Explaining tetrapter flight (Tetrapters/tetropters X)

Just a short post this time. 

The Book will not only contain paintings of animals, plants, mixotrophs and people, but will also contain explanatory diagrams. These are usually much more boring to produce than texts or paintings, but they still have to be done... I had postponed writing and illustrating the flight of tetrapters for quite some time, and have now decided to get to work and not to look up until it is done. 

The challenge here was how I could capture the complexity of tetrapter flight in static diagrams, although I already had videos dynamically showing how tetrapters move their wings. The two diagrams above form part of a set of eight. Together they depict one complete movement cycle. I decided that I would show the path of the tip of the wing in the diagram, and that a portion of the path would be shown with a bold line, to indicate the movement since the preceding diagram. I hope that works.

Click to enlarge; copyright Gert van Dijk

 

Click to enlarge; copyright Gert van Dijk

The two diagrams show the point in time where the wings are moving apart after the 'clap' phase, when they touch or nearly touch. When they then 'fling' away, they create the 'clap and fling' mechanism that provides part of the lift. For more on that, you may read some older posts indicated by their year of publication: 2009a, 2009b, 2011 and 2018. 

 

Click to enlarge; copyright Gert van Dijk

 By the way, I have started to update the main Furaha website. I will gradually add some new material, but do not want to give away too much of the content of The Book. Still, some newer paintings will creep in here and there. I changed the image on the welcome screen, and do not think I ever published that particular rusp image before. So there you are.

Postcard from Furaha

It took longer to get back to blogging than I thought, for several reasons. As usual I had less free time than planned and a shoulder problem made painting and other computer work unpleasant. Last but certainly not least, we had such a long hot spell here in the Netherlands where I live that heat records were shattered one after the other. A few nights ago we officially had the warmest night in the Netherlands since official records started in 1854: 23.6 degrees. The temperature in my computer room reached 29 degrees... If I can't sleep, I can't write, paint, or even think properly. If the climate continues in this direction, we should stop calling ours a 'temperate' climate. Global warming anyone?

Anyway, I have worked on a painting, but extremely slowly. As I save the files often, I thought I could produce a quick post in the form of a 'making of' video. I will let the video do its own talking.
 

Click to enlarge; copyright Gert van Dijk

The video is small, so here is the last frame at a larger size. The painting is not finished! The potator ('Amnesialata blansjarii') still needs much work. I think I will morph it into a microrusp. Rusps do not actually have necks, but I thought it would be useful for a tree climbing animal to be able to move its head around freely. The rusp's snout will of course solve that problem to a large extent, but another way might be to recruit the first several body segements: they could become slender and lose their locomotor function, with perhaps some tiny dangling remnant limbs. I'll see. The bioluminescent stayways may reappear in the from of tetrapters. It is fun tying the various Furahan clades together, while keeping room for new developments.     
 
The sooner the weather normalises, the sooner I will be back with more posts. 

How do tetropters walk? (Tetropters IX)

In a recent post I showed my latest animation of tetropter flight, using a brightly coloured farfalloid species as an example. As I wrote then, the reason to get down to the nuts and bolts of tetropter anatomy and movement was that I am painting a few tetropters paintings.

Click to enlarge; copyright Gert van Dijk

Here is a small fragment of the latest one. I had given most attention to tetropter wing movement, but naturalistic paintings also require details about the rest of their anatomy, such as eyes, mouth and legs. The radial nature of tetropters is very reminiscent of that of spidrids; tetropters obviously share a common ancestor with spidrids. On the whole, tetropters are much smaller than spidrids. Whereas spidrids are in the crab range, tetropters are more like insects in size. The Furahan atmosphere is denser than Earth's, which makes flying easier. The tetropter respiratory system does not wholly depend on passive diffusion, so it does not form a crucial limiting factor. Some tetropters, such as the Red Baron shown earlier, are quite a bit larger than current earth insects. There may well be tetropter species in remote areas that are as large as the giant dragonflies from Earth's Carboniferous era. These areas have not been explored in detail yet: they are far away and travel is expensive.

Tetropters have eight legs, just as spidrids do, and their gaits are in many cases exactly like those of spidrids. There are exceptions though. Tetropter legs differ in some aspects from spidrid legs. The most obvious difference is that the legs of a tetropter need not be all alike. In contrast,  all eight legs of any spidrid are virtually identical. Again, this is a bit like insects' legs, that usually differ markedly in size and shape between front, middle and hind legs. This probably makes sense because these legs have different mechanical roles, whereas tetropters do not even have a front or a back. The asymmetry of tetropter legs takes a shape that is peculiar to their radial nature, and quite fitting: there are four large legs and four smaller ones, and they alternate: big, small, big, small, etc. Over evolutionary time, the differences have become quite marked in some clades. In predators such as the 'Red Baron' the outer ring of legs has gained a grasping function. In most species both the outer and inner rings are used for walking. Some say that the differences came about in response to a need to stop the legs becoming entangled; that sounds good, but spidrids do not seem to suffer from tripping over their own legs! Others say that the small size of tetropters means they needed legs that are splayed very wide to stop them being blown over by the wind. But why should that hold for just four legs? Sometimes we just do not know... (meaning I will shelve the question for later, or perhaps I will leave it unsold. There are many things unclear in Earth biology, so perhaps I do not have to explain everything).

Anyway, here is a schematic tetropter using the 'double table' gait. Its wings are neatly held in their vertical resting position. At any time there are four legs of either the outer or the inner ring on the ground. For a brief moment there are eight. This system is just as stable as the 'double tripod' of insects. There is little or no chance of falling. Note that the body wobbles a bit. I did that just so you could see that there is a joint between the 'corpus' holding the legs and mouth on the one hand, and the cephalothorax holding eyes and wings on the other hand.

   
This specimen proves that the gait can be a bit more fanciful than the 'double table' without destroying overall stability. You may also note that the joints of the legs are arranged in a different way. In the previous species, and in all spidrids, the angles between the three big leg segments always bend in the same direction, so the leg gets curved more inwards and downwards as you progress from the proximal portions near the body to the distal parts at the tip. In this particular species, the first joint bends in the other way. In earth arthropods you can easily find these patterns too.

Finally, here is a walking tetropter in which the joints of the legs of the outer ring all curve inwards, while the inner legs have yet another pattern, starting with a downwards followed by an upwards bend. The gait is somewhat complex as well, which I like, as it gives the animal a more biological feel.

So there we are; now I can safely paint an explanatory diagram explaining how tetropters walk. After that, it's back to 'toe studies' again. I must say I am distracted because I watched season 4 of Game of Thrones again. There is a scene in a giant rides a mammoth. Hang on; as I calculated earlier, such a giant should weigh about 1440 kg! Mammoths are big and probably strong, but that is some weight! How much weight can a mammoth actually carry? That is obviously a very silly question, but also one quite worthy of this blog. I may need to find out...

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!'.

The wrong farf (Tetropters VI)

I made a few animations especially for the Loncon3 convention, some of them concerning tetrop
ters (see here for the previous tetropter post). The reason was that I wanted show some of the 'flight platforms' that tetropters could conceivable evolve into. So far, there are the 'standard, 'rowing', 'helicopter' and 'farf' modes.

Click to enlarge; copyright Gert van Dijk

These modes all have to do with the relative amount of movement in all the four ways a tetropter wing can move. The image above shows the idea: there is a general tetropter body, characterised by its vertical position, four jointed legs at the bottom and a head with sensors at the top (there is a head with smaller eyes and a mouth at the bottom end of the body, not visible here). The red, blue and green axes run through the attachment point of one wing and concern the movement of that wing. There are similar axes systems for the other wings, but these are not shown (the wings are, though, just). The arrows indicate the direction of rotation of each axes. A to and fro movement around the blue axis will result in a clockwise and anticlockwise movement. If you combine that with an up-and down movement around the red axis you get interesting patterns: the wing could describe a circle, but the most common pattern is a horizontal figure of eight. The wing moves clockwise and down, then at the end moves up quickly, so it can move down again while moving anticlockwise. That just leaves the green axis, which rotates the wing around its own longitudinal axis, allowing it to achieve the proper 'angle of attack'.

I said there are four ways to move a tetropter wing, and the fourth is not a rotation around an axis as are the first three, but warping the plane of the wing. Well, if you followed that an can envisage it, top of the class. Its more or less what you need to describe the movement of the wings of animals with hovering flight, so we are on common ground here.

I will probably come back to the other tetopter flight modes later, but let's talk about the farf mode. A farf is short for farfalla, the name the Furahan citizen-scientists gave to tetropters with a very long wing base. In fact, the image above has just such a wing membrane: you can see that the membrane lies against the vertical blue axis over its entire length. Actually, the wing membrane shown here would not be an actual one. It is just a rectangular placeholder, but is does show the principle of the thing nicely. This arrangement means that movement around the green axis cannot take place, and to get a good angle of attack the wing will have to warp considerably. If you think this scheme reminds you of a butterfly, you are right: butterflies also have wings with a broad long wing base. In fact, 'farfalla' is Italian for butterfly.

So here is an animation of a farf, made for this post, showing the placeholder wings. Not too bad, is it?

And this is the one I showed at Loncon3, with colours etc. Just about the day before I showed it, it dawned on me that I probably made a mistake in warping the wings. When the wings clap together, they have to be more or less flat, and then they should peel apart, first at the top, and then downwards towards the bottom. Well, that bit worked, but for some reasons I had also warped the wings in such a way that the distal end of the wings –that is the bit farthest away from the body- leans into the movement, so it moves before the part near the body. But the wings would encounter resistance from the air, and so the tip of the wings should probably lag behind the proximal part instead of leading it.

I do not think anyone noticed, but I also did not give the audience a long time to think about it. I will have to do another animation with the opposite effect, to see whether that looks better. But there's no time for that yet... Meanwhile, I hope you still enjoy the 'wrong farf', warped as it is.

Tetropters V: a livelier animation

Regular readers may know that I return to the subject of tetropters from time to time, in a slow and fragmented effort to produce a documentary video showing the little beasties hovering through the air as if they were real, perhaps with an appropriate narrator (as I wrote earlier, David Attenborough would be perfect).

New readers may however respond by saying "What on Earth is a tetropter!?". Part of the answer lies in rephrasing that as "What on Furaha is a tetropter!?" Well, tetropters are small exoskeletal insectoids with a radial base-four Bauplan using a double clap-and-fling wing movement. That is about as short a description as can be given, I think. Those who wish to read more can find the latest instalment ('Tetropters IV') right here, with links to the previous three chapters.

'Tetropters IV' had reached the stage where I could simulate tetropter wing movement, resulting in animations showing a completely immobile body in a completely immobile environment and a fixed camera position. To get there had required a lot of work, but so much more was needed: the animals' bodies should be detailed -and should probably have internal movement as well-; there should be a larger variety of wing shapes; the animal should tilt a bit in the direction of movement, and larger tetropters with slow wing beats should bob up and down in flight, like a butterfly does when flying. And to mimic the effect of a macro lens the scene the depth of field should be narrow, with blurring of nearby and far objects.

 Copyright Gert van Dijk

I used some time in the holiday season to work on the animation, pushing against the limitations of time and capability. The first result of that push stage is shown above, and had the animal moving about freely in three dimensions. To do so I wrote a program in Matlab to define a 3D path in x, y and z-coordinates. The movement is based on the number of frames per second and the numbers of seconds the film should last for. To keep the wings moving there is the number of frames per cycle to consider. I added a little tremor to the vertical component of the movement, so the animal bobs up and down a bit, in phase with its wing beats. All this resulted is a text file with a lot of numbers stipulating where the animal is and at which phase its wings are. The more difficult part was convincing the rendering program 'Vue Infinite' to accept all these numbers and produce a nice image per frame. I had to work on a program in the language 'Python', which I am hardly familiar with, but which can be used to control almost any function in Vue Infinite. I got over that and made the animation above. Not too bad, is it? In an earlier version Evan Black commented that an improved animation might have the effect that the coarser aspects of the design, such as wing attachment, would be less noticeable if the animation would be developed more. I think that that now proves to be true. By the way, the three axes and the balls are there to tell me whether the animal is with regard to local space. I also did not bother to set the wing cycle to match with the movement; in a real scene the wings should beat much more often over the course of such a movement.

Copyright Gert van Dijk

The next stage, shown above, involved 'lens blurring' and body tilting. After various tries and errors Vue Infinite could do lens blurring, but in a very complicated manner: there was a variable that had to entered as a percentage, so I stopped at 100%. The blurring only worked as intended when I set it to 2000%, something I learned after having received help from the Vue Infinite forum at E-on software.
  As for the body tilting, that involved rotations around all three axes. I wrote the program so i could control the rotations by hand, but added an automated feature that differentiated a position path. There should probably be a time delay in that the body should probably start to tilt in a given direction slightly before it starts to move that way, but the lack of such a delay is not noticeable. There could be various way for tetropters to change direction; they could change the aspect ration of specific wings or during specific phases of wing movement, or they could bend their bodies to change their centre of gravity. Regardless, I think the tilt adds a nice touch, rendering the flight a bit like that of a helicopter.

Copyright Gert van Dijk 

The animation above shows where I am now: camera movement. The camera follows the tetropter. As all this is a simulation that could be done perfectly, so every bob up and down would be followed, and the body would stay centred on the image with mathematical perfection. That would look very artificial: a human camera operator would lag behind the movement and would not follow tiny variations. I mimicked that by having the camera follow a smoothed path rather than the actual one, but I do not think the smoothing is good enough yet; it probably needs a delay function as well.

Oh well, there are enough things left for the next stage, such as adding a suitable body. I will probably sculpt one in Sculptrix or build one in Vue itself. The latter option will result in an artificial technical look but has the advantage of colouring the animal with ease. The Sculptrix option will produce a much more biologically looking body, but requires colouring in some other program, another new task to learn (apparently Photoshop can be used to paint 3D objects). So, do not hold your breath, but 'Tetropters VI' will probably be the final documentary, adding all the items mentioned earlier.

Except for the narrator, I am afraid...

Its a bird, it's a plane, it's... a tetropter (tetropters IV)

The nice thing about computer animation is that it allows you to actually see thing that you could only dimly imagine beforehand. One image that has been sitting in my mind for many years is the following: you see a dusty plain, and a herd of handlebars (Latifrons imperator) come galloping in from the right hand side of the image in the distance, and then wheel towards the viewer as if they were performing a well-rehearsed cavalry manoeuvre. I can almost hear them too...

Unfortunately I do not see anyone spending a small fortune to make this a reality, so I will have to content myself with what I can do myself, with my PC, at home. Some visions therefore remain locked in my head, but a few more modest ones do find their way out. Making tetropter flight visible is something I thought I worked on for quite some time; today I can show you a near-final result. Near final, because nothing creative is ever truly finished. In this case, the camera should move, the animals should vibrate in rhythm with the wing beats, there should be more details, there should be motion blur, and there absolutely has to be blurring to mimic a limited depth of field and through that create the illusion of small size.

Still, what I can show you is the principle of the thing. It's not a movie, but an illustration of wing movement in slow motion. Tetropters have been described several times on my blog. A summary of the tasks involved in animating them is found here, and entries on their design and wing movement patterns are here, here and here. In short, they are radial flying animals, whose four wings can do a 'double clap and fling', invented by yours truly, and later also by other people in the flying robot business. By the way, the movement of tetropter wings is not all that different from the complex way in which Earth insects move their wings.

This is an animated scheme to show how it all works: the wings are planes that are warped as they cycle through their movement cycle, so their shape is different depending on were they are. Where they are is governed by rotations along the x-, y- and z-axes, and all these paths can be altered and edited. The Matlab programs that do all this in the end write lots of 'obj' files: those are files describing 3D shapes; one is produced for each wing for each frame of the cycle (there are usually 120 frames in a cycle). A script written in Python then loads in a scene containing a body shape without wings in Vue Infinite, adds the appropriate wings per frame and stores the images. These are then used to form an animation, and those are what you see here.
The 3D shapes of the wings consist of 1600 small triangles, which is more than enough to show supple movement. As they are they do not look like wings at all, but there is another trick to take care of that.

The trick in question is to add transparency and colour. The transparency mainly makes unintersting parts invisible, but it is also useful to make the wing itself partly transparent as here. To create the fly-like animal above (Bombilator musca) I used an image of a real insect wing found on the internet, and used that to create a transparency mask. All of a sudden, the boring rectangular 'wings' produced by the Matlab program take on a biological appearance. Please do not look too closely at the body of the animal: it is a simple shape cobbled together in Vue. As you can see the animal has four legs and two sets of eyes: upper ones, presumably to scan for danger, and lower ones, near the food gathering end at the bottom.

A bit of colour makes a lot of difference, so here is a farfalloid, resembling a butterfly in overall appearance (Farfallapter caeruleus). Indeed, I stole its wings from a real Earth butterfly, albeit with some warping and editing. Mind you, quite a bit is lost in the conversion process.

Click to enlarge; copyright Gert van Dijk

To show that, here is a still of the Farfallapter; better, isn't it? Then again, you can see how crudely the wing is linked with the body...

I guess I now no longer have any excuse to put off work on the 'Flying with...' page. It is probably also time to redesign the site. I have already looked at that, but the days where you could learn HTML in two evenings seem to have gone for good.

Three years on

More than once in the three years I have been writing this blog I thought there were no more interesting speculative biology projects to be found on the internet, but each time I was wrong. Will the supply dry up? Perhaps not: there are more and more exquisitely detailed Z-Brush monsters, but mostly those are orcs, dragons and the like. In other words: they are not very interesting from a biological point of view. The reverse situation can also be found: well-thought out projects with artwork that does not do it justice. I guess I will simply have to wait and see how much content I can find to fill the 'allied matters' component of the blog. The number of page views slowly went up over time, which is rewarding.

So how about the 'Furahan biology' component? There is progress, if you account for the glacier-like advance of a very large project that you do not really have time for. Then again, in the last three years I got to grips with InDesign, Photoshop, Painter and XBrush (not that I am proficient in any). The most noteworthy skill I am trying to acquire is digital painting, which is the most needed one. I think I need to do some 10 additional illustrations of the "It's a fish" type, and then I will have some 15 two-page spreads to show to potential publishers. An example of those can be found in the New Hades book shop on the Furaha site: got to the brand new 'Living World Series' and you will find the 'Encyclopaedia of Furahan Wildlife' (also shown here). I aim to use that lay-out to present the book to publishers.

Rough tetropter animation; copyright Gert van Dijk

It is not difficult to think up many new animals or plants; many forms that I have now could do with some adaptive radiation. But my interest is mostly aroused by more complex puzzles. As an example I will explain the struggle to produce a good tetropter flight animation. The basic principles have been outlined before (start here to work back in time), but for good measure I have repeated an old animation above. As you can see the animal is shown from below, and the four wings move to and fro while rotating. They also move through one another, because the animation uses stiff planes for the wings: it is not good enough. I want a better one firstly, because I am curious: I wish to see what a spotted farfalloid looks like, when its beating wing reveal electric blue surfaces at one point in their cling and flap cycle, and bright orange ones the next! The second reason is that I would like to paint a variety of tetropters -talk about infinite variety-, and getting the perspective right of four warped surfaces in complex motion can be done by hand, but would be easier to manipulate by computer. I will break the problem into pieces:

Problem 1: defining movement
The wings can easily be modelled as surfaces in Matlab. These move through the wing cycle, meaning there are different requisitions for movement around the x- y and z-axes. To control them I wrote editing programs, now nearly done. The surfaces cannot remain simple planes throughout the movement cycle, but will have to be bent and warped. The animation above shows where I am now, meaning at the phase where all the 'warp factors' have to be tweaked to get it right. What you see here represents 'untweaked warping' though!

Problem 2: exporting the wings
The 3D program I am most familiar with is Vue Infinite. I had already written a program to convert Matlab patches to obj. files, which helps. But I then stumbled upon a new program, ad that was the imported wings for successive frames did not end up at the same spot in the scene. Apparently Vue calculates the mean of all x-, y- and z-coordinates to calculate the centre of an object, and if the object changes shape so does it centre. Well, I can counter that by shifting the object each frame to compensate. This needs work...

Click to enlarge; copyright Gert van Dijk

Problem 3: texturing the wings
Obviously, the wings will need interesting patterns on them as well as partial transparency. That, as well as bump maps, proved to be in the obj. definition and could be manipulated.
Here is a rough example of a warped wing with transparency and all in Vue.


So now you may understand why it has taken such a long time to put up a 'Flying with...' page, along the 'Walking with..' and 'Swimming with...' pages: the tetropter flight animation has to be ready first, and that is a big job.

Nereus (or how you can have radial flight with an odd number of wings)

As regular readers know, I am always on the lookout for creative projects concerning speculative biology. On places like Deviant Art you will find many interesting alien or alternate animals. Some feature new traits, others rework well-known themes; some are professionally drawn, others are less so. But what interests me most if there is a background: are there biotopes, is there a food web, do the predators match the prey, etc. That shortens the list considerably.

Some large projects have been in existence for very long times, and it does not feel entirely right to discuss them here. But there is one project, Nereus, that is relatively new. Its creator, Evan Black, does not mind, so that helps. Apparently Nereus received its name because humans first thought it was a water world (Nereus is a being from Greek mythology). The earliest post on the Nereus project on the Speculative Biology forum dates from May 2009. Evan has already produced 100 species and aims to achieve no less than 200 species. That is a lot or work: creatures have to be designed and described, and also drawn. I like the way Evan draws animals: while a bit stylised, they are very energetic, and as design they work: what you see are lively animals.

Click to enlarge (VERY much so!) Copyright Evan Black

Here is a start: a rather large cladogram of current Nereid species. Don't be surprised to find that the one on Evan's site differs from the one here, because he might have added a new species by the time you go there...

The Speculative Evolution pages contain discussions and comments on how Nereus develops, but I much prefer to see the result on Evan's own site. There, you can work your way through the menu, clicking on the Latin names of the various groups until you get to individual species, but you do not see what you are aiming for until you get to the species pages. Once there each species has two pages: one with text and a thumbnail, which leads to a much larger image with additional text. But there is another way to browse Nereus that I much prefer, and that is to choose 'world', and then 'cartography and climates'. That will take you to a list of 7 biomes, and clicking on them rewards you with an overview of that biome and small images of the species in it, that you can then pick and read at will.

Click to enlarge. Copyright Evan Black

As an example, here is the 'Sog Basin'. Sog "carpets the landscape like a thick tangle of spongy red veins", which sounds a bit like Well's Martian weeds. Luckily, there are no intelligent aliens around to regard Earth with envious eyes (or not yet). Sog sucks up water from the few available sources, and transports it across the otherwise dry biome. Leaks in the sog create watering holes, on which many species depend. Now that is why I prefer creations with a background: you immediately start to think how that works, how such species might look, etc.

Click to enlarge. Copyright Evan Black

Here is one such species: the kappa (Nothorana pratensis). It is a predator lying in wait in sog ponds, with just its dorsal eyes and its nostrils above the water. Take a good look: the kappa has three legs: two paired front ones and one unpaired jumping leg in the back. The illustration also contains a classification list containing the familiar Linnaean scheme, which starts at the species level and goes all the way up to the phylum Tetrabrachia (that would be 'four arms', if I remember my Greek correctly). One of the nicest things about Nereus creations is that it all fits together. Look up the Tetrabrachia, and you will find a page devoted to their anatomical Bauplan.

Click to enlarge. Copyright Evan Black

And here it is. The four arms in question concern four major nerve trunks emerging from the central brain. One trunks goes upwards, and that one deals mostly with sensory functions, which in modern Tetrabrachia has caused them to develop a head. The other three trunks control movement. In effect, what we are seeing here are radially organised animals, and I like the idea of taking radial animals rather further than they have managed to do on Earth (see the discussion on tetropters here, here, here and you can more on tetropters yourselves; here is something about radial symmetry; if that is not enough, just search for spidrids on this blog). But the kappa does not show radial symmetry; it is blatantly bilaterally symmetrical, and the legend includes information just when that happened.

Click to enlarge. Copyright Evan Black

I cannot resist showing one particular specimen, and that is because Evan and I discussed its s flight mode. Again, this is a radial life form. Most flying forms on Nereus are bilaterally symmetrical, resulting in flight plans that are superficially similar to the ones on earth. Not so the Cliff Whistler (Cadosmilos Aetopsis).

As you can see, it flies a bit like my tetropters. The tetropter discussions may have helped inspire the Cliff Whistler, which is flattering. Anyway, the Whistler flies by beating its three wings horizontally to and fro. Diehards out there may remember that I made extensive use of the 'clap-and-fling' principle to explain tetropter flight. The 'clap' involves two wings beating against one another at the end of their movement, then sweeping back to the other end of their range, where they then clap against another wing. Etcetera. That works with two wings (Terran insects and some birds), four wings (Furahan tetropters) and would work with more wings too, although no-one has yet invented any of those yet as far as I know. Besides offering increased lift through 'clap-and-fling', an even number of radial wings neatly solves the problem of torque: if a wing moves clockwise it pushes the body counter clockwise, which is useless. With two or four wings these forces even out.

Three-winged radial flyers run into problems. There is no clap-and-fling mechanism, and the wings move in unison: all three clockwise, and then all three counter clockwise. That leaves torque to be solved. Well, evolution, in the form of Evan, designed an adaptation of the Whistler's mouth parts at its bottom: these evolved into winglets beating in the opposite directions of the main wings, countering to a degree. Enough for the Cliff whistler to be a viable organism, or so Evan and I thought.

Recently I came up with a way to have a clap-and-fling mechanism with just three wings though. It would increase lift but introduce some new problems. Again, Evan and I thought that it might work, but not necessarily better than the Cliff Whistler approach. Perhaps one species will emerge on Nereus with this particular mechanism, we would have to ask Evan. I am not going to tell you how it works, merely that it can be done: each of the wings A, B and C claps against another wing on the extreme ends of its movement range. I wonder if anyone will take the bait...

Walking without Legs

Pardon? Is walking without legs possible? Well, if you stretch the definition a little...

There are quite a few terrestrial animals on Earth that have no legs; earthworms, legless lizards and particularly snakes come to mind. These are not evolutionary misfits whose leglessness will be their doom any day now. Snakes have been around for some 150 million years, after all. Limblessness in legless lizards seems to have evolved at least 8 times, also suggesting that 'not having a leg to stand on' is not necessarily a bad thing. It is probably a very good thing if your life style requires moving around in confined spaces where legs might hold you back, such as underground, in very dense growth and probably in crevasses between rocks. In fact, you may well wonder whether legless animals might be universal, found on many worlds across the universe.

If so, would all 'serpentiformes' or 'ophimorphs' (take your pick) move in the same way? That is debatable, as there may be one or two possible gaits that do not seem to be in use on Earth. How do animals without legs move on Earth? There are animals whose body length can vary, such as earthworms, but let's only look at those with a fixed body length, such as snakes. You can find more on that using Wikipedia etc., but here is a short summary.

The internet did not let me down in a search for interesting material. In the past I have found that some of my biomechanical ideas to design interesting life forms had also been invented by others designing robots, such as tetropters (radial flyers). In this case it was the other way around, and I came across a mechanical invention that might perhaps be 'biologified'. I found it on the website of the biorobotics laboratory of the Carnegie Mellon School of computer science, where they have lots of interesting material on the design of robotic snakes (there are other robot snake designers, but this site seems to cover all aspects).

Click to enlarge; copyright Gert van Dijk

Click to enlarge; source here

The basic element of robotic and live snakes is a segment (vertebrates are just as segmental as arthropods; the segments are just less apparent form the outside). In the picture above each segment is connected to the next with a universal joint, allowing movement up and down and sideways. The robotic snakes seem to have joints with just one axis of rotation (either up-down or sideways), but these alternate on consecutive joints. There is no movement along the longitudinal axis of the segments. Well, in animals there is almost always a bit of leeway, but not a lot; it's certainly not as if a segment could rotate 10 or 20 degrees along a longitudinal axis. It is tempting to adapt the design to allow more longitudinal rotation, and it would increase the 'alienness' of the design. (We need a word to describe how 'alien' an animal is compared to 'life as we know it'; 'alienosity'?)

Anyway, Earth's snakes can move in various ways. There is the 'rectilinear' mode, in which a bit of skin on the belly of the snake is lifted, moved forward, and put back on the ground again. The next bit of skin does the same thing but slightly out of phase, so you end up with a wave of skin rippling backwards along the belly of the beast. As the ripples push against the immobile earth, the snake moves forward. Think about this: part of the body, while lifted from the ground, swings forwards with respect to the centre of gravity of the body, and when it is on the ground it swings backwards: that is a description of what a leg does, if not what a leg is. A fine distinction, but an interesting one: do you define walking by its functional characteristics, or by the body parts that carry out the function? I tend to prefer the first option, but the consequence would be that snakes walk, and that departs too much from common use of 'walking'.

A very interesting snake gait is 'sidewinding'. Here, the snake lifts an entire segment of its body from the ground, moves it forwards, and puts it down again. You get the picture: a walking analogue again. The robotic snake does it too, with waves travelling down the body both in the up and down and sideways directions. In real life it is quite difficult to get a good understanding of how this works using just diagrams, but the videos shown here might help. Sidewinding provides snakes with their fastest way of locomotion: it is the 'running' of the snake world.

Now we get to the creative part: a gait snakes do not use. The robot's body is moved into a curve, so it lies in a plane. Now imagine that you change the direction of curvature a bit, so both ends of the animal would be lifted from the ground. That is not going to happen, as the uplifted ends of the body will fall towards the ground. The result is a C-shaped curve that rolls forward, a bit as how you would move a log by rolling it over the ground. I was struck by the creative beauty of this solution.

But before people trot off to design rolling metaserpents for their own worlds, they should think about why Earth's snakes don't do this. Rolling along the longitudinal axis of the body will cause the animals' head to spin quite literally. The poor animal will have difficulty in keeping its bearings. Regular readers may remember that there was a similar problem with cernuation. I wouldn't say this form of locomotion, which the robot designers called 'rolling', is impossible for animals, but the animal better have very sophisticated vestibular and equilibrium systems. Alternatively, or additioanlly, the head could do its own counter rotation, in the same way cernuating animals could temporarily keep their head still. Spinning ballerinas also rotate their head opposite their body to keep it still in space, and they are not alien (perhaps a tiny bit).

Here is another example of what 'rolling' can do: the designers have actually been able to make their robot climb a tree! Spectacular, isn't it?

And finally, a robot that is not very prominently displayed on their site. They call it the 'skin drive', and about the only information is that it uses its entire skin to move. From looking at the video, it seems to have flexible rubbery skin, and underneath that there must be series of elements that can be stuck out radially and retracted again. I guess that waves of extraction and retraction march backwards across the body, as if you would push successive fingers against a sheet of rubber. If these fingertips find enough traction against the ground, they will stay in place, and the body as a while will be pushed forwards. It is a bit like 'rectilinear' snake movement, but not exactly the same. I wonder where the inventors will take it, or where its evolution will lead to.

"Go, tetropters, go!", or, "Tetropters III-bis"

Originally, I had wanted to include the following material in the previous post, but I could not get hold of the material in time. What I am referring to is a paper in the 'Journal of Aircraft' by Zdunich P, Bilyk D et al., entitled "Development and testing of the Mentor flapping-wing micro air vehicle" (J Aircraft 2007; 44: 1701-1711).

In the paper, the author describe the development of the Mentor air vehicle and elaborate on the radial 'body plan'. They did not use those particular words, probably because they did not have biological mechanism in mind. The text makes it abundantly clear that the two pairs of wings beat against one another and use the 'clap-and-fling' effect. Here is a quote from the paper (I omitted references):

"In 1998, however, the primary source and inspiration for the Mentor's configuration came from the "clap-fling" hypothesis of Weis-Fogh, which was developed by observing the behavior of small hovering insects. It was found that they produced extraordinarily high values of average lift coefficient, which was well beyond any explanation based on attached-flow aerodynamic theories. The hypothesis, based on observation of the wings' kinematics, was that the two wing surfaces clap together and then peel apart starting at the leading edge. At the instance just before the trailing edges come apart, both wings have strong equal and opposite bound vorticity. Further, because the trailing edges were joined during this peeling action, the strength of the vorticity is much greater than that produced from Kutta condition considerations. As the wings fling apart they carry this "super circulation," which thus produces a high value of lift."

J Aircraft 2007; 44: 1701-1711; Click to enlarge

Here is a computer sketch of the vehicle. The wings are at the top, and the three blades below are control surfaces.

The authors did some proper preliminary experiments as a proof of principle. The most important such principle was that the clap-fling design indeed augmented lift. To do so they clamped their wing set-up to a lab bench and measured how much thrust it provided. They did this once with the complete wing assembly, i.e., the two pairs moved to and fro produced the double clap and fling movement. They then repeated the experiment with just one pair of wings moving back and forth. These wings obviously had nothing to clap against, thereby eliminating the clap-and-fling contribution to thrust. Thrust was of course less because there was only one pair of wings in this particular experiment, but that was easily solved by doubling the measured thrust value. A comparison shows how much the clap-and-fling effect contributes:

J Aircraft 2007; 44: 1701-1711; Click to enlarge

The resulting graph shows that the thrust-to-power ratio is higher at all wing beat frequencies if there is a clap-and-fling effect than if there is not. Well, that settles that! I will stop discussing the tetropter wing design now, as I think the case has been proven. Future posts may deal with some other intriguing flight designs I came across searching for 'micro air vehicles'. These could well be used for alien life forms.

But I cannot help adding a final remark, even though I may be accused of vanity. The quote above makes it clear that the design of the Mentor took shape in 1998. I checked my Furaha design sketch book for the first sketches of tetropter flight plans. I had worked out three 'gaits' producing different amounts of lift, tilt and rotary effects over each wing cycle, and remember settling on the one discussed here because it balanced all these effects nicely. The page dates from April 30, 1996. Perhaps there are others who came up with such a design earlier, but for now, I like to think that I was the first to design a radial body plan using a double clap-and-fling with a vertical axis. I need a snappier name for that. Anyway, I doubt that this invention will make me a millionaire...

Go, tetropters, go! (tetropters III)

In my last post on tetropter flight I tried to find some kind of proof that the way I imagined tetropters to fly is valid. Just to make certain everyone knows what tetropters are about I will provide two rough sketches of what tetropters look like:

A tetropter on the verge of being snapped up by a tetrapterate

A few examples of tetropters in flight

I turned to the world of 'micro air vehicles' for proof, but had to end the post with a question, as I could not find solid proof that a similar flight mechanism had indeed been invented.

Luckily, I can now report that there was indeed such a flying vehicle: the Mentor, and it flew in 2002! I emailed Roy Kornbluh (see the previous post), and he was kind enough to confirm that each of the Mentor's four wings clapped against both of its neighbours. Moreover, he directed me to a website with footage of the vehicle in flight. If you want to see it at its original place, you can find it here.

But you can also simply admire it here:



So the radial flight principle has been proven!

That does not mean that tetropters must exist on other planets. But my hypothesis is that they could, and that their mode of flying makes sense depending on what you start with. Perhaps ancestry is the simpleanswer to the question what determines whether evolution produces radial or bilateral flying body plans. Animals with bilateral symmetry that take to the air will probably end up with bilateral wings. All animal groups that evolved flight on Earth (insects, pterosaurs, bats and birds) started with a bilateral body plan in the first place. But if animals such as starfishes had gone for a more active mode of life, and had made it to land as well, perhaps their descendants would have made it into the air. If so, they would have started with a radial body plan. If evolution had taken this course, perhaps there would be animals with radial flight on Earth right now. For now, it's just machines.

Tetropters

Those who visited the land and sea pages on the site may have wondered why there is no page on the biomechanics of flight, seeing there are pages on 'Walking with...' as well as on 'Swimming with...'. So where is the 'Flying with...' page?

The simple answer is that I am not happy with it yet. There is material on ballonts and on tetrapterate (four-winged) large flyers, and some are in fact shown on the 'air' page. But these organisms are fairly like Terran birds. For a true oddity the tetropters should be considered; in their case, 'oddness' does not reside in them having four wings. After all, Furahan tetrapterates and Terran insects also have two pairs of wings, i.e., four wings, so that isn't really extraordinary. No, the ordinariness resides in the description: 'two pairs of wings', and that says it all: the wings are arranged in pairs. Insects and birds (and Furaha tetrapterayes) all have a body scheme with bilateral symmetry, so their limbs are arranged in pairs.

Not so the tetropters. To be honest, the very first sketches I did of them did show bilateral symmetry. The top animal in the following image shows that primordial tetropter. In fact, their wing movement patterns had already been worked out, and showed a pattern that was exactly the same for each wing. So the wings showed a radial pattern, like a four-pointed star, but the body hadn't kept up. Here is one of those early tetropter designs under attack from a larger tetrapterate.

With their radial wing pattern tetropters were excellent hoverers, and control over wing movements should have allowed omnidirectional movements. But the animals still had a front and aft side. If you have a flight system that allows such tremendous manoeuvrability, why limit it with a limited body design? That is where the concept of complete four-sided symmetry came from. The next sketch illustrates the next logical step in the evolution of the tetroper concept. The top animal has bilateral symmetry, but the bottom one represents a conceptual novelty: the body follows the wings! So the entire animal now shows complete quadriradiate symmetry. By the way, I was taught that you should not mix Latin and Greek roots, and that is explains the switches between 'tetra-' (Greek) and 'quadri-'(Latin). Can't be helped.


I know of no such designs on Earth, although there are animals with five-sided symmetry (starfish, sea urchins etc.). The rest of their body scheme hasn't been worked out in much detail. The design problems are like those of octapods, with eight-sided symmetry. Tetropters too have eyes above as well as below their 'equator', and the mouth parts are all on the ground side. But I haven't done a complete drawing or painting of one yet, so the details remain sketchy - for now.

I found that the flight patterns had much in common with the movement patterns of flying and walking organisms. After all, each leg or wing or flipper moves repetitively, and any gait is no more than a cycle in which the limbs move with a specific set of phase offsets. Although there are an infinite number of ways in which you can do so, only a limited number make much sense. And so tetropters have 'walks', 'trots' and 'paces'. The first pattern shown here is a rather silly one.



I can't show the animated gif here; to see it click here.

Imagine the sphere as the animal's body, seen from below and to the side. The four wings are rotated around their axis to provide lift while going clockwise as well as moving back anticlockwise. While such a pattern does provide lift, it would also result in a net rotation effect on the animal as a whole, which is impractical. To offset that, the rotation forces need to be cancelled by having two wings swing in the opposite direction from the other two. A rough animation of just such an effect follows:


I can't show the animated gif here; to see it click here.

You can see the wings going through one another; in reality they would of course not do so. That's why I need to do a better animation, but it is not as easy to do as it sounds. In the smallest tetropters the wings clap against one another and then to move in the other direction. Many Earth insects use this technique, by the way: the clap their wings together behind their backs, and this apparently generates lift when the wings move away from one another again. In insects, there is just one such 'clap' in each cycle. Tetropters have taken the idea one step further, and the clapping occurs twice in a wing cycle, not just once.

Larger tetropters usually avoid clapping the wings together, so they reverse direction without touching. Whether this is aerodynamicaly better or simply avoids damage to the wings remains to be seen. There is so much to be researched...