LINE,TALK: how to make annoying wallpaper patterns

[This is a repost.  The first copy got munged, so I canceled it.]

I saw a book in the library called something like How to Create Your
Own Escher Art.  I forget the exact title.  Skimming the book (I
mostly just looked at the pictures :) inspired me to try some
tessellation exercises in ascii.

The basic idea isn't hard.  You take a repeating tile pattern, like a
bunch of rectangles, hexagons, or whatever, and then distort the tiles
symmetrically.

Here are the exercises I've done.  This first one is probably a little
hard to see.

 \ `y'  ,  \ `y'  ,  \ `y'  ,  \ `y'  ,  \ `
,-`.7  /_ ,-`.7  /_ ,-`.7  /_ ,-`.7  /_ ,-`.
 | o)_.._7 | o)_.._7 | o)_.._7 | o)_.._7 | o
-'_..' , `-'_..' , `-'_..' , `-'_..' , `-'_.
y'  ,  \ `y'  ,  \ `y'  ,  \ `y'  ,  \ `y'
7  /_ ,-`.7  /_ ,-`.7  /_ ,-`.7  /_ ,-`.7  /
)_.._7 | o)_.._7 | o)_.._7 | o)_.._7 | o)_._
.' , `-'_..' , `-'_..' , `-'_..' , `-'_..' ,
   \ `y'  ,  \ `y'  ,  \ `y'  ,  \ `y'  ,  \
_ ,-`.7  /_ ,-`.7  /_ ,-`.7  /_ ,-`.7  /_ ,-
_7 | o)_.._7 | o)_.._7 | o)_.._7 | o)_.._7 |
 `-'_..' , `-'_..' , `-'_..' , `-'_..' , `-'

If you can't see what this picture is, then I haven't been too
successful.  I'm not really that happy with it myself.  It's pretty
cluttered, and not really shaped well.

Part of the problem is it's a little small.  Small ascii art is hard
to do.  The next thing I tried is larger.

O      ))   ( ( \ \_.-'           \ O      ))   ( ( \ \_.-
   \_.' |    `.  \           __    |   \_.' |    `.  \
\#_/     `-._/        .     / _`.   \#_/     `-._/
-'           \ O      ))   ( ( \ \_.-'           \ O     .
        __    |   \_.' |    `.  \ '         __    |   \_/
 .     / _`.   \#_/     `-._/        .     / _`.   \#_/
 ))   ( ( \ \_.-'           \ O      ))   ( ( \ \_.-'
' |    `.  \ '         __    |   \_.' |    `.  \ '
   `-._/        .     / _`.   \#_/     `-._/        .
       \ O      ))   ( ( \ \_.-'           \ O      ))   (
  __    |   \_.' |    `.  \ '         __    |   \_.' |
 / _`.   \#_/     `-._/        .     / _`.   \#_/     `-._
( ( \ \_.-'           \ O      ))   ( ( \ \_.-'
 `.  \ '         __    |   \_.' |    `.  \ '         __
_/        .     / _`.   \#_/     `-._/        .     / _`.
 \ O      ))   ( ( \ \_.-'           \ O      ))   ( ( \ \
  |   \_.' |    `.  \ '         __    |   \_.' |    `.  \
   \#_/     `-._/        .     /  `.   \#_/     `-._/

A bizarrely proportioned animal, but it's pretty easy to see.  Here's
a snapshot of this pattern at an intermediate stage.

                __________________                  _ __________
            (  /                 /                 /
             `.                 /                 /
_____________/          _      /_________________/
             \ O    \.-'/     /                  \
        __    |   \_/  (     /                    \
       / _`.   \#_/     `.__/          _    / ____ \_________
      ( ( \ \_.-'           \ O     .-'/   /      \/
       `.  \ '         __    |   \_/  (    \
______ /          _   / _`.   \#_/     `.__/
       \ O     .-'/  ( ( \ \_.-'           \
     /  |   \_/  (    `.  \ '        __     |
    /___ \#_/     `.__/          _  /  `.   \#______________________
   /                  \ O     .-'/  (    \_.-'
  /                    |   \_/  (    `.
 /                 __   \#_/     `.__/
/                 /  \__/            \
                 /                    \
________________/                  ____\____________

You can see the grid of parallelograms that I started with, and
a few alternate shapes around the two central figures.

The picture at this stage is actually almost finished.  It started out
much simpler.  I didn't consciously set out to make animals.  I began
by making simple, arbitrary distortions to the tiles, something like
this:
                            __
               __|         /  \
              /   \_______/ b  \__
              \ a                /
              /               __|
__________\__/               /   \_______________
            /         __     \ a                /
         __|         /  \    /                 /
        /   \_______/ b  \__/                 /
        \ a                /                 /
        /               __|                 /
____\__/               /   \_______________/
      /         __     \ a                /
     |         /  \    /                 /
      \_______/ b  \__/                 /

There are two basic bulges in this shape, labelled a and b, applied in
a repeated pattern.  Once I had a few bulges, I looked at the shape to
see what it reminded me of.  There are many possibilities.  I picked
one thing, and then slowly distorted the tiles to look more like what
I had in mind, filling in details as necessary.

The patterns above use just translational symmetry: each tile is
facing the same way.  The next exercise I did uses reflective symmetry
as well.

    |' _     |' _     |' _     |' _
-.' < < `-.' < ( `-.' < ( `-.' < ( `-.
" ) /-'  " ) /-'  " ) /-'  " ) /-'  "
-'.'    .-'.'    .-'.'    .-'.'    .-'
.'   . `..'   . `..'   . `..'   . `..'
 Y    >._ Y    >._ Y    >._ Y    >._ Y
`|     _ `|     _ `|     _ `|     _ `|
 > `.-' ) > `.-' ) > `.-' ) > `.-' ) >
-\ ( "  `-\ ( "  `-\ ( "  `-\ ( "  `-\
  `.`-.    `.`-.    `.`-.    `.`-.
    `..' .   `..' .   `..' .   `..' .
    Y _.<    Y _.<    Y _.<    Y _.<
    |' _     |' _     |' _     |' _
-.' < ( `-.' < ( `-.' < ( `-.' < ( `-.
" ) /-'  " ) /-'  " ) /-'  " ) /-'  "
-'.'    .-'.'    .-'.'    .-'.'    .-'
.'   . `..'   . `..'   . `..'   . `..'

This may be a little hard to see too.  I originally started with a
grid of large, wide rectangles, but somewhere along the way the shapes
became thin.

More complicated things are certainly possible, such as using more
than one interlocking shape.  Escher used fish and birds, angels and
demons, etc.

Rotational symmetry will probably be awkward to do, since rotating
ascii shapes is difficult.  3-fold rotational symmetry, like Escher's
interlocking lizards, may be impossible.  (But I suppose you could
probably do a reasonable job with a solid fill technique.)

(Congratulations if you can spot errors in the repeating patterns :).
Any errors here are unintentional.)
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