Sunday 21 November 2021

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!

Monday 1 November 2021

Are there dragons on Furaha?

 No, of course not!

Dragons are mythological beings, usually shown as very large scaly reptilian animals with four legs and two batlike wings. Did I mention that they breath fire and that some of them can talk? Of course, there are no such creatures on Furaha, but the human citizens of the planet did not shed their myths when they relocated to another planet, so they brought stories and depictions of dragons with them.

The citizen-scientists duly observed, with great interest, that six-legged beasties had taken to the skies and now had evolved into excellent flyers (‘not long’ should be taken literally: the animals flew around the spacers’ heads the moment they stepped out of their ship). Closer inspection revealed that some of these animals had four wings (and two legs) while others had two wings (with four legs). 

Click to enlarge; copyright Gert van Dijk

Later speculation suggested that both groups, the Quadrialata and the Dialata, had separately evolved from animals using membranes between all six legs to glide down from one tree to another. In one group, the middle pair of limbs had increased quickly in size, whereas the front and middle pair of limbs turned into wings in the other group.

While the scientists started studying mechanisms of lift and anatomical adaptations to flight, classifying everything meticulously, the general public took one glance at the four-legged two-winged avians and shouted ‘They’re DRAGONS!’. Now, scientists generally dislike lay people interfering with their subject matter, and protested that the animals were not dragons at all; they were ‘Dialata’, not dragons, and dragons did not exist anyway.

Of course, this resistance was futile, and the concept of ‘Furahan dragons’ was quickly assimilated by everyone except the scientists in question.                 


So much for the ‘in universe’ version of dragon lore. What happened is that the ‘Great Hexapod Revolution’ is in full swing, and I am now working on flying hexapods. The good news, by the way, is that I now think that I only need to do about four of five new paintings to finish The Book. I am aiming at some 140 pages, so you will get your money’s worth (if I find a publisher, that is).  

The unfeathered bird by Katrina van Grouw


I am working on my first painting of a Dialate flyer. I took the revamped general hexapod body scheme and thought about how it would need to be modified to become a successful flyer (also see here). Beautiful examples of such anatomical adaptations can be found in the book ‘The unfeathered bird’ by Katrina van Grouw. The image above was taken from that book, and shows the extent of anatomical  modifications.

The elongated hexapod body would have to go, to keep the mass centred. That meant that the frame of the animal had to be shortened, with the hind and front legs bending down towards the middle of the animal. These walking legs also became small and slender, whereas the wings, the middle limbs, increased in mass. The wing skeleton resembles the ‘bat mode’ more than the ‘bird model’, as it has  intact ‘finger’ bones. Of course the toe/finger pattern is not as nicely radial as in Earth’s vertebrates, but flows a Devonian branching pattern instead. The wings themselves are only partly membranous, so they do not really resemble bat wings that much.  


Click to enlarge; copyright Gert van Dijk

Here is a simple model done with Zbrush. People can achieve amazing results with Zbrush, but I am definitely not one of them (and I am not alone in disliking its complex convoluted completely counter-intuitive interface). The body and walking legs are sculpted and show the by now general zag-zig-zag basic hexapod pattern.  The wings are only shown as a sort of scaffolding (‘Zspheres’). Their Devonian branching is obvious. 

Click to enlarge; copyright Gert van Dijk

Here I have given up on making the sculpt follow the scaffolding, so you only see the scaffolding. The scaffolding is NOT the animal’s skeleton, but just a shape placeholder (the bumps on the body just indicate its size). Notice how the walking legs are tucked away against the body. 

Click to enlarge; copyright Gert van Dijk

And here is the same animal (Draco umbraferens), clinging on to a reed or stem, looking down to see if here is anything in the water it might eat. It unfolded one wing to provide shade, either to lure animals to the shade, to see better underwater, or both.

I liked that pose, so I developed it further. I am not going to show the painting, which isn’t finished yet anyway, but thought you might wish to see part of it. The Draco will be sitting on a reed in a marsh in bright sunshine. I used Vue Infinite as I often do to compose the scene to help with lighting and perspective, but only roughly. 

Click to enlarge; copyright Gert van Dijk

The scene provided a challenge, as it deals with reflections, transparency and shadows. The image above shows a detail of the future painting: a background plant. Panel A shows the shadow the plant casts on the marsh bottom; B shows the part of the plant that is underwater; C shows the shadow the above-water parts of the plant casts on the water surface; D shows the part of the plant that is above water, and E shows the reflections of that part on the water surface. Finally, panel F shown all parts together, with transparency adjusted to provide a realistic image; or I hope so anyway. The Draco and the reed it sits on will be constructed similarly.

That's it; the next post will probably be about hexapod gaits, and will include the sounds of some gaits, including a hexapodal gallop…