__ __ () _ _ __ __ _ _ __ __ ___ ___ _ ___ | \/ |--| '(| =| | \| |/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!
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