Original Usenet thread from alt.ascii-art, started 17 Sep 2001.
Mike Throll 5
alt.ascii-art
· 8 messages · 17 Sep 2001 - 22 Sep 2001
There is nothing to comment... Personally I had never seen popcorn ad.
MIKE THROLL AND ...
/^^^^^\
q O,O P
| `-' |
Gr `-----'
... THE POPCORN!
/ /|
/ / |
/ //^^^^\
/ / | C OO----- \\--\
/ / | >__ /\ ||\\ \
/ / /\__` \ \/ \ \--|| \\ \
/_/ // '|||` /| |\ || \|--\
| | / || ||\;;/|/ / ||\ \\ || |
| | / || ||CoRn| / \ \\|| |\
| |/___\| |_\___/ \ \\---| \
| '|||`\ \ \__ \ \
| \ \_/__\ \________\
|/\/\/\/\/\/\|_/__\ Gr || ||
|| ||
---------------------------------------------------
||-----------------------------------------------||
|| -Our POPCoRn is rich with Gr ||
|| vitamins A,B,C and D! ||
|| /////// ||
|| ||||||| q[o]/[o]p ||
|| | POP | | /_ | ||
|| |CoRn | | __ | ||
|| | | |`--' / ||
|| \____/ __/\___/ \__ ||
||____________________________/____________\_____||
| COOLLIGHTNINGPROOFTV |
| o o o o o [] o |
|_________________________________________________|
/---------------------\
)I hate that stupid ad!|
/ /| O (I'd advertised popcorn|
/ / | o ) in that way... |
/ //^^^^\ \______________________/
/ / | C OO----- \\--\
/ / | >__ /\ ||\\ \
/ / /\__` \ \/ \ \--|| \\ \
/_/ // '|||` /| |\ || \|--\
| | / || ||\;;/|/ / ||\ \\ || |
| | / || ||CoRn| / \ \\|| |\
| |/___\| |_\___/ \ \\---| \
| '|||`\ \ \__ \ \
| \ \_/__\ \________\
|/\/\/\/\/\/\|_/__\ Gr || ||
|| ||
________________________________
/^^^^^\ (Our POPCoRn is the best popcorn \
q O,O P O )in the world! Our pack contains \
| o | o (twice as much popcorn than others!\
/-`-----'\ ) bla-bla-bla... /
| ' ' | \-------------------------------/
| | | |
'|||' '|||'
| | |
| | | Gr
/ X/ \X\
\-/ \-/ |
|
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| _______
| | |
\\\\ | ______ | |
|C OO _______ | | | (o)| |
| > | | | |------| | |
| - | |<|| | | | C |
/ \_____|______/ | | | | |
| ______/ | | |______| | |
| | | | | |
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| | Gr ||| |||||||||||||||||||||||||||||||||
|====| /||
| || .'| |
| || | | \
|___|\_ | | \
| \__\ | | \
\_____\
Next day...
-Our POPCoRn is the best popcorn
/ /| in the world...
/ / |
/ //^^^^\
/ / | C OO----- \\--\
/ / | >__ /\ ||\\ \
/ / /\__` \ \/ \ \--|| \\ \
/_/ // '|||` /| |\ || \|--\
| | / || ||\;;/|/ / ||\ \\ || |
| | / || ||CoRn| / \ \\|| |\
| |/___\| |_\___/ \ \\---| \
| '|||`\ \ \__ \ \
| \ \_/__\ \________\
|/\/\/\/\/\/\|_/__\ Gr || ||
|| ||
o _____________________
( IT'S ME???? SOMEONE )
O ( SHOULD RESEARCH IT! )
\-------------------/
More ads in the next issue of MIKE THROLL!
--
Grue <grue sobaka mail.ru>
http://bugsoft.freeservers.com
We have the black blot on the white plane.
Every dot is added to the blot if the black
area of its neighborhood (radius 1) is more
than white area and removed if the white area
is larger. Is this possible that blot's area
will be 1000 times more than initial area?
Timofei Shatrov <gru...@mail.ru> wrote: : We have the black blot on the white plane. : Every dot is added to the blot if the black : area of its neighborhood (radius 1) is more : than white area and removed if the white area : is larger. Is this possible that blot's area : will be 1000 times more than initial area? I've been thinking about this puzzle... is this a correct rephrasing: Given an initial separation of the plane RxR into a subset A and not-A, and an iterative process which at each step assigns membership in A to each point outside A whose circular neighbourhood of radius 1 has a greater intersection with A than with not-A, and removes each point previously within A whose circular neighbourhood of radius 1 has a greater intersection with not-A than with A, is it possible to choose initial A such that its area will increase by a factor of 1000 or more during the process? Tell me, does the blot have to be simply connected in the beginning? Do we need the final limiting area to be more than 1000 times the initial area, or can some intermediate area be 1000 times? I imagine it is some impossible fractal shape to begin with. We need Bill or another real mathematician in this group to figure it out... nice drawings by the way.
On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to confuse everyone with this message: >Timofei Shatrov <gru...@mail.ru> wrote: > >: We have the black blot on the white plane. >: Every dot is added to the blot if the black >: area of its neighborhood (radius 1) is more >: than white area and removed if the white area >: is larger. Is this possible that blot's area >: will be 1000 times more than initial area? > >I've been thinking about this puzzle... is this a correct rephrasing: You are the first one who did this :). >Given an initial separation of the plane RxR into a subset A and not-A, >and an iterative process which at each step assigns membership in A to >each point outside A whose circular neighbourhood of radius 1 has a >greater intersection with A than with not-A, and removes each point >previously within A whose circular neighbourhood of radius 1 has a greater >intersection with not-A than with A, is it possible to choose initial A >such that its area will increase by a factor of 1000 or more during the >process? > >Tell me, does the blot have to be simply connected in the beginning? I think yes. It also has to be finite. >Do we >need the final limiting area to be more than 1000 times the initial area, >or can some intermediate area be 1000 times? I think all finite figures will eventually die. You need to make it 1000 times larger only at one turn. >I imagine it is some >impossible fractal shape to begin with. No way. It's not very complicated. Just try to invent blot that can increase and then magic word "asymptotics". -- Grue <grue sobaka mail.ru> Mike Throll comic strip at: http://grue.freeservers.com Bugsoft Perm at: http://bugsoft.freeservers.com
In article <3ba...@News.CIS.DFN.DE>, Timofei Shatrov wrote: >On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to >confuse everyone with this message: > >>Given an initial separation of the plane RxR into a subset A and not-A, >>and an iterative process which at each step assigns membership in A to >>each point outside A whose circular neighbourhood of radius 1 has a >>greater intersection with A than with not-A, and removes each point >>previously within A whose circular neighbourhood of radius 1 has a greater >>intersection with not-A than with A, is it possible to choose initial A >>such that its area will increase by a factor of 1000 or more during the >>process? >> >>Tell me, does the blot have to be simply connected in the beginning? >I think yes. It also has to be finite. Obviously it must have a well-defined finite area, for the question to make sense. Other than that, finiteness makes little difference -- see below. >>Do we need the final limiting area to be more than 1000 times the >>initial area, or can some intermediate area be 1000 times? > >I think all finite figures will eventually die. You need to make it 1000 times >larger only at one turn. Yes, all finite figures must eventually vanish. It's easy to see that all convex figures will vanish, and that if a figure vanishes, all its sub-figures must also vanish. As any finite figure may surrounded by a convex hull, the proof follows. The use of the word "finite" above is slightly vague, but things are simplified by the fact that any figure with a finite area must after one iteration be a subset of a circle with a finite diameter. Proof by contradiction left as an exercise for the reader. This offers no direct help with the original problem, of course. >>I imagine it is some >>impossible fractal shape to begin with. > >No way. It's not very complicated. Just try to invent blot that can increase and >then magic word "asymptotics". Ah, I think I got it, but I'm not sure. To verify my idea, I'd need a formula for the radius, after one iteration, of a solid circle with an original radius of R. This involves trigonometry, and I'm lousy at it. -- Ilmari Karonen - http://www.sci.fi/~iltzu/ "Control: cmsg newgroup sci.math.tasteless" -- Red Drag Diva in the monastery
Ilmari Karonen <ilt...@sci.invalid> wrote: : In article <3ba...@News.CIS.DFN.DE>, Timofei Shatrov wrote: :>On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to :>confuse everyone with this message: :> :>>Given an initial separation of the plane RxR into a subset A and not-A, :>>and an iterative process which at each step assigns membership in A to :>>each point outside A whose circular neighbourhood of radius 1 has a :>>greater intersection with A than with not-A, and removes each point :>>previously within A whose circular neighbourhood of radius 1 has a greater :>>intersection with not-A than with A, is it possible to choose initial A :>>such that its area will increase by a factor of 1000 or more during the :>>process? :>>I imagine it is some :>>impossible fractal shape to begin with. :> :>No way. It's not very complicated. Just try to invent blot that can increase and :>then magic word "asymptotics". Well, I found a blot that can increase, but not a thousand-fold... take a very large "sheet" of ink and punch holes in it, with diameter slightly less than 1/sqrt(2pi)... unless they are spaced too close together they will all be filled after one generation, while only the outer edge of the whole sheet will have started degrading... am I on the right track?
In article <9oachv$795$1...@news.fas.harvard.edu>, uncle monty wrote: >Ilmari Karonen <ilt...@sci.invalid> wrote: >: In article <3ba...@News.CIS.DFN.DE>, Timofei Shatrov wrote: >:>On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to >:>confuse everyone with this message: >:> >:>>Given an initial separation of the plane RxR into a subset A and not-A, >:>>and an iterative process which at each step assigns membership in A to >:>>each point outside A whose circular neighbourhood of radius 1 has a >:>>greater intersection with A than with not-A, and removes each point >:>>previously within A whose circular neighbourhood of radius 1 has a greater >:>>intersection with not-A than with A, is it possible to choose initial A >:>>such that its area will increase by a factor of 1000 or more during the >:>>process? > >:>>I imagine it is some >:>>impossible fractal shape to begin with. >:> >:>No way. It's not very complicated. Just try to invent blot that can increase and >:>then magic word "asymptotics". My original idea was simply a ring with inner radius R and outer radius R+0.5+epsilon, for some humongous value of R and the smallest value of epsilon you can get away with. It's obvious that such a ring will get thicker as it shrinks, but unfortunately it's not at all obvious if its area will increase or not. And just to add to the frustration, after struggling with the trig and computing the hard parts by brute force, it seems I still don't know. Yes, the area appears to increase, but very slightly, and I'm not sure if the possible increase has an upper bound or not. >Well, I found a blot that can increase, but not a thousand-fold... take a >very large "sheet" of ink and punch holes in it, with diameter slightly >less than 1/sqrt(2pi)... unless they are spaced too close together they >will all be filled after one generation, while only the outer edge of the >whole sheet will have started degrading... am I on the right track? Hmm.. you just gave me an idea. Take one big blot. Fill it with N > 1 large circular holes, just far enough apart not to disturb each other's shrinking. Now fill the *remaining* blot with smaller circular holes, and repeat until the holes get too small. Now your blot is a fractal foam. If you make it big enough, I see no reason why you couldn't get an arbitrarily high area increase. Not that I could prove this either, but I'm a lot more confident in making that conjecture than with any of my previous ideas. Of course, if there's a non-fractal answer, as Timofei seems to imply above, I still have no idea what it could be. ObAscii: foam _..._ _ __ ./' `\,---.-'"".--.(_) /" "\ ,' .'"`. ." / .--: : __: _ ; | `._.'-( _: ( )__.7' (_)_./ -'-._ ; `.(_)-"`--'-. ; ,--.|-. .--".--. /_ .---(_)/ ;_ | : ; `; ;(_)--`-. `;-.(_)-'--' -- . _, .. j u s t. h o w l.i n g i n .t h e n.i g h t .. ._, . , )'' . /\_ . ' ,/\ . , ``( , _\__/ |__.'\._______,--;_'_`-.___,.______,/_,_`.__,-.__'__,/`-._,_| \____ ,_f_)\. Ilmari Karonen ilt...@sci.fi http://www.sci.fi/~iltzu/ /(_|_,.
Ilmari Karonen <ilt...@sci.invalid> wrote: : In article <9oachv$795$1...@news.fas.harvard.edu>, uncle monty wrote: :>Ilmari Karonen <ilt...@sci.invalid> wrote: :>: In article <3ba...@News.CIS.DFN.DE>, Timofei Shatrov wrote: :>:>On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to :>:>confuse everyone with this message: :>:> :>:>>Given an initial separation of the plane RxR into a subset A and not-A, :>:>>and an iterative process which at each step assigns membership in A to :>:>>each point outside A whose circular neighbourhood of radius 1 has a :>:>>greater intersection with A than with not-A, and removes each point :>:>>previously within A whose circular neighbourhood of radius 1 has a greater :>:>>intersection with not-A than with A, is it possible to choose initial A :>:>>such that its area will increase by a factor of 1000 or more during the :>:>>process? :> :>:>>I imagine it is some :>:>>impossible fractal shape to begin with. : Hmm.. you just gave me an idea. Take one big blot. Fill it with N > 1 : large circular holes, just far enough apart not to disturb each other's : shrinking. Now fill the *remaining* blot with smaller circular holes, : and repeat until the holes get too small. : Now your blot is a fractal foam. If you make it big enough, I see no : reason why you couldn't get an arbitrarily high area increase. Not that : I could prove this either, but I'm a lot more confident in making that : conjecture than with any of my previous ideas. : Of course, if there's a non-fractal answer, as Timofei seems to imply : above, I still have no idea what it could be. : ObAscii: foam : _..._ _ __ : ./' `\,---.-'"".--.(_) /" "\ : ,' .'"`. ." / .--: : __: _ ; : | `._.'-( _: ( )__.7' (_)_./ : -'-._ ; `.(_)-"`--'-. ; ,--.|-. : .--".--. /_ .---(_)/ ;_ | : : ; `; ;(_)--`-. `;-.(_)-'--' ok Timofei, time to reveal the shape that solves the problem... we are clearly too thick to get your hints. thanks --monty
On 22 Sep 2001 04:54:59 GMT, uncle monty <unc...@babyfishmouth.org> tried to confuse everyone with this message: > >ok Timofei, time to reveal the shape that solves the problem... we are >clearly too thick to get your hints. thanks --monty /\ / \ / \ #\ /# /\##\ /##/\ / \##\/##/ \ / \\####/ \ #\ /####\ / /\##\ /##/\##\ /#/\ / \##\/##/ \##\/#/ \ / \####/ \###/ \ \ /####\ /###\ / \ /##/\##\ /##/\#\ / \/##/ \##\/##/ \#\/ / \####/ \ \ /####\ / \ /##/\##\ / \/##/ \##\/ #/ \ \ / \ / \/ Let's imagine this grid is infinite. After some time (t) it will fill all the plane. It's area increases k times (k>1000 is constant). Let's make finite but very big grid. After some time its center area will increase k times and its border can't affect dots which are more than t meters from border. If initial area of blot=a, then a'/a ~ k*((r-t)^2)/(r^2)) if k=1000*(x^2),x>1 then (r-t)/r must be greater than 1/x, r>xt/(x-1). So, we can choose any radius more than xt/(x-1) _.,----.._ ,-' '-. /' ## -. ' ########### \ / ################ \ / ################## \ .' ################## \ | #########<------------>| | ##############r### | | ################## / '. ############### | `. ########### / \ ^ _' `._ |t ,- `-.._v__.,-' -- Grue <grue sobaka mail.ru> Mike Throll comic strip at: http://grue.freeservers.com Bugsoft Perm at: http://bugsoft.freeservers.com
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