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TILING - ASCII ART


			
See 'escher' for another tiling and `bick_wall' for many simple ones!





      The Flowsnake
      -------------
asciied by Michael Naylor



Order 1 Flowsnake


________________
\               \
 \               \
  \               \
   \________       \
           /
          /
         /
________/



Order 2 Flowsnake


            ________
            \       \
  ________   \____   \
  \       \      /   /
   \____   \____/   /   ____
       /            \   \   \
  ____/   ________   \   \   \
 /        \       \   \  /
/   ____   \____   \   \/
\   \   \      /   /
 \   \   \____/   /   ____
  \  /            \  /   /
   \/   ________   \/   /
        \       \      /
         \____   \____/
             /
        ____/

Order 3 Flowsnake
                      ____
                 ____ \__ \
                 \__ \__/ / __
                 __/ ____ \ \ \    ____
                / __ \__ \ \/ / __ \__ \
           ____ \ \ \__/ / __ \/ / __/ / __
      ____ \__ \ \/ ____ \/ / __/ / __ \ \ \
      \__ \__/ / __ \__ \__/ / __ \ \ \ \/
      __/ ____ \ \ \__/ ____ \ \ \ \/ / __
     / __ \__ \ \/ ____ \__ \ \/ / __ \/ /
     \ \ \__/ / __ \__ \__/ / __ \ \ \__/
      \/ ____ \/ / __/ ____ \ \ \ \/ ____
         \__ \__/ / __ \__ \ \/ / __ \__ \
         __/ ____ \ \ \__/ / __ \/ / __/ / __
        / __ \__ \ \/ ____ \/ / __/ / __ \/ /
        \/ / __/ / __ \__ \__/ / __ \/ / __/
        __/ / __ \ \ \__/ ____ \ \ \__/ / __
       / __ \ \ \ \/ ____ \__ \ \/ ____ \/ /
       \ \ \ \/ / __ \__ \__/ / __ \__ \__/
        \/ / __ \/ / __/ ____ \ \ \__/
           \ \ \__/ / __ \__ \ \/
            \/      \ \ \__/ / __
                     \/ ____ \/ /
                        \__ \__/
                        __/





                       Flowsnake coloring sheet
                   (makes a great present for Mom!)
                           _
                          / `-_
                         /     `-_
                        /         `-_
                       /             `-_
                      /                 `-_
                     /                     `-_
                    /             ____        `-_
                   /         ____ \__ \          `-_
  color this      /          \__ \__/ / __          `-_
 region a dark   /           __/ ____ \ \ \    ____    `-_
     color      /           / __ \__ \ \/ / __ \__ \      /
               /       ____ \ \ \__/ / __ \/ / __/ / __  /   `
              /   ____ \__ \ \/ ____ \/ / __/ / __ \ \ \/       `
             /    \__ \__/ / __ \__ \__/ / __ \ \ \ \/             `
            /     __/ ____ \ \ \__/ ____ \ \ \ \/ / __                ` ,
           /     / __ \__ \ \/ ____ \__ \ \/ / __ \/ /
          /      \ \ \__/ / __ \__ \__/ / __ \ \ \__/                 ,
         /        \/ ____ \/ / __/ ____ \ \ \ \/ ____
        /            \__ \__/ / __ \__ \ \/ / __ \__ \              ,
       /             __/ ____ \ \ \__/ / __ \/ / __/ / __
      /             / __ \__ \ \/ ____ \/ / __/ / __ \/ /         ,
     /              \/ / __/ / __ \__ \__/ / __ \/ / __/
    /               __/ / __ \ \ \__/ ____ \ \ \__/ / __        ,
   /               / __ \ \ \ \/ ____ \__ \ \/ ____ \/ /
   `-_             \ \ \ \/ / __ \__ \__/ / __ \__ \__/       ,
      `-_           \/ / __ \/ / __/ ____ \ \ \__/
         `-_           \ \ \__/ / __ \__ \ \/               ,   Color this
            `-_         \/      \ \ \__/ / __                 region a light
               `-_               \/ ____ \/ /             ,     color, or
                  `-_               \__ \__/                 leave it blank
                     `-_            __/                 ,
                        `-_        /
                           `-_    /                   ,
                              `-_/
                                 `                  ,
                                    `
                  cut out around       `          ,
                    the outside           `
                                             `
                                                `



Flowsnake technical information

The Flowsnake was invented by William Gosper.  It is a space-filling
fractal curve.  "Space-filling" means that if this process were carried
out infinitely, this curve would pass through every point in the region
it occupies.  It is a fractal in that if any "segment" is enlarged, it will
be identical to the entire curve.  This curve has a fractal dimension of
log(3)/log(sqrt(7)) = ~1.129.


Detail of construction:

The Flowsnake can be thought of as being composed of seven segments.
At each iteration, each of these seven segments is replaced with the
original shape.  (The new segments should have length equal to 1/sqrt(7)
times the original length; in ascii, of course, we'll make do with an
approximation).  In the following illustrations, the original vertices
are labeled to make it easier for you to follow what happens at each stage.




Order 1 Flowsnake


4_______5______6
\               \
 \               \
  \               \
   \3______2       \7
           /
          /
         /
0______1/



Order 2 Flowsnake


            ________
            \       \
  ________   \____   \6
  \       \      /   /
   \____   \5___/   /   ____
       /            \   \   \
  4___/   ________   \   \   \7
 /        \       \   \  /
/   ____   \____   \2  \/
\   \   \      /   /
 \   \   \3___/   /   ____
  \  /            \  /   /
   \/   ________   \/   /
        \       \      /
         \____   \1___/
             /
        0___/

Order 3 Flowsnake
                      ____
                 ____ \__ \
                 \__ \__/ / __
                 __/ ____ \ \ \6   ____
                / __ \__ \ \/ / __ \__ \
           ____ \ \ \__/ / __ \/ / __/ / __
      ____ \__ \ \/ ____ \/ / __/ / __ \ \ \7
      \__ \__/ / __ \__ \__/ / __ \ \ \ \/
      __/ ____ \ \ \5_/ ____ \ \ \ \/ / __
     / __ \__ \ \/ ____ \__ \ \/ / __ \/ /
     \ \ \__/ / __ \__ \__/ / __ \ \ \__/
      \/ ____ \/ / __/ ____ \ \ \2\/ ____
         \__ \__/ / __ \__ \ \/ / __ \__ \
         4_/ ____ \ \ \__/ / __ \/ / __/ / __
        / __ \__ \ \/ ____ \/ / __/ / __ \/ /
        \/ / __/ / __ \__ \__/ / __ \/ / __/
        __/ / __ \ \ \3_/ ____ \ \ \__/ / __
       / __ \ \ \ \/ ____ \__ \ \/ ____ \/ /
       \ \ \ \/ / __ \__ \__/ / __ \__ \__/
        \/ / __ \/ / __/ ____ \ \ \1_/
           \ \ \__/ / __ \__ \ \/
            \/      \ \ \__/ / __
                     \/ ____ \/ /
                        \__ \__/
                       0__/




If you'd like to find out more, try Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
W. H. Freeman and Company, 1989.

                                                  --Michael Naylor





Truchet :

|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  `.   '    '    `.   `.   `.   `.   '    `.   `.   '    '    `.   `. |
|-.  --' ,--' ,--.  --.  --.  --.  --' ,--.  --.  --' ,--' ,--.  --.  -|
|  \    /    /    \    \    \    \    /    \    \    /    /    \    \  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  `.   '    '    `.   '    `.   '    `.   '    `.   '    '    `.   '  |
|-.  --' ,--' ,--.  --' ,--.  --' ,--.  --' ,--.  --' ,--' ,--.  --' ,-|
|  \    /    /    \    /    \    /    \    /    \    /    /    \    /  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  `.   `.   `.   '    '    `.   '    `.   `.   `.   `.   `.   '    '  |
|-.  --.  --.  --' ,--' ,--.  --' ,--.  --.  --.  --.  --.  --' ,--' ,-|
|  \    \    \    /    /    \    /    \    \    \    \    \    /    /  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  `.   '    `.   '    `.   `.   `.   `.   '    `.   '    `.   '    `. |
|-.  --' ,--.  --' ,--.  --.  --.  --.  --' ,--.  --' ,--.  --' ,--.  -|
|  \    /    \    /    \    \    \    \    /    \    /    \    /    \  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  |    |    |    |    |    |    |    |    |    |    |    |    |    |  |
|  `.   '    '    `.   '    '    '    '    `.   `.   '    '    `.   '  |
|-.  --' ,--' ,--.  --' ,--' ,--' ,--' ,--.  --.  --' ,--' ,--.  --' ,-|
Krogg







_\__/__/__\__\__\__\__/__\__\__/__/__\__\_
 \  /  /  \  \  \  \  /  \  \  /  /  \  \
 /  \  \  /   ) /   )(    ) /  \  \  /   )
_\__/__/__\__/__\__/__\__/__\__/__/__\__/_
 \  /  /  \  /  \  /  \  /  \  /  /  \  /
 / (  (    ) \  /  \  / (   / (  (    ) \
_\__\__\__/__/__\__/__\__\__\__\__\__/__/_
 \  \  \  /  /  \  /  \  \  \  \  \  /  /
 /   ) /  \ (   / (   /   ) /   ) /  \ (
_\__/__\__/__\__\__\__\__/__\__/__\__/__\_
 \  /  \  /  \  \  \  \  /  \  /  \  /  \
 /  \   )(    )  )  )  )(   /  \   )(    )
_\__/__/__\__/__/__/__/__\__\__/__/__\__/_
 \  /  /  \  /  /  /  /  \  \  /  /  \  /
 /  \ (   / (  (  (  (   /  /  \ (   / (
_\__/__\__\__\__\__\__\__\__\__/__\__\__\_
 \  /  \  \  \  \  \  \  \  \  /  \  \  \
 / (    )  ) /   )  )  ) /  / (    )  ) /
_\__\__/__/__\__/__/__/__\__\__\__/__/__\_
 \  \  /  /  \  /  /  /  \  \  \  /  /  \
 /   )(  (    ) \ (  (   /  /   )(  (    )
_\__/__\__\__/__/__\__\__\__\__/__\__\__/_
 \  /  \  \  /  /  \  \  \  \  /  \  \  /
  )(    ) /  \  \  /   ) /   )(    ) /  \
_/__\__/__\__/__/__\__/__\__/__\__/__\__/_
 /  \  /  \  /  /  \  /  \  /  \  /  \  /

Paul Gradenwitz

tiling.ascii.uk
888   d8b888d8b                 
888   Y8P888Y8P                 
888      888                    
88888888888888888888b.  .d88b.  
888   888888888888 "88bd88P"88b 
888   888888888888  888888  888 
Y88b. 888888888888  888Y88b 888 
 "Y888888888888888  888 "Y88888 
                            888 
                       Y8b d88P 
                        "Y88P"  
 _   _ _ _             
| | (_) (_)            
| |_ _| |_ _ __   __ _ 
| __| | | | '_ \ / _` |
| |_| | | | | | | (_| |
 \__|_|_|_|_| |_|\__, |
                  __/ |
                 |___/ 
                                          
        88 88 88                          
  ,d    "" 88 ""                          
  88       88                             
MM88MMM 88 88 88 8b,dPPYba,   ,adPPYb,d8  
  88    88 88 88 88P'   `"8a a8"    `Y88  
  88    88 88 88 88       88 8b       88  
  88,   88 88 88 88       88 "8a,   ,d88  
  "Y888 88 88 88 88       88  `"YbbdP"Y8  
                              aa,    ,88  
                               "Y8bbdP"   

ASCII Character Codes:

t = ASCII 116

i = ASCII 105

l = ASCII 108

i = ASCII 105

n = ASCII 110

g = ASCII 103

Capitalised:

T = ASCII 84

I = ASCII 73

L = ASCII 76

I = ASCII 73

N = ASCII 78

G = ASCII 71