**..*.*.**...*.* ..........*.***************************************.**..***..*.*.**.* .........**.******************************************.**...****..*.* ....*.**.*.*.............................................*.......*..** ....**.*.*.............................................*.*.**....*.*..* ...........********************************************.**..*****..*.* .........*...*********************************************.***..***.* .............................................................*..*.* ........*.*.*..............................................*.*..*.*.* ....**.*...*.**********************************************.**.*...** ....*.**.*.*************************************************** ........*.* #P -31 1 ........*.* ....*.**.*.*************************************************** ....**.*...*.**********************************************.**.*...** ........*.*.*..............................................*.*..*.*.* .............................................................*..*.* .........*...*********************************************.***..***.* ...........********************************************.**..*****..*.* ....**.*.*.............................................*.*.**....*.*..* ....*.**.*.*.............................................*.......*..** .........**.******************************************.**...****..*.* ..........*.***************************************.**..***..*.*.**.* ......**.*.*.......................................*.*.**..*.*.**...*.* ....*..*.*...........................................*....**.**...**.** ....**..*.**.*************************************.**...**.*....**.* .........**..**.*******************************.**..***..**..**.*..* ....**.**.**.*.*...............................*.*.**..*......*.*.* ...*.**.*....*...................................*....**.**...*..* ...*..*.***...**.*****************************.**...**.*.**..** ....**...*..***..**.***********************.**..***..** .***...*...*..**.*.*.......................*.*.**..* .*...***.*.**....*...........................*....**.** ..***.*.**.*.**...**.*********************.**...**.*.** ....*.......**..***..**.***************.**..***..** .....**........*..**.*.*...............*.*.**..* ...*.**.**..**.**....*...................*....**.** ..*.*.*..*..**.*.**...**.*************.**...**.*.** .*..*..*........**..***..**.*******.**..***..** .*.*...*.*.........*..**.*.*.......*.*.**..* **.**...**......**.**....*...........*....**.** ................**.*.**...**.*****.**...**.*.** ....................**..***..**.**..***..** .......................*..**.*...*.**..* ....................**.*.....*.*.*.....*.** .....................*..***...*.*...***..* .....................*...*..*.*.*.*..*...* ..................**.*.*...**.*.*.**...*.*.** ..................*.**.**......*......**.**.*