14 Years on (and one million views later)

The first post of this blog was published on 22 April 2008. It was an experiment, and I had no idea how long I would continue to keep writing posts. I still don't,  but the fact that the blog is still here after 14 years, was not something I foresaw at the time and for now I shall continue. Let's start this post  update with an overview of past results, as per 23 April 2022:

Number of posts: 278 (not counting this one)
Number of comments: 2485
Number of followers at present: 220
Number of views: 1,001,012

This means that each posts generates an average of 9.8 comments. I like the idea that the number of views surpassed 1 million but have no idea how many of these views represent people taking an active interest, and how many 'views' in fact represent bots.

Which posts attracted the most interest?

Swimming in sand 1: the sandworms of Dune                                             10,100  
The anatomy of giants in 'Game of Thrones'; did they get it right?                9,500
A future book on future evolution from France                                             6,470
Avatar's "Walking with hexapods" or "Don't walk this way"                        6,380
Warren Fahy's "Fragment"                                                                             4,340
More future evolution in Japan                                                                      4,250
Alternate future evolution in Japan                                                                3,890
Future evolution from France: "Demain, les animaux du futur" Review I   3,340
A century of thoats                                                                                        3,070
The future is wild... and it is Manga!                                                            3,030

Comparing the list with earlier ones show that the top 10 hasn't really changed that much. The lesson is the same as before: if I would want to maximise the number of views, I should write about popular films, TV series and books. I largely stopped doing that, which explains why the top 10 is stable.

   

Click to enlarge

It is interesting that the attraction of posts can differ much over time. For instance, the sandworm post attracted a great deal of interest in the beginning, followed by a steady trickle of about 20 to 100 views per day. In contrast, the two posts with Japan in the title showed a comeback in 2020 and 2021.  

Just another dragon

A post without any new material or thoughts is at best mildly interesting, so here is a minor illustration showing a schamtic view of a 'Megadraco' taking off. This is a species of the clade Dialata, discussed here.

Click to enlarge; copyright Gert van Dijk

This animal is much larger than Earth's birds, so how does it fly? Well, readers will realise that pterosaurs grew much larger than birds. pterosaurs definitely flew, so how did they outsmart birds in this respect? Well, you may remember that lift is proportional not only to wing area but also to the square of air velocity. In other words, doubling velocity has the same effect on lift as a fourfold increase in wing area. Speed pays to remain airborne. The problem is how to get to such a speed from a start on the ground (jumping off a branch or a cliff is a much easier way to achieve speed) . The problem is more difficult for larger animals; if you have seen a swan or heavy goose take off, you may realise just how difficult it can be for a heavy bird to achieve that all-important speed.

The idea is that pterosaurs achieved high starting speed in a radically different way: they jumped into the air, powered not just by their hind legs, but also by their much more powerful front legs: the wings! That quadrupedal launch should be enough to get them high enough in the air for a first powerful downwards wing stroke, and from then on, they were in business. 

I like that idea and thought that evolution might well do its familiar 'parallel' trick again. If your basic body plan involves six limbs, of which the middle pair are wings, you have four legs left to propel yourself up into the air. That should help! Of course, once in the air, those four limbs weigh something but do not contribute to flight, so perhaps the resulting animals do not grow as large as the biggest pterosaurs. But even so, with a quadrupedal launch and a clap-and-fling first wing beat, these Furahan dragons get up fast enough to fly, large as they are.          

The future

The 'Great Hexapod Revolution' means that the anatomy of various animals in various already finished paintings was no longer correct. Sadly, these paintings were therefore instantly no longer 'finished'. I am working my way through them, changing legs and heads left and right. I have only about 5 more of such reviews to do, and after that I will make only two or three completely new paintings. Meanwhile, I will work on some additional material such as a Glossary, and then the manuscript of The Book is all done. I expect to achieve that goal this year, but will also move from one house to another, which always takes more time than you think, even if you take that into consideration.

And then there is the matter of finding a publisher. That is an open question. I wonder what the post '15 years on' will have to say on that subject...   

Lend me your ears! (Hearing 2)

In nature, localising the source of a sound has obvious survival value, to localise prey, predators, mates, competitors, etc. The previous post started the subject, but this one deals with how mammals, humans in particular, try to solve that problem. As we shall see, localising sounds is not all that easy. Of course, some animals are much better at this than others, but there are some fundamental problems. Humans make use of no less than three different mechanisms. This post might be a bit technical, but I left the mathematics to a nice free good review, here.   

The main problem is that sound can bend around obstacles, and so change direction. A sound reaching your ear can therefore come from just about anywhere. You can therefore hear things you cannot see, which is good news in the dark or in a jungle. Of course, you do not know where it is coming from. Sound provides a good alerting but a poor localising system, whereas a well-developed eye is a localising organ (see here for a comparison of echolocation with vision). 

Click to enlarge; copyright Gert van Dijk

If we would have just one simple ear of the hole-in-the head variety, but with an eardrum and vibration sensors, we would be stuck at that level. But bilateral symmetry provides us with two ears, and evolution made clever use of that. The image above shows that the waves from a sound source travel directly to the nearest ear but must travel further to reach the farthest ear. The sound arrives at the ears with a time difference: the 'interaural time difference (ITD)'. The difference in arrival time depends on the extra distance the sound has to travel, shown in red. That difference depends on where the sound comes from, relative to the axis between the two ears. The maximum arrival distance occurs with sources placed on that axis, because the sound must travel farthest around the head. The minimum is no difference at all: this occurs when the source is placed on the plane of symmetry. You could make a table telling you which difference corresponds to which angle, and that is basically what the nervous system does for you. 

Click to enlarge; copyright Gert van Dijk

 

Unfortunately, this is not a perfect solution. The arrival difference tells you what that angle is, but not whether the source is up, down, to the front, the back, or anywhere in between. The image above tries to explain that. The source could be anywhere on the brilliantly named ‘cone of confusion’; that is the surface you get if you rotate the angle around the ‘hearing axis’. One way to get around this problem  is to rotate your head and listen again, because then you get a different cone of confusion, giving you an additional clue where the sound comes from.  

Mammalian ears make use of a second trick. When sound bends around an object, its volume decreases. Your head provides a ‘sound shadow’: The volume of sound in the nearest ear is louder than that in the farthest ear, in the sound shadow, so there is an 'interaural level difference (ILD)'. The difference in volume depends on the angle, and again the brain constructs a table telling you which difference in sound level corresponds to which angle. But that irritating cone of confusion is still there...

Mammal evolution came up with a third trick: the external ear! The complex shape of the external ear alters the spectrum of the sound, and how it is altered depends on the location of the source of the sound: the 'head-related transfer function ('HRTF)'. This works to an extent with just one ear. When I first read this, I wondered how that could work, because people have such differently shaped ears. Well, the solution is brain learns to live with the filtering characteristics of the ears you happen to have. This has been put to the test by altering people's ears by placing a mould on the ear, and that indeed that fooled the brain to make mistakes in sound location. 

Click to enlarge; source and rights here

You may wonder why you would have three systems for the same purpose. One part of the answer is that the efficacy of each system depends on sound frequency. The figure above shows the frequency: ITD ('arrival time') works best at low frequencies, and ILD ('loudness') and HRTF ('external ear') work best at high frequencies. Together, they do a nice job for all frequencies. But there are strong clues that the situation still is not optimal, and that is behaviour. Many animals can move their ears, and people can tilt and turn their head to locate the source of a sound: that shrinks the cone of confusion. But we still start a visual search of the general area of the sound, hoping that vision will provide the ultimate localisation. Of course, that is in part because we are diurnal mammals with very good vision; but part of the explanation is that localising sounds is inherently difficult.

Could animals on other planets do better? I think so, but that speculation will have to wait for another post.

Tabulae Mortuae V (Archives XV): Digital paintings die too...

 Every now and again I show an image from the Creature Vaults, those hidden domains where old sketches, failed paintings and discarded designs find their final resting place. 'Final', unless they are dragged out to be presented to the world, usually for the first time.

Click to enlarge; copyright Gert van Dijk

This image is one such, and it is the first to come from a vault without physical form. Other vaults consist of large cardboard folders, or of stacks of oil paintings carelessly stacked against the back wall of a closet. This vault is digital.

I started the conversion of the Furaha project from oil paintings to digital art some 11 years ago. The project, now nearly done, changes as time passes. The Great Hexapod Revolution had as a result that legs, heads and jaws or earlier hexapods no longer followed my self-imposed rules. The changes were too large to be solved with moderate cosmetic changes (I tried), so many paintings are now seeing a 'Mark II". In fact, some started as oil paintings (MkI), were later redone as digital paintings (MkII), and are now revisited to become MkIII. Mind you, most paintings these days are entirely new.

Click to enlarge; copyright Gert van Dijk

Here is some more detail of the head of this now defunct animal. It is a pity that I had to discard it, as I rather like the painting. But I kept the overall design and colour scheme for the MkIII version, which is nearly finished, and looks just as well or better, I think.

The animal is a 'thresher', with the Latin name 'Ira tarda'. That means 'slow anger', a name that was inspired by memories of an old teacher of mine. Threshers are solitary, grumpy and are best left to their own devices. They do have to meet from time to time, in view of the perpetuation of the species, but their behaviour at such times gives little indication of a mood upswing. Best not talk about it, really.

Hear, hear! (The sense of hearing 1)

There have been many attempts to design interesting sensory systems for alien animals. Some tried to equip animals with radio or radar, which poses the difficulty that such radiation passes easily through biological tissues, making them hard to detect. There have been attempts to do away with vision altogether and replace it with something else, such as echolocation. The most famous example is probably Barlowe's Expedition. Although his artistic prowess made the result look spectacular, life without vision on a planet with light seems very unlikely. The echolocation was explored in four posts: one, two, three and four. 

I cannot remember a fictional world in which the total absence of hearing is presented as an interesting twist. That absence suggests that hearing is accepted as a simple given. Are there environments in which hearing cannot work? Yes, there are. If we define hearing as the ability to pick up mechanical vibrations in a surrounding medium, close to the Wikipedia definition, then the absence of that medium will abolish hearing. The resulting environment coins the nice phrase 'In space no-one can hear you scream'. True, but you cannot breathe there either, and that is definitely a bigger problem than not being able to scream. I intend to write two posts about hearing in a terrestrial environment with an Earth-like atmospheres. The present one will have a look at evolution of hearing on Earth, to see if that helps designing alien hearing. 

Picking up mechanical vibrations from the air is not fundamentally different from doing so in another medium, such as water. The medium could be expanded to include touching an object, such as the ground. Picking up ground vibrations is so close to hearing that you could arguably include that in the 'hearing' concept. The ability to register vibrations lies at the heart of our kind of 'air hearing'. Where it is easy to evolve 'air hearing' for animals that once came out of water will depend on their starting point. Here is a very nice paper comparing vertebrate and insect hearing. The basic problem has to do with being surrounded by air. Bodies are mostly water, so vibrations in water will readily pass into watery bodies, where they can be picked up. But picking up air vibrations in a watery body requires a signal transformation. The main way to do that, in vertebrates and insects, is to use a taut membrane to pick up air vibrations. 

Click to enlarge; source and copyright: https://www.frontiersin.org/articles/10.3389/fevo.2021.667218/full

 Vertebrates 

Vertebrates apparently evolved their eardrum, or tympanic membrane, from skin. Making an eardrum work means the drum must be open to the air on one end, but there also must be air on the other side of the drum, inside the animal. Having bubbles of air in the body is not a standard part of animal anatomy though, so the middle ear had to evolve from scratch too. The illustration above shows that eardrums were present at the start of the Mesozoic, not earlier. As if that was not difficult enough, the system also needed pressure transducers, for which rearranged jaw bones were press-ganged. 

It seems that hearing was not really an easy process for Earth vertebrates, so perhaps 'air hearing' is not an automatic given. The paper suggests that vertebrates, before they evolved proper 'air hearing', may have picked up vibrations through the ground, perhaps to sense predators. That makes me wonder whether predators at the time would have been under evolutionary pressure to walk softly. 

Insects 

The paper also goes into insect hearing and makes the point that insects had it much easier: forming an eardrum was a matter of thinning the exoskeleton, and the insects' exoskeleton, right at the air-body interface, already carried lots of mechanoreceptors that could easily be given a new job. Insects have air-filled tracheae (breathing tubes) everywhere, so forming the equivalent of a middle ear was not difficult either. Apparently, hearing evolved in insects independently at least 19 times, resulting in a great variety of ear designs, found all over insect bodies. 

Click to enlarge; source here

Another paper provided details of such insect ears. A few examples are shown above the arrows indicate ears. The authors write that about the only place where you will not find insect ears is on the sides of their heads. Instead, insect ears are most often found on the body itself, but they can also be situated on the legs, mouth parts and even on wings. As for the number of legs, many insects have just two ears, but some grasshoppers have no less than 6 paired 'functional auditory organs in their abdomen', giving them 12 ears. Some insects have two ears per leg, giving them four ears. Mantids are perhaps the oddest, with just one ear in a groove on the midline of the thorax. Although there is a tympanic membrane on each side of a narrow grove, these are so close together that they function as one ear. Mantids are 'the only known terrestrial animal with a single ear'. The figure above shows an exception: some mantids do have two ears, but both are in the midline, and they are sensitive to different frequencies. 

click to enlarge; source here

 Spiders 

There are no tympanic membranes to be found in spiders at all, so for a long time it was thought that they were deaf. However, they are apparently able to pick up sounds with hairs on the tip of their legs. This was only published in 2016, so there will be probably more discoveries in the field of spider hearing. 

 

The investigators made a very nice video of their somewhat accidental findings, that you can find on their website (they allow downloading, and the quality there is better than shown here; I just enclosed it for ease of use). If you need more, the authors went on to study hearing in 'ogre-faced spiders' later, also with a nice video). 

What does it all mean for speculative biology? 

As usual, there are various solutions to the problem (and we haven't even touched upon frequency ranges and other intricacies!). People who design vertebrate analogues might do well to think about how Earth vertebrates and insects developed eardrum-based hearing: you need some suitable tissue with easy access to outside air, so that tissue can be thinned to form a membrane. You also need a way to have air on the inside of the membrane too. That alone would suggest a place near the mouth. It will also help if that place is already equipped with the ability to sense movement, of jaws, hairs, scales, etc. But the spider example shows, as usual, that there are other ways too, and hairs seem to excellent starting material to evolve hearing. 

The next post will be about sound localisation. Sound does not travel in neat straight lines, which is just one of the things that complicate that particular problem. 

What does it take to make a reindeer fly?

This blog is about 'Furahan Biology and Allied Matters', and today we will stretch the 'allied matters' a bit, to produce this special Christmas post. Somewhere in Speculative Biology there must be a place to think about re-engineering mythological life forms, which is what this post is about.

The starting condition is simple. Thanks to globalisation, a most unusual subspecies of reindeer (Rangifer tarandus) has spread widely from its original area, so it can now be observed in skies over many parts of the world. In the skies? Yes, because these reindeer fly.       

It is not clear whether these reindeer can fly in their natural state, as they are only observed to do so when tethered to sleighs. This is slightly worrying, but even so, the force that keeps them in the air must be magic, as the reindeer lack any observable physical means to provide lift. While magic is a potent force in the imagination, in the real world it is noticeably difficult to acquire, so we need a more pragmatic approach. 

What would it take to make a reindeer fly in the real world? And I mean 'fly', not hurtling it through the air by strapping a jetpack to its back or using a large catapult. No, it must fly though biological means. The first problem is that reindeer have no wings, so we will have to use advanced creative bioengineering and splice in some wings. Done! That was quick...

Reindeer weigh around 100 kg, if we average estimates of male and female weight. But even these brand-new wings won’t make a 100-kg reindeer fly. And don't you start objecting that some pterosaurs weighed more than 100 kg and could still fly. We could in fact probably re-engineer the flying reindeer to achieve pterosaur-like mass, but the result would definitely look a lot like a pterosaur, and it should look like a reindeer, right?
 
Where was I? Oh yes, the 100 kg mass is a problem. Why? Well, take a 0.6 kg pigeon with a 70 cm wingspan. If you double its length, width and height, you get a wingspan of 140 cm and it will weigh 8 times the original weight. That factor 8 represents doubling of all three of length, width and height, so it is doubling to the third power (2 to the power of 3). By the way, for more on basic scaling of animals, see these posts here and here.

The problem is that lift is proportional to wing area, and area is proportional to the square of length. Doubling the pigeon's size makes the wing area four times larger, but that four times larger wing must carry eight times the weight. That won’t fly. (Sorry for that one.) We can make the wings extra large to compensate for the larger weight, but that will also increase weight. As explained in another post, at some point of increasing body size the wings can no longer carry the body.  

The obvious solution is to shrink the reindeer until it weighs as much as something that can fly. Say a rather massive goose at about 5 kg. Some calculations reveal that the reindeer's length should then be 25-30% of the original length of 180 cm.

To allow room for massive wing muscles, everything else must be reduced in weight: to decrease gut size it needs a new diet, mostly sugar; we can then also abolish the teeth, because it doesn't need them and won't get caries. We'll give it slender legs, tiny light hooves and fluffy hair. You will probably insist on antlers, so antlers can stay, but they will be much reduced. We can splice some red bioluminescence into its nose, to put the cherry on the cake.    

Done! A realistic flying reindeer! 

Click to enlarge; copyright Gert van Dijk & Roelien Bastiaanse

 

Happy holidays!

The aliens of the TV-series ‘Invasion’ (also: ‘Inversion Fish II’)

All episodes of the first season of the TV series ‘Invasion’, from Apple, are now available for viewing. If you are still planning to see the series later, stop reading now, because there are spoilers ahead.

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The series shows an alien invasion of Earth from the viewpoint of a few individual people, here and there on the globe. The protagonists at first seem to be people randomly caught up in the events, but some later wind up playing more important parts. I wouldn’t be surprised if all of the remaining apparent bystanders will end up being close to the centre of things, but that will have to wait for future series (a second series has been ordered).   

In the early episodes no-one has a clue what is going on, an that includes the protagonists as well as the viewers. That uncertain state lasts quite a while, because the series is no hurry at all to speed up the story or to explain where it is going. This may be a reason why the ratings haven’t been very high. Personally, I do not mind that the story unfolds slowly. This ‘strategy of keeping the viewer in the dark also means that the makers do not explain much, and so did not have to insert the kind of technobabble that is often used in science fiction series to explain alien technology or biology. In fact, there was almost no explanation of how anything works, which was fine with me. 

There was one instance of an irritating wilful neglect of knowledge in the series: a child lies shaking in an apparent MRI machine with an EEG cap on, resulting in an apparent MRI image with overlaids spots of colour, prompting a passing neurologist to say that the EEG was flat. That's not how MRIs or EEGs work; I guess that a real EEG wasn’t considered impressive enough.  

Anyway, it takes quite a while before you see the actual aliens. When you finally do, they are just dark blobs from which spikes shoot out towards a nearby floor, wall or ceiling. You typically do not see them moving in great detail, but it is clear at one point that they more or less ‘invert’ themselves. That is not easy to explain in words, so it is good that the producers posted a short video on YouTube about how they designed the aliens. 

Here it is. The commentary at one point includes the following: ‘A biological entity that we cannot even begin to understand’. Well, I am not going to take that at face value... 

In science, it is always time begin doing just that. Of course, here we do not have have to deal with real alien biology, but just with a human design, and what one human can design, another can understand.
   
You may have to watch the video a few times to see exactly what happens. I still found that difficult, so I made a slow-motion version of part of the video.

And here is that version. Aha. Let’s analyse what we have seen. 

The aliens are roughly cylindrical, about 60-80 cm in length, with a diameter about half that. If they would be solid cylinders they would have a volume of 42 to 100 L, but they must be hollow, so I estimate their volume to be 30 to 60 L. If their density is the same of that of Earth animals, their mass would be 30 to 60 kg. If they would be denser, say with a density of 1.4 kg/L, their mass would be 40-80 kg. That makes them quite hefty.  

‘Inversion fish’
The animation shows rings coming in from the centre, moving forwards and outwards, after which the rings move backwards again, where they no doubt move back inwards and forwards again. The spikes on the rings can be seen to point forwards at first. Then they move backwards over the surface of the rings. I do not think that the rings are separate objects. It seems to me that they form a contiguous surface instead, one that moves over the substance of the animal. You could say that they invert themselves.

Believe it or not, but inverting animals, consisting of a torus with exactly such a gliding surface, has already been discussed on this blog, back in 2013. That discussion was inspired by Thomastapir’s ‘Moebius fish’. I called the resulting type of animal ‘Inversion Fish’, assuming such animals would be small and simple sea creatures, like jellyfish. With all the inversion going on, it would be difficult for them to form brains or guts, so such animals might have non-invertible parts. I meant to follow that first post later with a second one on the same subject, but I never did, for a variety of reasons. The good news is that I can label this post ‘Inversion Fish II’, bringing closure to that long-open end.

I now resurrected some old Matlab routines to animate the inversion fish and pimped them a bit. Here is the result of that; the Inversion Fish is still a simple ring, but it is now rotated to make it swim horizontally. The lines sticking out represent hairs that will help propel it through the sea. The animal was supposed to be at most a few mm in size. 

 

Here is a second animation: I stretched the animal to give it a cylindrical appearance, so it begins to resemble the aliens. 

 

And a third one Inversion Fish, cut in half. The cut surfaces help to visualise the movement of the surface. Note that the surface moves forwards on the inside of the animal, while it is moving backwards on the outside, with not much distance between the two. There is no way to attach the surface to the inner substance of the body, in the way our skin stays close to the underlying tissues. In essence,  something like this can only work if the surface is essentially loose from the subsurface. The easiest way to achieve that is with a fluid between the surfaces. That is why I compared the Inversion Fish to jellyfish: jellyfish are essentially also membranes with jelly in between. But in their case, the membranes do not move in opposite directions.     
     
The spikes
The spikes appear at various points on the bodies, shoot out quickly and in doing so vary in length. They are always straight, never curved, and their width tapers to a pointy end. These ends apparently attach themselves to walls, ceilings or the ground. I did not see anything in the way of suckers, feet, hooks, nails or anything else that could help to attach a fairly large mass to a ceiling or wall. The spikes do not leave any marks either, as far as I could see. What also struck me is that I did not see the spikes sagging in any way. If you use a rope to suspend a weight from a wall or ceiling, the rope will sag a bit. These spikes are also used as rigid legs, and so must be very rigid. All in all, they must be able to withstand compression as well as tension easily, even while they are being formed.  

Now making such a material presents quite a design challenge. Which material can be extruded and absorbed at will and can remain very rigid and strong while it also behaves as a fluid? The commentary says ‘It’s made of ferrofluids, so it can be hard, but when you touch it, it moves like mercury.’ I cannot say I know much about ferrofluids, but my short foray into the subject suggest that the term 'fluid' should be taken quite literally. I did not see examples of hard ferrofluids.

Could you evolve animals using ferrofluids biologically? Obviously, evolution has no preset aim and cannot set out to evolve a ferrofluid. Evolution could start with a readily available source of ferrofluids, or there should be a reasonable reason for an animal to produce them, and after that it can evolve in a different direction. In other words, how do you wind up with tiny magnetic particles permanently suspended in a fluid? And how would you wind up with a handy biological way to acquire and control magnetism? Those are extremely tough challenges, and I doubt they can be met.    

Conclusion
Are these aliens original? Yes, very much so, unless you feel that ‘original’ may only be used for something that that has never been proposed anywhere. That would not be the case here, as witnessed by Thomastapir’s Moebius Fish and the later Inversion Fish. But that is asking too much: I really like the inventiveness shown here.   

Are they realistic as products of biological evolution? I very much doubt it. It will not be easy for biological evolution to come up with an animal whose living matter is essentially the fluid surface of a torus, and in which that living matter can become strong and rigid at will. We should probably add some additional problems here: the animals have no recognisable sense organs, and their brain and other relevant organs would have to be malleable and able to continue working while being inverted (but perhaps you could actually do something like that to an octopus brain, while it would continue working; don't try it!). At the end of the series, the aliens all collapse when the mother ship is destroyed, which is in Earth orbit. The aliens must therefore have a means of constant communication that functions immediately over large distances; should we add radio to their list of improbable biological feats? 

Perhaps it makes more sense to treat them not as the product of biological evolution, but as the result of engineering? Are they in fact bio-inspired robots? I guess we'll see in future series.

What does a Hexapod gallop sound like? (1)

Click to enlarge; copyright Gert van Dijk

 The image above represents one of the very first Furaha images ever, painted way back in the previous century. The planet did not even have a name yet, and I certainly had not thought much about biomechanics. I just tried to paint an interesting and pleasing picture. These primal hexapods were fairly insect-like, with a stiff-looking body. The details where the legs join the body suggest exoskeletal parts as much as they could represent skin flaps. I can show the painting here, as it will not feature in The Book: it doesn't fit anymore. 

But I still like the scene very much. In my minds' eye, I can see a large herd of these impressive animals ('handlebars' or 'handlebar-horns') enter the scene from the left, advancing towards the right, until they turn towards the camera, wheeling like cavalry. That scene deserves to be done again, with new and updated handlebars. The update does not only require revising their anatomy, as part of the Great Hexapod Revision, but their gait as well. After all, if you paint a fast-moving hexapod, you should have an idea how its legs should be positioned. Imagining six-legged walks is apparently not something that comes naturally to all illustrators: many, including brilliant artists, fell back on on four-legged locomotion patterns, and simply added additional pairs of identical hind legs until the required number of legs was reached (see here, here, here and here). I never liked that, even though I realise that doing otherwise asks a lot of an artist who may not be familiar with the gaits of insects and other invertebrates. 

Perhaps I am being too difficult about this; after all, the viewers are likely to accept the result anyway. When you looked at the handlebar painting, did you think 'I wonder whether that gait is correct?' My guess is you did not, but I still wanted to do better. I like to think that a fairly thorough biomechanical background is a selling point of Furahan fauna; I also do not think I could let it slip anyway... 

Click to enlarge; copyright Gert van Dijk

I therefore wrote a suite of programmes to help me design decent hexapod gaits. In fact, I wrote them again, as I had done so once before, in 'BBC Basic' on an Acorn Archimedes. There are still a few animations on the main Furaha website that survived the transition to other operating systems. The programmes did not. This time, I wanted to do better, meaning that the programme should find out how to fold a leg by itself, rather than requiring me to control each minute limb movement by hand. I thought that that would be tricky, and it was... I had to settle for limbs with three main segments, as I could not yet add a fourth one the position of which looked convincing enough. You will just have to imagine the feet. I will use the program as background material to design paintings, and I can add details myself. The programme does allow body position to adapt to the chosen gait, so that part works. 

 

Here is an example of such a three-segment limb. The programme uses segment length, built-in movement restrictions of the joints, and the phase of the movement cycle to control the thigh angle. The other bit of information is where the foot should end up on its motion path. Together, that is enough. The movement is a bit uneven, because the programme chooses from an array of possibilities, and I should have increased the number of possible solutions. 

 

This shows what happens when you vary the choice which joint should 'stick out' the most. The further a joint is from the vertical, the more energy is needed to keep it in that position. You can see here that making life easier for one joint makes it more difficult for another. The middle position looks like it provides a nice middle ground in that respect. In biology, an optimum usually represents a compromise that minimises the overall energy required. 

Click to enlarge; copyright Gert van Dijk

 

The basic hexapod anatomy these days consists of six fairly similar legs that all have 'zagzigzag' pattern, (see here , here and here), meaning the most proximal segment ('coxae' or thighs) generally point backwards. I chose that as I could not find a convincing argument to state whether zigzagzig or zagzigzag was better. The legs are not identical, though, and future hexapods will see more pronounced differences. In the pattern shown here, the middle pair of legs is stouter than the front and hind pairs, and their feet are placed wider apart. That latter bit of information is only visible if you look at the 'support diagram' under the beastie. Placing some feet wider apart is a trick to avoid leg collisions, although it is not strictly necessary: Earth tetrapods manage to avoid collisions just fine with similar distances between pairs of limbs. 

 

And here is one complete hexapod in a slow walk. The sounds were taken from sound recordings of horse hoof beats, because I had to use something; it doesn't mean the animal has hooves! Keen observers may well deduce some as yet undescribed anatomical information from the animation. 

So how about the gallop sound? Next post!