From freezing the anatomy of tetropters to op art (Tetropters VIII)

Tetropters have been discussed in this blog several times. Eight posts were devoted to them (one, two, three, three bis that doesn't really count, four, five, six, and seven) and they were mentioned more often. In fact, they first featured in the third post ever, published on April 27, 2008. Attentive readers may note that the 10 year anniversary of this blog is coming up, and I intend to write more posts this year to honour the occasion.

Tetropters are flying animals with a radial symmetry, something that was not common at their time of invention, well before they featured in the blog. They fly with a 'clap and fling' mechanism, also used by various flying animals on Earth: the animal brings its wings together over its back and then separates them again, starting at the top. This apparently creates a lower pressure above the animal, which helps the animal to stay in the air. Earth animals, with their two wings, have one 'clap' in each movement cycle of the wings; Wikipedia has a short section on it. Tetropters have four wings and move them in such a way that there are two 'clap' events in every wing cycle. I was delighted to learn, years after their 'evolution' as Furahan animals, that someone had had the same idea but with the purpose of building an actual flying robot using the double flap and wing scheme. I wrote about that in this post.

At present I am working on the second of what will probably be three two-page spreads on tetropters. The first detailed paintings of a specific animal (or plant or mixomorph) always represents a bit of a crisis, as the characteristic features of a group, its Bauplan, have to settled for good: it has to be frozen. Tetropters had  four wings and I knew their movement pattern, but that left many other decisions to be made. How many eyes should they have and where are these eyes placed? They are presumably related to spidrids, so which features should they share? Should they have eight legs or four? If the mouth is placed at the underside of the animal, how does that reach its food? The list goes on. I have frozen the Bauplan of spidrids, cloakfish and Fishes I to VI in the past, so the process is familiar by now. I confess that I have kept one of the most difficult decisions for last, and that is the suspension system and leg anatomy of large hexapods: I wish to avoid a mere doubling of hind legs or of front legs, which is how most illustrators solved the problem of designing animals with six or eight legs (see my posts on Avatar and thoats).

The first decision regarding tetropters was that it dawned on me that I had not considered the etymology of the word well. The word is derived from the Greek roots for four, 'tetra', and wing, which is either 'pterux' or 'pteron'. In biology just the stem 'pter' is used often. So where did the 'o' come from? I guess I just used 'o' to string the two roots together, or perhaps because of an association with 'helicopter' (a combination of 'helikos', meaning winding, rolling, turning, and 'pter'). As an aside, the Lexilogos websites for Latin and Classical Greek are useful for such things). But as 'tetra' already ends in a vowel, no other sound is necesary to connect the two words, so 'tetropters' are now 'tetrapters'. In the posts I will stick to tetropters or other posts will be difficult to find.

Click to enlarge; copyright Gert van Dijk

Readers will be more interested in what the animals look like. Well, here is a drawing from the famous 'Field Guide to Imparian Tetrapters', showing the male and female forms of the 'Red Baron'. These animals are large, for tetropters that is, predatory tetropters that prey on other tetropters, catching them in flight. They have long wings and are very manoeuvrable. You may note that the outer legs have evolved into grasping limbs, leaving just the inner legs as a landing gear and to walk around on.

To help me get a good idea of tetropter wings in flight I dusted off earlier tetropter animation programs, relying on an unwieldy combination of Matlab, python and Vue Infinite. When I first made these programs I dreamed of producing 5 or 6 minutes high quality films; the one above was made with this idea in mind. Later I realised that these required considerable investments in time, time that might be better used working on The Book directly. So I gave up on nice backgrounds with leaves moving in the wind, etc., and just use animations as a scaffolding for the paintings.

This first animation shows a general undetailed tetropter in 'helicopter mode': the wings are relatively long, and when they move through their 90 degree movement from one clap to the next, they do not move down very much. The 'angle of attack', that is the angle of the plane of the wing compared to the direction of movement, is low. One extreme angle of attack would be a flat plane moving at a right angle to the wind, creating maximum drag but no lift. The other extreme has the plane moving exactly parallel to the wind: no drag, but again no lift. The optimum angle of attack should be one that for a given air speed creates the most lift for the least drag. This is also the flight mode for the Red Baron.

I have played with the structure of the wing, which is transparent with some bright red spots. The structure is much like that of insects, with a thin membrane, taut between 'spars' that give it its shape. There are two main spars to help control the curvature of the wings during flight. I tried to envisage completely unearthly spar structures, but all my attempts ended up looking like insects; let me know if you find a workable unearthly design. Note that the speed of movement shown here is not at all the natural one: for earth insects, wing frequency varies between 4 and 250 Hz, with low frequencies for large butterflies (I might write a short post on tetropter wing beat frequency taking air density and gravity into consideration).

This second example shows a 'rowing' mode of flight. Here, the wings beat down over a large angle and the plane of the wings is at a large angle to the direction of movement, somewhat in the way the blade of an oar is at a right angle to the direction of the stroke.  I should probably have made the body a lot smaller in relation to the wings, so the animal can beat its wings like Earth moths or butterflies: slowly, so the colour pattern can be appreciated. Just think of the animations as showing the animal in extreme slow motion.

Still, I could not resist adapting the animation to show a wing movement at 4 Hz, which is really low for Earth insects.  The colours stand out less.

The third and last movement concerns a mixture of the two flight patterns shown above: not too flat nor too steep, but just right. Again, this should be probably a large animal with a smaller body. There is some reasoning behind the bold colours.

I assumed that animal vision in relevant Furahan animals deals separately with colour contrast and with luminance contrast, just as the human visual system does. Generally, if you wish to see detail, use a large contrast between light and dark (i.e., a big luminance difference). You might think that colour differences are more important, but they are not. Designers know such things; here is a nice NASA image that explains the use of both types of contrast from a design point of view.

Click to enlarge; copyright Gert van Dijk

Colours can do strange things: the visual resolution differs between colours, with blue as a particularly poor colour to use for spatial information. Here is a trick to show that: the original is at the top left. I used that to blur two of the three colours red, green and blue, leaving one colour in its original sharp form. You will see that the clarity of the image really suffers f the green channel is blurred, but that the image does not suffer that much if green is unaffected. What this simple experiment shows is that blue and red, mostly blue, have a poor spatial resolution. Interesting things happen if you put two contrasting colours side by side, and tweak their luminance until they appear equally light or dark. This contrast has a poor spatial resolution, making shapes seem to float or flicker. This is just one of the properties of the visual system that op art relied on. Just type in op art in Google and do an image search.

I used such a design for the wings in this tetropter. Each wing has a bold pattern of two colours. Two wings have their colours placed opposite to the other two. The idea was that the wings in a near-clap position would provide a visual shock. Theoretically the to and fro sides of each wings could have contrasting patterns as well, to provide even more dazzle.

Here it is again, manipulated to result in a 4 Hz cycle. Does it work? Such visual effects rely on the properties of the visual system, and those will differ greatly between different animals. One species op art is another species' drabness. I have often wondered whether the colour patterns of some  Earth animals evolved to create a specific visual effect in a specific visual system. For instance, what effect do the stripes of a zebra have on the visual system of a lion, perhaps at night?

I will equip a Furahan farfalloid tetropter with a similar pattern, in the expectation that its colours will ignite at least one visual system, probably those of potential mates, to make it something like 'Wow!'.