From: "Fred lunnon" <fred.lunnon@gmail.com>
I've been spending quality time with Hilbert walks (finite approximations to Hilbert curves) [...]
While I have some ideas about an appropriate general definition, it's still not very clear to me exactly what properties --- combinatorial or possibly staistical --- of such a path might be significant in applications --- such as multiple-key database, and equation solving in many variables.
Calendars! _ _ _ _ +-----------+-----------+-----------+-----------+ / \ / \ / \ / \| 12 13 14| 17 18 19| 4 5 6| 9 10 11| / | | | | \_/| +---+ + +---+ | +---+ + +---+ | / | | | | / | 11 10| 15 16| 21 20| 3 2| 7 8| 13 12| --- \_/ \_/ / +---+ +-------+ +---+---+ +-------+ +---+ | 8 9| 4 3| 22| 25 26| 1| 20 19| 14 15| | +---+ + | + + +Mar| + +---+ | | 7 6 5| 2| 23 24| 27 28| 21| 18 17 16| |Jan+---+-------+-------+---+ +-------+-------+ +-----------+ | 1 2| 15 16 17 18| 31Feb1| 17 16| 13 12| 22| 25 26 27| +---+ | +---+---+ | +---+ + + + | + +---+ | | 4 3| 14 13| 20 19| 30 29| 18| 15 14| 11| 23 24| 29 28| | +---+---+ | +---+---+ | +---+---+ +-------+ +---+ | 5| 8 9| 12| 21| 24 25| 28| 19 20| 9 10| 5 4| 30 31| | + + + | + + + +---+ | +---+ + +---+Apr| | 6 7| 10 11| 22 23| 26 27| 22 21| 8 7 6| 3 2 1| +-------+-------+-------+-------+ +---+-----------+-----------+ | 7 6| 3 2| 22 21| 18 17| 23 24| 7 8 9| 12 13 14| | + + + | + + + +---+ | +---+ + +---+ | | 8| 5 4| 1| 23| 20 19| 16| 26 25| 6 5| 10 11| 16 15| | +---+---+Aug| +---+---+ | +---+---+ +-------+ +---+ | 9 10| 30 31| 24 25| 14 15| 27| 30May1| 4| 23 22| 17 18| +---+ | +---+---+ | +---+ + + + | + +---+ | | 12 11| 29 28 27 26| 13 12| 28 29| 2 3| 24| 21 20 19| | +---+-------+-------+---+ +-------+-------+ +-----------+ | 13| 16 17 18| 6 7 8| 11| 20 19| 16 15| 25| 28 29 30| | + +---+ | +---+ + | + + + | + +---+ | | 14 15| 20 19| 5 4| 9 10| 21| 18 17| 14| 26 27|1Jun 31| +-------+ +---+---+ +-------+ +---+---+ +-------+ +---+ | 27 26| 21 22| 2 3| 28 27| 22 23| 12 13| 8 7| 2 3| | + +---+ | +---+ + +---+ | +---+ + +---+ | | 28| 25 24 23|1Jul 30 29| 26 25 24| 11 10 9| 6 5 4| | +-----------+-----------+-----------+-----------+-----------+ | 29| 1 2 3| 26 27 28| 31Nov1 2| 15 16 17| 20 21 22| | +Sep+---+ | +---+ + +---+ | +---+ + +---+ | | 30 31| 5 4| 25 24| 29 30| 4 3| 14 13| 18 19| 24 23| +-------+ +---+---+ +-------+ +---+---+ +-------+ +---+ | 12 11| 6 7| 22 23| 18 17| 5| 8 9| 12|1Dec 30| 25 26| | + +---+ | +---+ + | + + + | + +---+ | | 13| 10 9 8| 21 20 19| 16| 6 7| 10 11| 2| 29 28 27| | +---+-------+-------+---+ +-------+-------+ +-----------+ | 14 15| 28 29 30Oct1| 14 15| 29 28| 25 24| 3| 6 7 8| +---+ | +---+---+ | +---+ + + + | + +---+ | | 17 16| 27 26| 3 2| 13 12| 30| 27 26| 23| 4 5| 10 9| | +---+---+ | +---+---+ | +---+---+ +-------+ +---+ | 18| 21 22| 25| 4| 7 8| 11| 31 | 21 22| 17 16| 11 12| | + + + | + + + +---- | +---+ + +---+ | | 19 20| 23 24| 5 6| 9 10| | 20 19 18| 15 14 13| +-------+-------+-------+-------+ +-----------+-----------+ Yeah, I know it's only 2D but I couldn't resist. --Steve