Re: The Waterfall
From Veronica Karlsson <e93...@nospam.sm.luth.se>
· alt.ascii-art
· 22 Jul 1997 00:00 · View full thread
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DaSmurf wrote: > > Veronica Karlsson wrote: > > Michael Naylor wrote: > > [ 8< ] > > > WOWZERS! I wanted to add the waterwheel, but it seemed awfully tough. > > > Nice job Veronica! > > > > :) *blush* > > > > I just looked at the picture.... (and I happened to know that it is > > based on two "impossible triangles" placed above each other. > > Understanding how it works probably made it a little bit easier for me > > to draw it) > > > > The idea behind it looks something like this: > > > > __ __ > > /\ \ /\ \ > > / \ \ / \ \ > > / /\ \ \ / /\ \ \ > > / / /\ \ \/ / /\ \ \ > > / / /__\_\/ / /__\_\ \ > > / / /______\/ /________\ > > \/_____________________/ > > -> waterfall -> > > > > (you'll have to turn it 90 degrees to get it right) > > -- > > Have to change a little in your explanation... ;) No, you misunderstand, the discussion was about a specific painting by M.C. Escher where water runs away in a canal system into the distance and then it falls down a waterfall and back to the beginning of the same canal system. That particular picture is based on a "double impossible triangle" such as I have drawn above as an attempt to _illustrate_ my words. This little sketch-like illustration is not what we were interested in, we have seen that one before. You can admire Escher's picture here: http://www.cs.utah.edu/~dmcallis/Pic/Escher/waterfall.jpg > > The first picture made that way was like this: > __ > /\ \ > / \ \ > / /\ \ \ > / / /\ \ \ > / / /__\_\ \ > / / /________\ > \/___________/ I know that, but that is not what we were talking about. We were talking about this: The Waterfall Michael Naylor (7/97) ,__--"^-_. ,__--"" ;__--_ : "-_. _--",~__--"" .:|:"-_.~.`"-_. !-_`. "-_ .:;;|:::::"-_.'`."-_. |::"-_`. "-_'::::"-_::::::"-_.'. "-_. |:::::"-_))))" '::::"-_:::::::"-_. . '"-_. |::::::::;!)!) ':::(()-_::::::::"-_. ` "-_. |::::::::;!!!) ((o))::"-_::::::::";-_.` ;"-_. |::::::::;'!!! .. (()):::::"-_::::;_-" ',_-" | |::::::::; !!! ::::..!! '::::::"_-" , ,_-" | |::::::::;.!!! '' ;_-"' ,_-" | |::::::::; !!! ,_-" ~,_-" | () |:::::::.( !!!') ,_-" . ,_-" | (()) |::::::(:(`!!!!'),_-". ,_-" _-" ((()o) |::::::.((,!!!_)~.,~,_-" () _-" ... (()) |:::::::',((!'),~;_-" (o)) _-" ::::..!! |::::::(.:~(_;_-" ) : ((()o) () ''' |:::::::::"::| .) :::,_(o)) (o)) |::::::::.:::| ;-:..!! ((()o) |::::::::::::| _-" ... (()) |::()):::::::| _-" :::::..!! .."(()o)::::::| _-" ''' ..((o)))):::::| _-" ...((())"-_:::| _-" .. '|| "-_|-" mn :::..!! '' of which I made my own version (complete with big wheel and power station): _.-'\ _.-' \ _.-' \ _.-_-'\ _.-'`-._ |\ _-| _.-'_.-'`-._`-._ | | | |_.-' `-._`-._|`-._ \ \ | | / / _ ``---._ `-._ \ \|_-' | / / .-' `-._|`-._ ``-._ `-._ \ || || / /|-'|`-._ `-._ `--._`-._|`-._ \_.-' | | ||| `-._ `-._ ``---._ `-._ | | | | | ||| |||`-._ `-._|`-._ ``-._ `-._ | | __ ||| ||| `-._ `-._ `-._ `-._ | | | |_.-|||. ||| `-._ _.-'| `-_.'| | | | ||/ ||| \ ||| _.-'|_.-'_.-' _.-' | | | | | . ||| . ||| _.-' __.---'' _.-' | | | | || ||| |||'|_.-'_.-'' _.-'|_.-' _.' | || || ||| |'|||----'' _.-' _.-' | | | | ||| '||| _.-'|_.-' _.-' | | || _.\ ||| / |||.-' _.-' | | | ' |_`.|||' _.-' _.-' | _.-|| | | ||`-' _.-' |`-._ | _.-' _.-' | `-._ _.-' _.-' | | _.-' | | _.-' -._| | _.-' `-._ | _.-' `-._ | _.-' `|' And that is what Michael Naylor was commenting on. I then explained that the picture by Escher that is obviously the idea behind our, somewhat simpler, pictures is based on two impossible triangles placed above each other in the way that I tried to describe above and that that is why my picture looked better than his "three-and-a-half-sided" version... Then, a day or two later, I made this picture, which looks more like the original by Escher: _.-"""-._ .' `. / \ | | | | | | \ / _.-"""-._ _.`. .'. .' `. |`-._`-.._..-'_.-| / \ | _ `-._ _.-' | | | | | `-._ " _.-'| | | | | | || | | | | | | | || | | | \ / | | || | | | _`. .'. | | || | | | |`-.`-.._..-'.-'| | | || | | | | `-._.-' | | | _.-'| |_ | | | |`-._ _.-'| | | |'_.-'| |_`-.| | | | || | | | |_.-' | | `-._ `._|`-._ | | || | | | / / | | ``---._ `-._ | | || | | | | / / .-' `-._|`-._ ``-._ `-._ | | || | | | || || / /|-| |-._ `-._ `--._`-._|`-._ | | || | | | | | ' || |\ `-._ `-._ ``---._ `| | || | | | | - | | | || | \ | |`-._ `-._|`-._ ``-| |`-.|| | | | _.-' | | || | \ | | `-._ `-._ | |-._ | |._ | | _.-' | | || | \| | `-._ `-.| | `| |_ `-| | | | | || | | | `-._ _.| | | | `.-| | | | || || | | | _.-'|_.-'_.-' | |_.-' | | | | . || | | | _.-' __.---'' _.| ' | | | || || | | |\_.-'|_.-'_.-'' _.-'|_.-' _. | | | | || | | |' _- _.-' _.-' | | || || || |_.-'| |_.---'' _.-' _ | | | \ | | | || |_.-'| | _.-'|_.-' _.-'|| | | | \ | || .'_| | | |_.-' _.-'| | || | | | \ | | |._ | | | `-._ _.-' | | || | | | \ || | | `| | ```-._`-._|`-._ _.-' | | || | | | |\_.-| | `-._ ``---._ `-._ | | || | | | | | `-._|`-._ ``-._ `-._ | | || | | | | || || | `-._ `--._`-._|`| | || | | | | | | | `-._ ``---.| |`|| | | | | | | | |`-._ `-._|`-._ | |-.| |-._ | | | | ||`-._ `-.| | | |._ `-| | | | | | || | `-._ _.| | | | `-_| | | | | ||__ | | | `-._ _.-'|_.-'_.-' | |_.-' | | | | | ._.-| |. | | `-._ _.-' __.---'' _| | | | | ||/ | | \ | | _.-'|_.-'_.-'' _.-'|_.-' | | || || | | .'| |-' __.---'' _.-' | | | | | |.| '| |-'' _.-'|_.-' | | | || _. | | | | | _.-' | | | | ' | | | | |_.-' | | || | | \ | | / _| ' _.-' |_.-' | _`.| |'-' _.-' |`-._ _.| _.-' | `-._ _.-' _.-' | |' _.-' | | _.-' | | _.-' | | _.-' | | _.-' | | _.-' | | _.-' _ | | _.-' `-|_ | _.-' `-._ | _.-' `-.|.-' If you look at it you should be able to find the "double impossible triangle" (the waterfall itself is the bar that is mutual between them). It even has an extra side to it so maybe it should actually be described as a "triple impossible triangle": ____________ /\ ________ \ / \ \______/\ \ / /\ \ \ / /\ \ \ / / /\ \ \/ / /\ \ \ / / /__\_\/ / /__\_\ \ / / /______\/ /________\ \/_____________________/ -> waterfall -> (turned 90 degrees because that made it easier to draw in ascii) [ 8< smurfs 8< ] -- :) Veronica Karlsson ( e93...@sm.luth.se http://www.ludd.luth.se/~vk/ )
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,5c0fa69c17ad05a2 X-Google-Attributes: gidf996b,public From: Veronica Karlsson <e93...@nospam.sm.luth.se> Subject: Re: The Waterfall Date: 1997/07/22 Message-ID: <33D...@nospam.sm.luth.se> X-Deja-AN: 258171942 References: <33C...@nospam.sm.luth.se> <33C...@math.fsu.edu--remove.to.reply> <33D...@nospam.sm.luth.se> <33D...@lords.com> Organization: Junk e-mail gladly reported (I have got credit for chucking several spammers out of their accounts) Newsgroups: alt.ascii-art
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