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Bats and Lizards

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Click on any picture below to enlarge it!

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 two rhombuses.


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 ways.

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 between them.

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.

Here 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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2001 John A.L. Osborn. Please point all links directly to Ozbird.net. You may distribute images found on this site freely, but please attribute all to John A.L. Osborn. None of the art on this site may be sold without the permission of John Osborn.