__  __ () _ _ __    __  _  _ __ __   ___ ___  _ ___
     |  \/  |--| '(| =|  |  \| |/o \ " /|_/ O | O )|/(  _|
     |_\__/_|__|_|_|__|  |_|\__|_/\_|_|___|__/|_\_\ |___)
            __   ___ ,___ () ()   __    __  ___ ____
           /o \ (  _|  _/.--.--. (__)  /o \| O )_  _|
          |_/\_|___) \__\|__|__|      |_/\_|_\_\/__\




          Knots I
 (60 degree folded strips)

    by Michael Naylor 


      __          __
     / /\        / /\
    / /\ \      / /\ \
   / /  \ \    / /  \ \
  /_/____\ \__/_/____\ \
  \_______\ \_________\/
           \/ /
           / /\
          / /\ \
         / /  \ \
        /_/____\ \
        \_______\/


     
       __        __
      /\ \      / /\ 
     / /\ \    / /\ \ 
    / /__\ \__/_/__\ \  
    \/____\ \_______\/ 
           \/ /
           / /\
          / /\ \
         /_/__\ \
         \_____\/
        

         ________
        /_______/\   
        \ \    / / 
      ___\ \__/_/___ 
     /____\ \______/\ 
     \ \   \/ /   / /
      \ \  / /\  / /
       \ \/ /\ \/ /
        \_\/  \_\/
            


          ______
         /_____/\   
        _\ \__/_/_ 
       /__\ \____/\ 
       \ \ \/ / / /
        \ \/ /\/ /
         \_\/\_\/



          ______            ______            ______
         /\_____\          /\_____\          /\_____\          ____ 
        _\ \__/_/_         \ \__/_/_         \ \__/_/         /\___\
       /\_\ \_____\        /\ \_____\        /\ \___\        /\ \___\ 
       \ \ \/ / / /        \ \/ / / /        \ \/ / /        \ \/ / / 
        \ \/ /\/ /          \/_/\/ /          \/_/_/          \/_/_/
         \/_/\/_/              \/_/


         ________      ________
        /_______/\    /_______/\   
        \ \    / /    \ \    / / 
      ___\ \__/_/______\ \__/_/___ 
     /____\ \___________\ \______/\ 
     \ \   \/ /          \/ /   / /
      \ \  / /\          / /\  / /
       \ \/ /\ \        / /\ \/ /
        \_\/  \ \      / /  \_\/
               \ \    / /
             ___\ \__/_/___ 
            /____\ \______/\ 
            \ \   \/ /   / /
             \ \  / /\  / /
              \ \/ /\ \/ /
               \_\/  \_\/





         ________    ________    ________    ________
        /_______/\  /_______/\  /_______/\  /_______/\    
        \ \    / /  \ \    / /  \ \    / /  \ \    / /
      ___\ \__/_/____\ \__/_/____\ \__/_/____\ \__/_/___ 
     /____\ \_________\ \_________\ \_________\ \______/\ 
     \ \   \/ /        \/ /        \/ /        \/ /   / /
      \ \  / /\        / /\        / /\        / /\  / /
       \ \/ /\ \      / /\ \      / /\ \      / /\ \/ /
        \_\/  \ \    / /  \ \    / /  \ \    / /  \_\/
            ___\ \__/_/____\ \__/_/____\ \__/_/___ 
           /____\ \_________\ \_________\ \______/\ 
           \ \   \/ /        \/ /        \/ /   / /
            \ \  / /\        / /\        / /\  / /
             \ \/ /\ \      / /\ \      / /\ \/ /
              \_\/  \ \    / /  \ \    / /  \_\/
                  ___\ \__/_/____\ \__/_/___ 
                 /____\ \_________\ \______/\ 
                 \ \   \/ /        \/ /   / /
                  \ \  / /\        / /\  / /
                   \ \/ /\ \      / /\ \/ /
                    \_\/  \ \    / /  \_\/
                        ___\ \__/_/___ 
                       /____\ \______/\ 
                       \ \   \/ /   / /
                        \ \  / /\  / /
                         \ \/ /\ \/ /
                          \_\/  \_\/


         ________      ________      ________      ________
        /_______/\    /_______/\    /_______/\    /_______/\    
        \ \    / /    \ \    / /    \ \    / /    \ \    / /
      ___\ \__/_/______\ \__/_/______\ \__/_/___   \ \__/_/___  
     /____\ \___________\ \___________\ \_______\  /\ \______/\
     \ \   \/ /__________\/ /          \/ /   / / / /\ \/   / /
      \ \  / /_____________/\          / /\  / / / / /\ \  / /
       \ \/ /   ________   \ \        / /\ \/ / / / / /\ \/ /
        \_\/   /\_______\   \ \      / /  \/_/ / / / /  \_\/
               \ \    / /    \ \    / /       / / / / 
             ___\ \__/_/______\ \__/_/_______/ /_/_/___ 
            /____\ \___________\ \___________\ \______/\ 
            \ \   \/ /          \/ /          \/ /   / /
             \ \  / /\          / /\          / /\  / /
              \ \/ /\ \        / /\ \        / /\ \/ /
               \_\/  \ \      / /  \ \      / /  \_\/
                      \ \    / /    \ \    / / 
                    ___\ \__/_/   ___\ \__/_/___ 
                   /____\ \__ \  /____\ \______/\ 
                   \ \   \/ /\ \ \ \   \/ /   / /
                    \ \  / /\ \ \ \ \  / /\  / /
                     \ \/ /\ \ \ \ \ \/ /\ \/ /
                      \_\/  \ \ \ \ \_\/  \_\/
                             \ \ \ \ 
                           ___\ \_\_\____ 
                          /____\ \______/\ 
                          \ \   \/ /   / /
                           \ \  / /\  / /
                            \ \/ /\ \/ /
                             \_\/  \_\/


        ____________
       /___________/\
      _\ \________/_/_
     /__\ \__________/\
    _\ \_\_\____/ /_/_/_ 
   /\_\ \______/ /______\
   \ \ \ \ \ \/ / / / / /
    \ \ \ \ \ \/ / / / /
     \ \ \ \/\ \/ / / /
      \ \ \/ /\/ / / /
       \ \/ /\/ /\/ /
        \/_/\_\/\/_/

        ____________
       /___________/\
       \ \        / /
       _\ \______/_/_
      /__\ \________/\
   ___\ \_\_\__/ /_/_/___ 
  /\___\ \____/ /_______/\
  \ \   \ \ \ \/ / /   / /
   \ \   \ \/\ \/ /   / /
    \ \   \/ /\/ /   / /
     \ \  / /\/ /\  / /
      \ \/ /\_\/\ \/ /
       \/_/      \_\/



        ______________
       /_____________/\
       \ \          / /
     ___\ \________/_/___
    /____\ \____________/\
    \ \   \ \    / /   / /
  ___\ \___\_\__/ /___/_/___ 
 /\___\ \______/ /_________/\
 \ \   \ \   \ \/   / /   / /
  \ \   \ \  /\ \  / /   / /
   \ \   \ \/ /\ \/ /   / /
    \ \   \/ /  \/ /   / /
     \ \  / /\  / /\  / /
      \ \/ /\ \/ /\ \/ /
       \_\/  \_\/  \_\/


    ________________
   /_______________/\
   \ \            / /
    \ \    ______/_/_______
     \ \  /\______________/\
   ___\ \_\_\__/ /_      / /
  /\___\ \____/ /__\    / /
  \ \   \ \ \ \/ / /   / /
   \ \   \ \/\ \/ /   / /
    \ \   \/_/\/ /   / /
     \ \      / /\  / /
      \ \    / /\ \/ /
       \ \  / /  \_\/
        \ \/ /
         \/_/
      

        ____________________
       /___________________/\
       \ \                / /
     ___\ \________      / /
    /____\ \______/\    / /
    \ \   \ \    / /   / /
  ___\ \___\_\__/ /___/_/___ 
 /\___\ \______/ /_________/\
 \ \   \ \   \ \/   / /   / /
  \ \   \ \  /\ \  / /   / /
   \ \   \ \/ /\ \/ /   / /
    \ \   \/ /  \/ /   / /
     \ \  / /\  / /\  / /
      \ \/ /\ \/ /\ \/ /
       \_\/  \_\/  \_\/



        ____________________          ____________________          ____________________
       /___________________/\        /___________________/\        /___________________/\
       \ \                / /        \ \                / /        \ \                / /
     ___\ \________      / /       ___\ \________      / /       ___\ \________      / /
    /____\ \______/\    / /       /____\ \______/\    / /       /____\ \______/\    / /
    \ \   \ \    / /   / /   __   \ \   \ \    / /   / /   __   \ \   \ \    / /   / /
  ___\ \___\_\__/ /___/_/___/ /\___\ \___\_\__/ /___/_/___/ /\___\ \___\_\__/ /___/_/___
 /\___\ \______/ /_________/ /______\ \______/ /_________/ /______\ \______/ /_________/\
 \ \   \ \   \ \/   / /   / /  \ \   \ \   \ \/   / /   / /  \ \   \ \   \ \/   / /   / /
  \ \   \ \  /\ \  / /   / /    \ \   \ \  /\ \  / /   / /    \ \   \ \  /\ \  / /   / /
   \ \   \ \/ /\ \/ /   / /      \ \   \ \/ /\ \/ /   / /      \ \   \ \/ /\ \/ /   / /
    \ \   \/ /  \/ /   / /        \ \   \/ /  \/ /   / /        \ \   \/ /  \/ /   / /
     \ \  / /\  / /\  / /          \ \  / /\  / /\  / /          \ \  / /\  / /\  / /
      \ \/ /\ \/ /\ \/ /            \ \/ /\ \/ /\ \/ /            \ \/ /\ \/ /\ \/ /
       \_\/  \_\/  \_\/              \_\/  \_\/  \_\/              \_\/  \_\/  \_\/



                               Knots II
                           (Celtic Knots)
                       by Michael Naylor (7/97)    


                           ._____. ._____.
                           | ._. | | ._. |
                           | !_| |_|_|_! |
                           !___| |_______!
                           .___|_|_| |___.
                           | ._____| |_. |
                           | !_! | | !_! |
                           !_____! !_____!

                   ._____. ._____. ._____. ._____.
                   | ._. | | ._. | | ._. | | ._. |
                   | !_| |_|_|_! | | !_| |_|_|_! |
                   !___| |_______! !___| |_______!
                   .___|_|_| |_________|_|_| |___.
                   | ._____| |_____________| |_. |
                   | !_! | | |         | | ! !_! |
                   !_____! | |         | | !_____!
                   ._____. | |         | | ._____.
                   | ._. | | |         | | | ._. |
                   | !_| |_|_|_________| |_|_|_! |
                   !___| |_____________| |_______!
                   .___|_|_| |___. .___|_|_| |___.
                   | ._____| |_. | | ._____| |_. |
                   | !_! | | !_! | | !_! | | !_! |
                   !_____! !_____! !_____! !_____!

   ._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____.
   | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. |
   | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! |
   !___| |_______! !___| |_______! !___| |_______! !___| |_______!
   .___|_|_| |_________|_|_| |___. .___|_|_| |_________|_|_| |___.
   | ._____| |_____________| |_. | | ._____| |_____________| |_. |
   | !_! | | |         | | ! !_! | | !_! | | |         | | ! !_! |
   !_____! | |         | | !_____! !_____! | |         | | !_____!
   ._____. | |         | |                 | |         | | ._____.
   | ._. | | |         | |                 | |         | | | ._. |
   | !_| |_|_|_________| |_________________|_|_________| |_|_|_! |
   !___| |_____________| |_____________________________| |_______!
   .___|_|_| |___.     | |                 | |     .___|_|_| |___.
   | ._____| |_. |     | |                 | |     | ._____| |_. |
   | !_! | | !_! |     | |                 | |     | !_! | | !_! |
   !_____! !_____!     | |                 | |     !_____! !_____!
   ._____. ._____.     | |                 | |     ._____. ._____.
   | ._. | | ._. |     | |                 | |     | ._. | | ._. |
   | !_| |_|_|_! |     | |                 | |     | !_| |_|_|_! |
   !___| |_______!     | |                 | |     !___| |_______!
   .___|_|_| |_________|_|_________________| |_________|_|_| |___.
   | ._____| |_____________________________| |_____________| |_. |
   | !_! | | |         | |                 | |         | | ! !_! |
   !_____! | |         | |                 | |         | | !_____!
   ._____. | |         | | ._____. ._____. | |         | | ._____.
   | ._. | | |         | | | ._. | | ._. | | |         | | | ._. |
   | !_| |_|_|_________| |_|_|_! | | !_| |_|_|_________| |_|_|_! |
   !___| |_____________| |_______! !___| |_____________| |_______!
   .___|_|_| |___. .___|_|_| |___. .___|_|_| |___. .___|_|_| |___.
mn | ._____| |_. | | ._____| |_. | | ._____| |_. | | ._____| |_. |
   | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! |
   !_____! !_____! !_____! !_____! !_____! !_____! !_____! !_____!


What would happen if this were expanded one more time?

As this expands fractally, what-to-do with the empty space in the middle? . . .



knot in a knot:
 ._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____.
 | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. |
 | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! |
 !___| |_______! !___| |_______! !___| |_______! !___| |_______!
 .___|_|_| |_________|_|_| |___. .___|_|_| |_________|_|_| |___.
 | ._____| |_____________| |_. | | ._____| |_____________| |_. |
 | !_! | | |         | | ! !_! | | !_! | | |         | | ! !_! |
 !_____! | |         | | !_____! !_____! | |         | | !_____!
 ._____. | |     .___| |_______. ._______|_|___.     | | ._____.
 | ._. | | |     | ._| |_____. | | ._________. |     | | | ._. |
 | !_| |_|_|_____| |_|_|_____|_|_| |_____| |_|_|_____| |_|_|_! |
 !___| |_________| |_____________| |_____| |_________| |_______!
 .___|_|_| |___. | | | |     | | | |     | | | | .___|_|_| |___.
 | ._____| |_. | | | | |     | | | |     | | | | | ._____| |_. |
 | !_! | | !_! | | !_| |_____|_|_| |_____|_|_! | | !_! | | !_! |
 !_____! !_____! !___| |_________| |___________! !_____! !_____!
 ._____. ._____. .___|_|_____| |_|_|_____| |___. ._____. ._____.
 | ._. | | ._. | | ._________| |_________| |_. | | ._. | | ._. |
 | !_| |_|_|_! | | ! | |     | | | |     | | | | | !_| |_|_|_! |
 !___| |_______! | | | |     | | | |     | | | | !___| |_______!
 .___|_|_| |_____|_|_| |_____|_|_| |_____|_|_| |_____|_|_| |___.
 | ._____| |_________| |_________| |_________| |_________| |_. |
 | !_! | | |     | !_|_|_____! | | !_____| |_! |     | | ! !_! |
 !_____! | |     !_____________! !_______| |___!     | | !_____!
 ._____. | |         | | ._____. ._____. | |         | | ._____.
 | ._. | | |         | | | ._. | | ._. | | |         | | | ._. |
 | !_| |_|_|_________| |_|_|_! | | !_| |_|_|_________| |_|_|_! |
 !___| |_____________| |_______! !___| |_____________| |_______!
 .___|_|_| |___. .___|_|_| |___. .___|_|_| |___. .___|_|_| |___.
 | ._____| |_. | | ._____| |_. | | ._____| |_. | | ._____| |_. | mn
 | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! |
 !_____! !_____! !_____! !_____! !_____! !_____! !_____! !_____!


knottier knot in a knot:
 ._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____.
 | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. |
 | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! |
 !___| |_______! !___| |_______! !___| |_______! !___| |_______!
 .___|_|_| |_________|_|_| |___. .___|_|_| |_________|_|_| |___.
 | ._____| |_____________| |_. | | ._____| |_____________| |_. |
 | !_! | | |         | | ! !_! | | !_! | | |         | | ! !_! |
 !_____! | |         | | !_____! !_____! | |         | | !_____!
 ._____. | |     .___| |___.     ._______|_|___.     | | ._____.
 | ._. | | |     | ._| |_. |     | ._________. |     | | | ._. |
 | !_| |_|_|_____| |_|_|_| |_____|_|_____| |_|_|_____| |_|_|_! |
 !___| |_________| |_____| |_____________| |_________| |_______!
 .___|_|_| |___. | !_| |_|_|_____| |_____|_|_! | .___|_|_| |___.
 | ._____| |_. | !___| |_________| |___________! | ._____| |_. |
 | !_! | | !_! | .___|_|_| |___. | | .___| |___. | !_! | | !_! |
 !_____! !_____! | ._____| |_. | | | | ._| |_. | !_____! !_____!
 ._____. ._____. | !_| |_! | | | | !_| |_|_|_! | ._____. ._____.
 | ._. | | ._. | !___| |___! | | !___| |_______| | ._. | | ._. |
 | !_| |_|_|_! | .___|_|_____| |_____|_|_| |___. | !_| |_|_|_! |
 !___| |_______! | ._________| |_________| |_. | !___| |_______!
 .___|_|_| |_____|_|_| |_____|_|_____| |_|_|_| |_____|_|_| |___.
 | ._____| |_________| |_____________| |_____| |_________| |_. |
 | !_! | | |     | !_|_|_____! |     | !_| |_! |     | | ! !_! |
 !_____! | |     !_____________!     !___| |___!     | | !_____!
 ._____. | |         | | ._____. ._____. | |         | | ._____.
 | ._. | | |         | | | ._. | | ._. | | |         | | | ._. |
 | !_| |_|_|_________| |_|_|_! | | !_| |_|_|_________| |_|_|_! |
 !___| |_____________| |_______! !___| |_____________| |_______!
 .___|_|_| |___. .___|_|_| |___. .___|_|_| |___. .___|_|_| |___.
 | ._____| |_. | | ._____| |_. | | ._____| |_. | | ._____| |_. | mn
 | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! |
 !_____! !_____! !_____! !_____! !_____! !_____! !_____! !_____!



Here's a sign I made for my office.  Feel free to use the frame to make your own sign!

   ._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____.
   | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. | | ._. |
   | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! | | !_| |_|_|_! |
   !___| |_______! !___| |_______! !___| |_______! !___| |_______!
   .___|_|_| |_________| | | !_________! | | !_________|_|_| |___.
   | ._____| |___________! !_____________! !_______________| |_. |
   | !_! | | |                                         | | ! !_! |
   !_____! | |                Office of                | | !_____!
   ._____. | |                                         | | ._____.
   | ._. | | |      __  __ () ___ _ _  _   __ _        | | | ._. |
   | !_| |_! |     |  \/  |--/ __/ ' |/o \| =| !_      | !_|_|_! |
   !___| |___!     |_\__/_|__|___\_|_|_/\_|__|___|     !_________!
   .___|_|___.        __  _  _ __ __   ___ ___         .___| |___.
   | ._____. |       |  \| |/o \ " /!_/ O | O )        | ._| |_. |
   | !_! | | |       |_|\__|_/\_|_|___|__/|_\_\        | | ! !_! |
   !_____! | |                                         | | !_____!
   ._____. | |     Mathematics and Other Weirdness     | | ._____.
   | ._. | | |                                         | | | ._. |
   | !_| |_|_|___________. ._____________. .___________| |_|_|_! |
   !___| |_____________. | | ._________. | | ._________| |_______!
   .___|_|_| |___. .___|_|_| |___. .___|_|_| |___. .___|_|_| |___.
   | ._____| |_. | | ._____| |_. | | ._____| |_. | | ._____| |_. |
   | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! | | !_! |
   !_____! !_____! !_____! !_____! !_____! !_____! !_____! !__mn_!




Back to > 
Transfer interrupted!
 tml>