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 :
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Paul Gradenwitz