Here is my work sheet from the morning of April 9, 1993. That morning
I sketched 3 different but workable tilings, (even if one of them
is rather embarrassing!), One of these was to prove rather remarkable,
but I merely noted, as you see, “One curve, 2 critters”
By “one curve”, of course, I meant that I used the same
amphographic line segment to form each of the eight sides of the
It was perhaps a year later that I got around to reviewing my work
and attempted tilings
using both critters. I saw immediately, then, that the 2 critters
could form VATs (Variably Assemblable Tiles). And I set out to refine
their rather clunky shapes. I got two reasonably nice shapes: a
bat and a lizard, using this line variously disposed around 60-120
rhombi just as used for the arachnoid / insectoid pair shown in
the patent to the right..
But with this simple and not deeply re-curved
line there was room to flex and vary the angles of the rhombi. I
skinnied-down the rhombus in 15 degree decrements, giving acute
apices of first 45 degrees and then 30 degrees, which gave me progressively
skinnier bats and lizards. Then I fatted them up from 60 degrees
to 75 and then
90 degrees. Thus I had five different bat shapes and five different
lizard shapes, all of which would tile together.
Since one single amphographic line segment forms the four sides
of each of the 5 bats and 5 lizards, each one of these shapes will
fit and “mesh” with each of the ten shapes in four different
Once two shapes are joined, however, the angle between them may
or may not accommodate one or more other shapes. Usually putting
two shapes together fully determines what shape will fill the angle
The following text repeats some of the information given in
the "HOW TO PLAY" booklet, but in slightly different form:
Several shapes, if fited together, will not admit of any other of
the ten shapes. Those are “NO NO” combinations. Here is
a list of them: Pink and pink, pink and purple, purple and purple,
either pink or purple with either orange or blue, and either yellow
or lavender with either red or yellow green. This is more easily
remembered by Lulu’s rules, for which see the text of the book,
“The Adventures of Lulu Lizard and Bubba Bat” in its own
“gallery”. Briefly, the rules are : No skinny with another
skinny. No skinny with a slender. No chubby with a fat.
But all of them have their uses, as you’ll see below.
Here is a sampling of an endless number
of what I call “quilt-like patterns”, or patterns that
repeat themselves across the plane in rectilinear grids.
Varied though they are, those periodic patterns seem to me far
less interesting than the radial patterns one can build around “seeds”
such as these.
In building outward from centers such as you see above, there is
a constant interplay of free choices followed by their fully determined
consequences, and then more free choice, and repeat. Thus the feeling
of creation is mingled with the feeling of discovery in what is
a very pleasurable process. You guide this process. You build the
tiling, but you are again and again utterly surprised by the patterns
that develop. Are they created? Or are they discovered?
This addictive activity was particularly poignant, I recall, when
I put together these tiles.
When I had built this tiling just a little bit out from the center
of twelve Lulus I felt that the result was just going to be too
chaotic, and I almost quit to start over again. But I persisted:
plugging the required shapes into their places, and then I was amazed
to find these hyperbolas of pinks and purples plunging in toward
the center, crossing one another, and then receding outward again!
A strange and highly ordered tiling! Did I make it, or did I discover
it? And this same discovery / creativity mix recurs every time I
sit down to work / play with the Bats and Lizards.
follows a tiling I consider remarkable. Notice the “background
tiling” of brown and green,( Bubbas and Lulus), and how it
fits the polychrome radial arms.
Like many of these bat / lizard tilings, if the bright
colors are toned down,(here done by computer magic), a remarkable
oriental carpety feeling results.