Through the heroic efforts of Jack Holloway, the book mentioned in Neil's Minsky Circle Algorithm blogpost (http://nbickford.wordpress.com/) is now commercially available: http://www.blurb.com/books/2172660 , $59.95 (hardcover, 70pp). Also, Neil has tweaked some pictures and captions, with one yet pending: http://gosper.org/x=1_y=1o2_d=9_e=1o3.png , clarifying that x=1,y=1/2,δ=9 and ε=1/3 makes an infinite triangular spiral, despite 0 < δ ε < 4. --rwg
me>Also, Neil has tweaked some pictures and captions, with one yet pending: http://gosper.org/x=1_y=1o2_d=9_e=1o3.png , clarifying that x=1,y=1/2,δ=9 and ε=1/3 makes an infinite triangular spiral, despite 0 < δ ε < 4.
This should bother you. The recurrence is reversible, so no point is repeated. But how can the time-reversed spiral shrink indefinitely if the points are quantized? http://gosper.org/x=1_y=1o2_d=9_e=1o3.p<http://gosper.org/x=1_y=1o2_d=9_e=1o3.png>df . (LCD screen must be perpendicular to line of sight.)
--rwg
2011/5/15 Bill Gosper <billgosper@gmail.com>
me>Also, Neil has tweaked some pictures and captions, with one yet pending:
http://gosper.org/x=1_y=1o2_d=9_e=1o3.png , clarifying that x=1,y=1/2,δ=9 and ε=1/3 makes an infinite triangular spiral, despite 0 < δ ε < 4.
This should bother you. The recurrence is reversible, so no point is repeated. But how can the time-reversed spiral shrink indefinitely if the points are quantized? http://gosper.org/x=1_y=1o2_d=9_e=1o3.pdf . (LCD screen must be perpendicular to line of sight.)
--rwg
And Gmail must be on the level. Which it isn't. (Only clue it would screw up like that was failure to underline "df")
participants (1)
-
Bill Gosper