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...

Crabs as spidrids, spidrids as crabs...

I recently realised that Earth crab locomotion resembles Furahan spidrid walking more than I expected. I may have spent too much time on spidrids or not enough on crab locomotion, as there was a lot to learn about radial walking, odd as that may sound. I found a very nice paper on walking patterns of decapod crustaceans (basically crabs and lobsters) beginning with the sentence 'Most decapod crustaceans can walk in any direction they please'. 

From: Vidal-Gadea et al. Arthropod Structure & Development 2008; 37: 95–108 (adapted)

The image above is from that paper and shows leg movements of a sideways-walking crab, a forwards walking crab, and a forwards-moving lobster. The ability to move in any direction without turning the body is one of the main features of a radial walking design, something I thought did not exist on earth. Apparently crabs, particularly forwards walking ones, are quite 'radial'. In fact, the paper uses the very word 'radial' to describe leg positions for the forwards walking crab. A peculiar convergence with spidrids is that its common name is 'spider crab' (Libinia emarginata).

 Source: http://www.youtube.com/watch?v=_wZZ6N8aM3Y

While most crabs preferentially walk sideways, they can combine directions and walk diagonally if they so wish. The video above shows a crab that starts walking backwards but gradually adds a horizontal element until it ends up walking sideways only. (Click the link to see the source at a better quality).

Source: http://www.youtube.com/watch?v=uYXJ5Ww361s

And here is an example of a forward walking crab. Again, the original has better quality. If you look carefully you will see that the legs do not all point sideways: the front ones are angled to the front, and the hind ones point almost backwards. In short, they are almost placed and held radially around the body. Are spidrids crustaceoid or are crustacea spidridoid?

Click to enlarge; copyright Gert van Dijk

Spidrid legs, although the mere result of a thought exercise, are rather like real crab legs. The image above shows the simplified leg anatomy, say of a sideways-walking crab (or of a spidrid leg). The bottom part shows that the leg can turn forwards and backwards around a vertical hinge close to the body, movements labelled 'promotion' and 'remotion' in technical papers. Let's call that the 'body-leg joint'. The other joints, the 'intraleg joints', in spidrids have horizontal axes allowing the leg to be straightened and flexed (see the top part). There would be muscles for every joint, but I only showed them for one.

If the animal moves in the direction shown here the leg does not need  action of the promotor and remotor muscles: the power for movement comes from the intraleg joints.  If you rotate the direction of movement 90 degrees, muscle force for this leg has to come from the body-leg joint, meaning the promotor and remotor muscles.

Click to enlarge; Copyright Gert van Dijk

So what does all this mean for spidrids? Well, regardless of the direction it walks in, a spidrid has some legs parallel to the direction of movement and some at a right angle to it. The image above shows how that relates to the direction of movement and to the necessary range of motion. The legs parallel to the movement function as the legs in sideways-walking crabs, and  depend on intraleg flexion and extension, pulling and pushing the beastie. The legs at largely right angles to the movement depend on promotion and remotion. The leg in between simply make use of both sets of muscles to varying degrees. (Mind you, the word 'promotion' in crabs always refers towards the front end of the animal; in adapting it for spidrid use it must mean 'in the direction of movement', there being no front end.)

The next evolutionary spidrid twist stemmed from the idea that one of these two types of force production might be superior to the other. How would spidrids make use of that edge, while staying radially symmetrical? Before tackling that I realised I had never shown the spidrid's ability to change direction without turning. Solving that posed some interesting Matlab programming problems, but never mind, it works. I added height for fun and slanted the body a bit when the beastie is on a slope to make it look more natural.

 Copyright Gert van Dijk

Here it is! Finally, a spidrid that negotiates terrain and make a sharp turn. As you can see, the sharp turn calls for some interesting leg movements. With a shallow turn you would not see the changes well. So this is how real radial animals walk. By the way, should a rich Hollywood director wish to buy the concept for a film, I am available! Anyway, it is now time to adapt this standard spidrid walk to more energy-efficient gaits.

Copyright Gert van Dijk

The one above is built on the assumption that flexion/extension is more efficient than promotion/remotion. So, this species uses its promotion/remotion muscles to swing the legs as far parallel to the direction of movement as they will go. There are probably anatomical limits to this, so some legs still stick out at a right angle to the direction of movement regardless. The turn becomes odd, as some legs have to swing a long way to end up in their new position.

Copyright Gert van Dijk

But the existence of forwards-moving crabs shows that under given circumstances using promotion and remotion as the power house is feasible. The animation above has a spidrid moving its legs with a preference for positions at a right angle to the movement. This movement also calls for large leg swings when the animal changes direction. The legs bump into one another, which can be solved with phase changes, but I left it as it is for now. The anatomy of the animal is the same in all three variants, which may be unwise; I can see the last type having shorter legs to improve leverage, at the cost of stride length.

So there we are! Rampaging spidrids! What else is left for spidrid movement? An obvious additional adaptation would be to include slanting, but I will not provide an animation of that; what you see here was quite complex. Then again, I now have a program resulting in 3D coordinates for any part of a spidrid negotiating a 3D terrain. Perhaps I should go for a photorealistic animation? How about the 'Crown of Thorns' (Coruna spinea) making its way over rocks? Or the 'Blue Jester' (Fossor azureus) walking on the forest floor? The 'Lesser Strandsprab' (Nepa aranea) would do well on a beach, but the 'Hairstar' (Coma confusa) would be difficult to depict, with its hair cover. By the way, all of these appear in paintings I am working on...                    

Skitters ('Falling Skies'), spidrids and footless crabs

The previous post was devoted to spidrids, Furahan radially symmetrical walking animals. In thinking about their movement my attention was drawn more and more to Earth crabs, because the anatomy of their legs proved to resemble the anatomy I had chosen for spidrid legs. I admit that spidrid leg anatomy mostly came about because of a wish to see them walk. There are programming problems that I cannot solve myself (inverse kinematics) and I do not have any of the high-end graphics programs that can do it for me. So that is why I came up with the simple scheme I discussed before: at the hip joint there is a vertical axis of movement allowing clockwise rotation, but all other leg segments have horizontal axes enabling shortening and extension of the legs. Later, the exact same scheme proved popular with robot builders.

Last time I discussed a feature of crab (or spidrid) legs that I still do not understand well: slanting. I tried to contact arthropod experts but without luck so far. But there is another feature of crabs I do not understand: why do they not have feet? Crab legs more or less just end in rounded points. This is odd, because crabs, often living in tidal water, need to be able to get to good hold on the ground they are walking on, or else they may be swept away by the current. You would expect feet with curved claws for that. I have not found a discussion of why crabs do not have feet, just one mention of the fact that they do not. As I was considering adding feet to spidrids, I wondered whether there could be an anatomical reason for their absence. That will be discussed first, and only then will the 'skitters' of  'Falling Skies' be discussed: they have feet.

Click to enlarge; copyright Gert van Dijk

In the past I discussed the influence of leg posture on the anatomy of leg joints, and in particular how many axes are needed. The image above shows a new version of an old design (Mechanicus disneius). In the left image the leg is simply rotated forward around the vertical axis of the hip/shoulder joint: the foot ends up rotated with respect to the ground. While walking, the foot should move along a path shown as a stripe on the ground; in reality the animal moves forwards and the foot stays on the ground; it's the same relative movement. The foot should point forwards during the entire step, and that requires rotation around an axis parallel to the most distal leg segment, shown by an axis sticking out of it. The image on the right shows where the foot should be: many joint positions need to be adapted, but the one important here is the rotation of the feet around that longitudinal distal leg axis. By the way, rotate your hands palm up and palm down: what you are doing is pronation (palm down) and supination (palm up), which is just such a movement, due to the long bones in the forearm crossing and uncrossing.

The need for pronation and supination must be present for any animal with sprawling legs. That does not only include lizards and turtles, but arthropods -and spidrids and radial robots!-. I have not found any mention of how arthropods solve this problem. The robot builders just ignore it. Insects have a series of short segments at the need of their legs, the tarsus, linked through ball and socket joints. Are they how insects cope? Does the tarsus more or less flip around during a leg cycle? As said, crabs have no feet, so the end segment of their legs must turn in place during a step, rotating against the ground. Do crabs have no feet because there is no mechanism for pronation and supination? I cannot believe that. All this rotation with friction without a proper way to grab the ground seems an odd way to design a leg, and yet it seems to be there. If anyone knows an arthropod limb expert, please ask them...

Click to enlarge

What does all this have to do with the skitters of the television series 'Falling Skies'? Well, they have radial legs with feet, in an interesting example of 'convergent speculation'. A skitter is shown above, along with my simplified version to illustrate its anatomy (Disneius horrificus). Skitters have invaded an conquered Earth, but as the story unfolds it seems they did so under duress, so to speak. Their top end shows bilateral symmetry but their nether end has radial symmetry, which is odd. There are more aspects that suggest we should be well prepared to suspend disbelief (I like the series). For one, the legs are overly thick given that there are six of them. In itself that might indicate evolution in a very high gravity, but the sprawled position of the legs argues strongly against that. They can walk along vertical walls, a feature so unlikely there is little need to discuss it. They communicate through radio, an old favourite of speculative biology that seems difficult to get underway in an evolutionary sense. (All right, here is why I think so: the evolution of biological radio might well start with a primitive capability to receive radio waves, but can you see/hear with that sense? Where is the benefit?).

                            
The video fragments above show skitters in action. I have repeated the very short fragments to make it easier to see what is going on. It is clear that their nether ends are indeed fully radial, and that the feet accordingly stick out in all directions.

Above you see another fragment, one I rather like. I have repeated this one a few times as well. The skitter turns as it negotiates the path between the furniture. It must turn, as its top end has clear front and back sides: if it has to face the humans, it has to turn. With that clear preference you would expect its bottom end to have an equally clear fore to aft distinction, but that part is radially symmetrical. The one distinguishing feature of radial symmetry is that it allows movement in all directions. With such feet, a skitter might be expected to walk in any direction with equal ease, even directions in which it cannot see...  

The feet remain planted on the floor during the turn, so the legs in fact rotate around a longitudinal axis of the distal leg segment. That is nice; a pity that the anatomical mechanism is not visible. I very much like the way the animators solved the problem of how an organism with such a wide leg base negotiates the limited space between the furniture, designed for the much narrower forms of humans. The skitter behaves like an all-terrain vehicle and simply puts its legs on the furniture where needed, evening out the differences in height between its feet as it goes. That is very well done, I think.

But still... Leaving spidrids with leg points that pirouette against the ground at every step is very unsatisfying. The feeling is a bit like when you are unable to solve a puzzle, the answer of which must be staring you in the face. I think I will equip spidrids with feet, if only to end the irritation. That still leaves crabs, presenting the same puzzle...    
          

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.

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...

Illustrating symmetry

On the assumption that I might need to explain spidrids in some detail, I thought I could use some diagrams of how radial symmetry works. In turn, that gave rise to the idea that bilateral symmetry could be used to contrast radial symmetry with. Perhaps no such explanations are necessary, but the images proved easy to produce, so here they are! I made rough 3D versions of a hexapod neocarnivore and of an eight-legged spidrid in ZBrush, and exported the result to Vue Infinite.

Click to enlarge; copyright Gert van Dijk

The image above shows a fairly robust hexapod as a good example of an animal with bilateral symmetry. The three images show a translucent plane bisecting the animal. The horizontal plane (top) and the vertical plane separating the front from the hind sides (bottom) show that the resulting two parts of the animal do not resemble one another. The middle image separates the left from the right sides of the animal, and these sides are mirror images of one another. The plane in the middle image, called a sagittal plane, is therefore a plane of symmetry dividing the animal into two mirrored halves. The two is translated as 'bi' and 'side' as lateral, hence 'bilateral'. The result of all this is that the top differs from the bottom, so it pays to distinguish the two. Likewise, front and back denote completely different aspects and hence functions. Only left and right are identical if mirrored. Easy, right? In real life bilateral symmetry should not be taken too far: internal organs can be quite asymmetrical, and organs with symmetrical external appearances may still show different functions for left and right sides, such as the human brain. But never mind that.

Click to enlarge; copyright Gert van Dijk

The next image shows a Furahan spidrid with radial symmetry. Its body contains eight equal segments -it is octomeric-, forming the body rather like slices of a pie form an entire pie. One such slice is shown in yellow, once in its normal position, and just for fun also as if one slice is shifted a bit, like people tend to do with pie charts. On Earth, there are quite a few radial animals. Starfish are a nice example. One of their odder characteristics is that their larvae show bilateral symmetry, suggesting that radial symmetry is a later development in these animals. While starfish have five segments, spidrids have eight, but the number does not really matter. Spidrids do have tops and bottoms, but what they emphatically do not have are front and rear sides, nor left and right sides. The terms simply do not apply; it might be better to speak of central and peripheral to distinguish which spot of the animal you are referring to.

Some of you may point out that the spidrid can be divided into two mirror halves using a plane, just like the neocarnivore. This would be absolutely true, but does not make the animals bilaterally symmetrical. The thing is that the resulting half would still contain four equal portions, so this way of dividing it does not go far enough. Using a plane of symmetry is not really valid to describe such an animal; it does not have a plane of symmetry but an axis of symmetry, running from the top to the bottom right through the centre of the animal.

Click to enlarge; copyright Gert van Dijk

Is there a minimum number of slices for radial symmetry? Theoretically there is no maximum, but the minimum number is intriguing. The red thingy in the image above shows an animal with three such segments, a state you might call 'trimerism'. I do not think any such scheme exists on Earth, and the results does not look at all like something I aim to have on Furaha. Perhaps someone can find a use for such a scheme as a floating life form hidden in plankton. The blue ridiculosity shows 'biradial symmetry'. You might think it has bilateral symmetry, but it doesn't: there still is no front or rear, nor left and right, to this beast. Rather than right it seems to be wrong. Still, believe it or not, 'biradial symmetry' exists! Just check Wikipedia. But do not expect anything with legs as shown here...

Click to enlarge; copyright Gert van Dijk

At this point all should seem clear, which is the right time to complicate matters. Going back to the spidrid, its eight slices can be shown up by cutting the animal up with four planes. The top image shows how this results in the sort of segment we started with. But the image below is equally valid, in that it too results in eight identical slices. Still, the slices are different. The way to reconcile this is to look closer at one segment on its own: it has bilateral symmetry with a plane of symmetry! Take care though: this does not hold for the animal as a whole, but for its slices. In fact, there are eight clockwise half segments and eight anticlockwise half segments. You could say that animals such as spidrids and starfishes do not exhibit perfect radial symmetry becuase of this, but that would take 'biological correctness' too far, I think...

Anatomy of an Alien V / Greenworld I

This is the fifth and final post on the 1997 BBC documentary 'Anatomy of an Alien / Natural History of an Alien. Just like the previous instalment, this one deals with the work of Dougal Dixon. Although I did not plan it this way, keeping this one for last turns out nicely, as yesterday (January 29) Dixon's brand new book on Greenworld was published in Japan. More on that subject later, which explains why this post is also called 'Greenworld I'. Meanwhile, don't go rushing to your local book store to buy the English, French or whatever versions, as there aren't any. You Japanese readers, please do rush out now and buy ten copies each, so the publisher may give the rest of us an English version.

The video fragment is shown below. It does a good job of showing the evolutionary origins of the two major animal groups on Greenworld. Their common ancestor was a starfish-like animal with radial symmetry, but, unlike Earth's starfish, it had six legs, not five. When these animals came out on land they had not yet developed beyond radial symmetry, and still had no hard skeleton. Their solution was to use massive clumsy muscles first, but they developed a more practical skeleton later. In effect, their legs more or less started out as tentacles but developed into proper legs, much as I explained in my series on 'Why there is no walking with tentacles'. These animals secondarily developed bilateral symmetry. In one group the plane of symmetry came to lie in the groove (sulcus) between the legs, so the animals ended up with three pairs of legs; these are sulcosyms. In the other lineage the symmetry plane neatly divides an arm ('brachium') on one end of the animal and another at its other end. These are the 'brachiosyms', which therefore have two unpaired legs, one at the front and one at the end, as well as two pairs of legs in between. Those who have already watched the video at the end of this post may have noticed that not everything I have written here is mentioned in the video, so how do I know this? Well, Dougal Dixon sent me some notes and sketches on Greenworld a long time ago, and that's how. Mind you, the names might have changed since then, because this was 20 years ago...

If you search the internet you will find bits and pieces of Greenworld here and there, probably because the book has had to wait such a long time before it was published. Puyamaster from Japan, whose comments you can find following the two posts before the present one, searched more diligently than most and came up with some interesting material. Here are some of the things he found (with thanks!).

Source unknown

So there are (or were) models of some Greenworld animals. One is an 'anteater-sized insectivore (or equivalent)'. It is also visible in the video. My notes say it is the biggest of the brachiosyms.

Source unknown

Aha! Jack Cohen, also featuring in 'Natural History of an Alien' (and featuring in previous segments, such as the one on 'Europan waters', is shown holding some Greenworld models. When it comes to biologically sound aliens Jack Cohen is undoubtedly one of the usual suspects to round up, so his appearance here is not surprising. Still , I wonder what the occasion was. Puyamaster provided the web addresses of these photographs; their original sites are here and here. I would be curious to have a look at the site they are meant to illustrate; usually this is a simple matter of successively cutting off the end of the address until you find a readable htm file, but that does not help here. If anyone does know where these picture are from, I, and presumably others too, would be interested.

In a next post I will write a bit more about Greenworld. Here I would like to finish with some thoughts on the alien nature of radial symmetry. I guess that many of those designing alien animals consciously search for features to strengthen the 'alienness' fof their creatures, and radial symmetry has that in abundance. In discussions on the subject some seem to accept it as an acceptable body plan for big and possibly intelligent animals, whereas others dismiss it. Quite often the lack of any such animals on Earth is used as an argument. Indeed, we do not have hog-sized starfish digging up the flower beds in our gardens, and personally I deplore the absence of elephantine centipedes. But before dismissing them it may pay to try to specify the reasons why there are no such animals. A first and simple reason why there are no big starfish walking around on Earth is evolutionary competition; their seat is already taken!

Another, and possible more important reason may be sought in a respiratory system. Some arthropods have tubes entering the body supplying each cell of the body with air for gas exchange. Beyond a certain size passive gas exchange in this way is simply unsuitable, so that limits growth. Our own respiratory system does of course allow large body size, possibly exactly because it does not attempt to reach every cell; instead, that task is relegated to the circulation. Altering an unsuitable respiratory system may need going back to the drawing board to start all over again, but evolution does not do that. It either adapts another organ, or tinkers with what there is instead.

Having an exoskeleton is another difficulty: for the same strength you need more material than for an endoskeleton, and growth is a major design problem. But this particular problem does lend itself to gradual change: if you simply strengthen one side of an exoskeletal tube and weaken the other side, you keep the weight-bearing function intact while sparing weight. Repeat this a few times, and you have a weight-bearing strut that does not envelop the limb. This is evolutionary tinkering, and this is how Furahan hexapods developed a practical skeleton. This also explains why dermal armour crops up so easily in hexapods; their skin, a secondary development, can easily revert to armour production. Luckily for them, protohexapods already had a nice pumping system in place pumping blood as well as air, so they did not have to solve too many problems at one. If Earth's arthropods had has another respiratory system, who knows what might have happened?

In the end, of course, all this remains speculation. And as we all read the same books and are subjected to the same sources, we come up with the same alien designs. I've called it 'speculatory convergence' or 'convergent speculation', a concept related rather closely to convergent evolution. Dougal developed secondary bilateral symmetry for brachiosyms as well as sulcosyms. I developed secondary bilateralism as well, but only for some predatory neospidrids. You will find an example here. Spidrids, of course, are radially symmetrical, but these neospidrids have a symmetry plane going through one leg, just like the brachiosyms. Convergent speculation...

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.