(Oops! How does copy&paste cause spelling errors??) On Thu, Aug 15, 2013 at 5:32 AM, Bill Gosper <billgosper@gmail.com> wrote:
In the totalaperiodic case (i.e., minus the block), if a single shuttling glider leaks, so will all subsequent ones, via the same mechanism, and total aperiodicity will fail. In http://gosper.org/gliders-formatted-2.pdf, NeilB seems to have a leakproof leakproof proof. --rwg
On Sat, Aug 10, 2013 at 9:16 PM, Bill Gosper <billgosper@gmail.com> wrote:
(This was for the Life list, but you might find it interesting.) I tightened it so you can watch the first couple of deletions.
#CXRLE #C Total periodic #C #C Without the block, every cell in the universe is aperiodic. #C #C The block starts to delete the nth shuttling glider at time #C 14 - 35 (-1)^n - 2 n + (1 + 12 n) 3^(2 + 5 n) #C = 28478, 13286000, 4778186074, 1537671920812,... #C each time lurching slightly northeast. Thus every cell in #C the universe is eventually permanently vacant. #C #C It would be nice to "shew that" no shuttling glider escapes #C the reflecting walls, although all that is required is that #C infinitely many hit the block. Which would also be nice to shew. x = 56, y = 60, rule = B3/S23 38bo$37b3o$36b2obo5bo$36b3o5b3o$37b2o4bo2b2o3b3o$43b3o4bo2bo$53bo$49bo 3bo$53bo$37b3o10bobo$37bo2bo$37bo$37bo$38bobo7$35b3o$35bo2bo11bo$35bo 13b3o$35bo3bo8b2obo$35bo12b3o$36bobo10b2o3$32b3o$27b2o2b5o$27b2o2b3ob 2o7b2o5bo2bo$34b2o7b4o8bo$43b2ob2o3bo3bo$45b2o5b4o5$18bo32b3o$16bo3bo 32bo$21bo31bo$b2o13bo4bo30bo$4o13b5o8bo2bo$2ob2o29bo$2b2o26bo3bo$31b4o 15b2o$47b3ob2o$21b2o24b5o$22b2o24b3o$21b2o$21bo3$22b2o$13b4o4b4o$12bo 3bo4b2ob2o$b5o10bo6b2o$o4bo6bo2bo$5bo$o3bo!
--rwg