The case of the Dancing Dune Spidrids: are they intelligent?

The second episode of my spidrid microdocumentary series has just been published on YouTube and Instagram and is now visible on this blog too. The YouTube version has the highest quality. 

This episode focuses on a species of spridrid in a dune habitat, but the episode is not so muuch about the habitat as it is about behaviour of the animals. That is complex, because any choice I make regarding animal behaviour immediately triggers many implications and assumptions. 

While making these videos, I quickly found that making a film requires a different focal point than the painting-plus-text approach that I used so far. For a painting to work, its composition, use of colour and of dark and light tones are of prime importance. I will go so far as to say that the subject matter comes second. In video, things need to happen, so the animals need to do something that forms a story. I started making spidrid animations with an initial emphasis on their radial build and their locomotion. This was the logical thing to do, but you cannot show some spidrid changing direction without rotating its body ten times and still expect people to remain interested. What can spidrids do, besides walking, that attracts interest? 

 

Well, in nature documentaries carnage always grabs the attention, but spidrids aren't big fierce predators, so no spouts of crimson blood there (greenish blue blood, actually, but never mind). There is also the fact that animating the spidrid's four mouth limbs as well as its central ventral beak on its tentacular 'neck' would require as much programming effort as the rest of the animal put together. 

There's also sex of course, but you may be surprised to learn that I focused on biomechanics to such a degree that I never gave any attention to whether spidrids produce eggs, live young, or something else. It works, that's enough for now. One fundamental matter here is that producing sperm cells is metabolically much cheaper than to produce all the material needed to build functional offspring. It should be much easier for large animals than for small animals to afford the high metabolic cost of that latter, female, route. And yet many male animals are larger than females, showing that other considerations, such as scaring off male competition, may be more important. Somewhere in that balance between costs there should be room for animals to change sex in accordance with their size as they grow throughout life. That was in fact what I thought when I designed the large spidrid in the video. That giant specimen in the video is one and a half time larger than the smaller ones, so it is at least three times as heavy (it has appropriately thicker legs). Its size ensures dominance, but the video leaves it open whether the animal is a male approaching females or the opposite. At any rate, you may safely assume that the giant has reproduction in mind. 

The third aspect that may attracts interest is social interaction, which the video focuses on. These spidrids use complex body movements and vocal cues to interact with one another. Their colours are probably also a social sign. The more animals there are, the more complex their interactions become. Does that mean they are then signalling to several others at the same time? That would make them rather clever. The existence of complex social interactions is probably tied to intelligence; the 'social intelligence hypothesis' even holds that social interactions were a major driver of human brain evolution. The same may well apply to other bright social animals, such as ravens and other smart birds. Could spidrids have a level of intelligence approaching or equalling that of birds? Why couldn't they? I for one do not believe that the obligatory requirements for intelligence throughout the universe include being an upright ape with opposable thumbs.

Furaha microdocumentary 1: The spiny desert slantie

Well, here we go: a Furaha microdocumentary. I gave it the number one, although that is not entirely accurate. I have made several videos in the past that might also be called 'Furaha microdocumentaries'. Those older videos reflected ideas about Furahan wildlife that are no longer current, with as the most obvious example the presence of ballonts. That is one reason to regard them as behind the times; another is that my new breed of microdocumentaries is of higher quality, or at least I like to think so. Finally, the new microdocumentaries tie in with the Furaha book and will hopefully increase sales. The Book is set to become available at the end of this month, October 2025, or next month. (The reason for the uncertainty is rather sobering: the books are printed in India and have to be shipped to the UK, but unrest in the Red Sea may cause a detour around Africa.)

  

Here it is! Blogger only shows videos at a rather small size, so I strongly recommend that you have a look at the video on my YouTube channel, where you should be able to see it in its full 1920 by 1080-pixel glory.

 I aim to produce more such videos, although they take a long time to produce. I thought beforehand that ray-tracing the images would take the most time, at three to five minutes per image for 24 images per second for something like a minute and a half. Although that amounts to about 144 hours, rendering can be done at night without paying much attention to the process. Programming the animals' movements takes devoted attention though, and that costs time, as witnessed by my previous post on such animations.             

If all goes as planned, there will be three or four microdocumentaries for each of the clades spidrids, cloakfish and tetrapters. Don't expect one every week! There will also be a general 'advertising video' out shortly.

As for the spiny desert slantie, its scientific name is Obliquambulator serratus. This is probably the first time I use the word 'slantie' in this blog; it occurs more often in The Book and represents a colloquial term for 'slanted spridrids', as described here first. In 'normal' spidrids, the legs move in a vertical plane and each leg segment is bilaterally symmetrical. In slanties, the plane of the leg is at an angle to the vertical and that angle is now part of the anatomy: slanties cannot in fact rotate their legs to become fully vertical. The slanting had no effect on leg shape early in slantie evolution, even though one side of the leg was now habitually up and the other side down. But later the legs segments evolved asymmetry, as shown clearly by the spines on the legs: these spines stick out in a horizontal direction, both on the top side and on the bottom side of the segments.

There is more to tell about slanties and spidrids. Making a video raises questions that paintings do not, such as whether the animals make sounds, what kind of sounds, and what they do, socially or otherwise. The video answers a few of those questions.                     

"Future Spidrid Microdocumentary May Feature Silly Walks"

 Well, there's a headline for you. This post contains a quick update on the evolution of the intended 'microdocumentaries' about spidrids, cloakfish and tetrapters. 

Why microdocumentaries? Because even animations of a few minutes take a long time to make if every frame is raytraced. Why spidrids and the other mentioned clades? Because seeing these animals move definitely adds value, compared to a diagram or a still image. There won't be hexapod microdocumentaries because my animation skills do not include such soft-bodied animal shapes. Not yet, anyway. 

The key elements of programming tetrapter movement are already there and I expanded the Matlab programmes that control cloakfish movement. I have almost completed work on programming spidrids, allowing visualisation of walking over uneven ground, separate movement of the abdomen and cephalothorax, slanted spidrid legs, and spidrid social signalling. I am considering having multiple spidrids walk about in a scene; that would be nice but is not essential.   

There was a very major snag along the way. I had intended to use Zbrush for 3D modelling, and had thought that I could use ZBrush, Sculptris, Photoshop or even Window's 3DPaint to paint body parts and produce texture maps. Unfortunately, Sculptris and 3DPaint no longer work well, maybe because Windows changed too much. Adobe abolished 3D painting in Photoshop because they now have a separate program for that. A glance at internet sources convinced me that ZBrush made texture exporting extremely complex, in true ZBrush style (for some reason the people at ZBrush keep clinging on to a horribly unfriendly user interface). What now? Well, with trepidation I turned to Blender, which had scared me off years ago because it was equally unfriendly. But the Blender user interface was said to have become friendlier now, so I downloaded Blender and selected the subjects of sculpting and texture painting for study. About 9 days later, I had modelled and painted all body parts of a new species of spidrid and had exported them successfully along with roughness and colour maps. I think that is telling, as I started with zero Blender knowledge. Mind you, Blender is still complex, because it does complex things; but there is a solid logic behind it.

 

So here is a try-out of a new spidrid species, produced with Matlab, Blender and Vue. There is a version with better resolution on my YouTube channel.  You may expect this species to feature in scenes of higher quality with sound, plants and more scenery.

 

 

And here is my rough starter species walking with a 'pronking' gait to impress potential mates. In this spidrid gait, two sets of four legs move together. It is an eight-legged version of the 'double tripod' gait used by insects, so I am calling it a 'double table' gait. In the pronking version, the body is held high and the legs are lifted much higher than needed. I think this walk is objectively silly, but you should ask the intended audience what they think of it, and that would be other spidrids, not me.       

By the way, I am trying my hand at Instagram too; you should be able to find me using 'J.Gert van Dijk' 

Photorealistic spidrid animation (maybe...)

 Now that The Book is out of my hands, I can pick up some old Furaha projects that I had to pause earlier on. I used Matlab, a programming and analysis tool, to produce animations to see how various animals moved. The resulting 3D representations helped a great deal to get a better feel for the gist of the movement and were very useful to get the paintings right. However, I also wanted to produce more lifelike, even photorealistic, animations. Those with good memory may remember that I used to do entire Furahan scenes using a 3D rendering programme called Vue (or Vue Infinite) from the firm E-on. There are some on my rather inactive YouTube channel.  

Producing even short animations proved to be extremely time-consuming. Vue is a raytracing programme that produces very good atmospheric results, but each frame took ages. I used to leave my PC running for one or more nights. The problem with animations is then that you only get to judge the the quality afterwards, and you may then have to do it all over again. 

The main reason I stopped making visually rich animations was that they did not contribute to The Book; by consuming time, they in fact postponed its completion. Another important reason was that programming animations was often frustrating. I could achieve my goals in Matlab, where the problems boiled down to defining rotations and translation of every body part of a radially symmetric eight-legged spidrid walking on uneven ground, with the body attitude compensating for the slope. That was complex in that it was difficult to keep track of everything, but the key parts required fairly basic trigonometry. The seriously frustrating part was to reinterpret the resulting data with Python code to direct Vue. The coordinate systems never really matched up, even if I started with both the y-axes up in both systems and similar handedness orientations of axes (that means whether the positive x,- y- and z-axes pointed in the same direction in both programmes. Even though I made sure of that, I still had to swap y- and z-axes, which in turns messed up all rotations.  

Here is an old example I posted back in 2013. There was a problem with the legs: sometimes the leg segment closest to the body (that wasn't shown) flipped around, so the pale underside is suddenly placed the wrong way. This happened when that segment rotated beyond the vertical position; let's say the rotation angles moved from 85 to 95 degrees. This was almost certainly because a function such as arc tangent interpreted 95 degrees as 5 degrees. At the time, I gave up and shelved the programme. 

I have now tried again, helped by the fact that I now have the latest and much more stable version of Vue. Sadly, Vue's parent firm (Bentley) decided that it would no longer develop Vue at all, so the 2023 version is the last one ever. The good news is that Vue is now available completely free. This version is a pleasure to work with. You do not need to be able to code at all to use it.

Here is a Matlab example of expanded spidrid animation functionality. You can see that the spidrid follows the terrain perfectly, meaning that the body posture echoes the terrain under the body precisely. You can also see something new, present in my spidrid paintings, but not yet in earlier spidrid animations. In earlier animations, the body consisted of one part whereas theyere should be two: a bottom part (the abdomen) that bears the spidrid's eight legs and a top part (the cupola or cephalothorax). The cupola can move on the abdomen. In this animation the copula is stuck firmly to the abdomen. 

In this second example, the abdomen is partly stabilised and no longer follows the terrain completely, so it stays more horizontal than in the previous animation. The cupola now moves independently and has its own tilt-dampening stabilising reflexes, so it stays even more horizontal than the abdomen. That should help the animal get a more stable platform for its senses.

After rewriting the python code the next step was raytracing with Vue. After suffering much misery and new dents in my wall where I banged my head, I got it working. The next phases include adding an abdomen and a cephalothorax, perhaps even feelers, and then it is time to add plants swaying gently in a breeze. 

Wish me patience...

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For those who wish to use Vue, or its associated plant editing software 'PlantFactory', you can download them here. 

As I said, this last version is quite stable. With Vue it is not that difficult to produce an image of a forest with prehistoric trees or something like that. If you wish to have more control over Vue's myriad options, be advised that this is a complex piece of kit that needs attention and time. 

For tutorials, there are several; GeekAtPlay provides good ones. 

From erect dinosaurs to pivoting fly feet (Frustrating feet 2)

This post is long, fairly complicated and rambles along a bit, so do not say I did not warn you. We are so used to seeing big mammals that most ‘alien’ legs in drawings and films are just mammal legs. One thing you will find in many books is that a key feature of mammal locomotion is that the legs are 'erect'. 

 

Click to enlarge. From Box 4.3 in: Fastovsky & Weishampel. Dinosurs A concise natural history. Fourth Edition Cambridge University Press 2021

 

The image above shows such a scheme, making the point that dinosaurs legs are as erect as mammal legs, using a human as an example. I have always felt that the legs of the dinosaur in the picture are not really 'erect', while the human's leg both are less erect than they usually are in a standing human. 

Click to enlarge; copyright Gert van Dijk

Let's explore this further. Above, you see the species Disniformis inexpectus and on the left its cousin, D. expectus. The elbows and knees of D. inexpectus stick out sideways, while those of D. expectus do not. Which animal stands in the most energy-efficient way, and which is the most 'erect'?

 <pause to think>

Many readers may feel that D. expectus wins on both accounts. But have a closer look: in both animals the feet are placed precisely underneath the hips, and the leg segments are tilted in opposite directions as you move down. Because the joints are angled, energy has to be spent to keep these joints from bending further under the influence of gravity. How much energy depends on the angle of the joints and how far these joints are situated from the vertical line connecting hips and feet. Guess what: the legs and joints angles are exactly the same. The legs were just rotated, except for the feet, so exactly the same amount of energy is needed to keep the joints stable.

Personally, I would call a leg fully 'erect' only if the segments are all vertical, as they largely are in standing elephants (and standing people!). If all segments are fully erect, the feet must end up directly underneath the hips. In the dinosaurs and both species of Disniformis, the feet are also placed directly underneath the hips, and it seems some authors use the word 'erect' to mean only that aspect. The opposite of 'feet underneath hips' (FUH) must be 'feet away from hips' (FAFH). If the feet are placed well to the side of the animal, you get a sprawling stance, like salamanders and insects use.         

Perhaps you feel that all this changes when the species start to walk, and then we will see that D. inexpectus can only plod along while D. expectus trots elegantly out of sight. Not so! The legs of both species can extend to the same length and the joints move through the same arcs. This means that  elbows and knees can be kept close to the centre of the animal regardless of whether they deviate to the inside, outside, back or front.

 

Click to enlarge; copyright Gert van Dijk

Still, D. expectus will have a gait advantage in that its joints can be designed much simpler than in D. inexpectus. The dinosaur drawing and the reworked D. expectus above show simple hinge joints that allow the legs to move only in a fore-and-aft direction. That save energy; nice, right?

It would be nice if animals were like trains, only moving along predefined linear tracks. But they also need to turn and to step sideways and do other things beside walking in a straight line. An animal must be able to move its feet fore and aft, but also to the side, and must also be able to turn toes in or out. This requires rotation along all three axes. You can be creative and appoint different movements to different joints, but iff you wish to obtain the largest reach for the foot, you should give the hip joint the most freedom. That is probably the reason mammal hips have ball joints (and dinosaur hips too, as far as I know). My guess is that the most proximal joints (hips/shoulders) in alien animals will also have three axes of rotation. Mind you, the three axes do not have to be used to the same degree in daily life (fore-aft movements will see more use than toe in/out movement).

The ankle joint should allow the foot to adapt to uneven ground, so the joint must allow a toe up/down rotation and also a thumb up/down rotation. That is two axes already; we will get back to the third axis. This leaves joints in between, and these need only have one direction of rotation, like mammal knees (that need not be universal though and is probably something for another post).

 

Click to enlarge; copyright Gert van Dijk

We are now getting to something that has vexed me for years. Above is an image from a post from 2010, showing D. salamandris. This is what I wrote at the time: "To get a movement suitable for walking, its foot should move in a straight line from front to aft … But ensuring that the foot always points forwards also requires that there is a way to rotate some of the bones around a longitudinal axis."

It is the need for that third rotational movement in animals with FAFH ('sprawling') legs that vexes me. Humans are very good at this movement, called pronation and supination (if you hold your arm in front of you, turning the palm down is pronation and turning it up is supination). But I couldn’t find good discussions on this type of movement in the prototypical sprawlers: arthropods. If readers know about such studies, please let me know.

I looked at some internet videos of walking insects to see whether their feet remained fixed to the surface while the leg rotated; if so, these insects had pro- and supination. I would expect the tarsus to allow that movement, even though the text I found previously said that the tarsus only allowed flexion and extension. If the foot would rotate along with the leg, it would pivot over the ground, something hardly compatible with a firm grip.

There weren't that many videos that allowed such close scrutiny, but here is one, showing a fly walking across glass. The foot stays in largely the same position and does not rotate along with the leg. To allow it to that while the hip is moving forward, something has to 'bend'. The tarsus indeed seems to bend a bit, but not much. In fact, the tarsus keeps on pointing in the same direction all the time. 

 

Click to enlarge; copyright Gert van Dijk

I thought of a possible explanation, and it involves a different kind of hip movement. Above are two spidrids. The first has a typical vertical axis of rotation through the hip; that's a normal spidrid. The rest of the leg lies in a plane, and the movement is shown by two 'ghost legs' (this is typically how crabs move). The second image has another hip, with the axis horizontal. The animal can still reach fore and aft, but the results looks different.

 

Here is what the differences amount in an animated view: first a typical spidrid movement with a vertical axis. The gray structures indicate the planes in which the legs move.

 

And now a Neospidrid with a horizontal axis (the model caters for intermediate angles too).

An thay means we can get back to flies; in a textbook of arthropod anatomy (Manton 1977) I found indications that insects hips have an added 'rocking' movement that would indeed allow some rotation around a horizontal axis. But there's a rub. With such an axis, you still need pro- and supination to keep the insect's 'palm' against the surface. I still do not know how insects solve the need for this longitudinal foot movements. Crabs are probably easier, as they have no feet in the common sense, so they can just pivot on the tips of their legs. 

I confess that designing alien animals is sometimes easier than studying Earth animals. In particular when it comes to feet!                    

 

 

Explaining Spidrid walking

 This will be another fairly short post. In the previous post I explained that I was working on pages for The Book that explained some biomechanical tricks of Furahan lifeforms. Other such explanatory pages deal with things such as rusp snouts and gaits (done), photosynthetic spectra (done), cloakfish movements (to be done) and spidrid gaits (done).

I will not show the actual spidrid illustrations, but can show you some of the underlying thoughts by way of animations.  I used the programs -all Matlab- to produce such animations to choose a single frame, which I then rotated this way and that until I was pleased with the composition. The resulting image was then imported into Corel Painter and used as the guideline for a digital painting. But I will not show these here.

 

The first animation shows your typical run of the mill garden-variety spidrid. It is walking slowly, meaning that each leg is on the ground for one half of the walking cycle. With eight legs, it is easy to have enough legs on the ground to provide a stable support platform at all times. The ‘support diagram’ is a polygon connecting all feet that are on the ground at any one time.

The gait used here is what I call an ‘alternating ripple’. Imagine that the legs are numbered 1 to 8, going round the animal. If the phase differences are 1/8, 2/8, 3/8, up to 8/8 in the same leg order, then legs that are close in phase would also be close in space, so many legs on one side of the beast could be off the ground at the same time, so it would tipple over. So, we introduce an additional offset for even-numbered  legs: 1/8, 5/8, 2/8, 6/8, 3/8, 7/8, 4/8 and 8/8. You will probably need some graph paper to get to grips with all this...

The red lines show the path a legs traces in 3D space. Because the ‘camera’ follows the body, the tracer paths are also respective to the body. The effect is like that of the animal walking along on a treadmill.  

The second one is very similar, but the main difference is that the legs are on the ground for less than half the time. Such schemes are typical for fast movements. The animation runs at the same number of frames per second, so you cannot appreciate the speed difference. There are fewer legs on the ground at one time. The polygons of the support diagrams have now morphed into lines or even points, if there is only one leg on the ground.       

  

Now we move to a more specialised racing spidrid. The camera no longer moves along with the beastie, but is fixed in space. The animal has relatively long legs, and runs the risk of knocking them into one another. That has to be avoided by reducing stride length a bit and adapting the gait: adjacent legs should not be at opposite phases in the cycle, as they then will certainly knock into one another. This one is using the ‘slow’ leg pattern at which a foot is one the ground half the time.   

This is the same racing spidrid at high speed. Each leg is now on the ground for less than half the time, more suited to fast movements. The animal changed its gait in two ways: the first is that the phase differences between legs are smaller, and arranged in such a way that at times there is no leg on the ground at all. It is effectively jumping! The second change is that the leading leg could only contribute to forwards movement by powerful and fast flexion movement, and I decided that the flexion muscles are relatively weak, so the animal simply lifts that legs into the air. (It should really move the body up and down as well, but the animation was not designed for complete realism.)

Many of the principles here are quite common for earth animals: walking faster is often achieved by increasing cycle frequency, stride length, reducing the fraction of the cycle that a leg is on the ground and adapting gaits to achieve jumps. Most mammals and reptiles always use all four legs at all speeds, with a few exceptions (kangaroos, probably hadrosaurs; no doubt there are more). But these poor unfortunate creatures have to make do with only four legs anyway, leaving them little choice. Earth crabs do have choices, and when they speed up, they actually use fewer legs, down to just two. Spidrids, not to be outdone by Earth creatures, have similar tricks up their virtual sleeves.

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...

Spirally slanted spidrids II

The post has the simple purpose of showing that there is progress with The Book. Readers with good memories may remember that I write about spidrid gaits back in 2013. In one post, I toyed with the idea of changing the plane of movement of the spidrid legs from a purely vertical to an angled one. This was inspired by the legs of many crabs and by those of scorpions.

Click to enlarge; from Wikipedia

Here is a nice image of a scorpion from Wikipedia, showing that the plane of the legs is not vertical but at an angle to the ground.

Click to enlarge; from Wikipedia

And here is a 'sally lightfoot' crab (Grapsus grapsus) also from Wikipedia. Note that the hind legs are seen edge-on, so the plane in which they operate is at an angle of that of the surface on which it stands. 

This inspired a very lively discussion in the comments sections why the legs would be slanted. Among the possible advantages were that the animal would be less high, so it could fit in a crevasse among rocks, or it would be less likely to be swept away by tidal waters. Another argument was that the slanted posture allows more muscles to be recruited for propulsion.

Well, I can now add that I found some evidence for the latter argument, in Mantons's Arthopods (There is more on that book in this post). It is difficult to find anything on the biomechanics of arthropod joints. It seems that most of the relevant work was done in the 1960 and 1970's by Manton. In the end I bought a second-hand copy of her book, which proved to be one of the most densely-written science books I have ever read, but it contains an enormous amount of information. She wrote about 'rocking' of arthropod legs, the word she used for what I described as 'slanting', and her reasoning was that it recruited additiopnal muscles for propulsion. No formal proof though! It does not mean the other arguments are invalid though!

In 2013, I produced this quick and rough animation of what a 'spirally slanted sipidrid' might look like.  I recently sat down to do justice to spidrids in The Book, which means doing a few proper paintings with accompanying size diagrams and maps. I chose to add a slanted spidrid to the introductory page showing the variety of shapes spidrid bodies can take. I do that more often: designing various shapes is fun, and it nicely illustrates adaptive radiation. It also allows me to paint various colours and different surface textures.

Click to enlarge; copyright Gert van Dijk

Here it is. It is just a fragment of the original 4200x6000 pixel illustration, and is just meant to give you a taste, not to satisfy your appetite! As you can see, I chose to go with the shiny texture of the sally lightfoot, as well as its riotous colours.  The text introduces it as follows:

"Mad Sickle
This species represents a major spidrid clade. While ‘square spidrids’ move their legs in a vertical plane, the ‘slanted spidrids’ do not: the basic leg joints have tilted. The most likely reason for this is that the flexion and extension muscles can now more easily help with propulsion. Most ‘slanties’ are very flat and live in crevasses. There are clockwise and anticlockwise slanties; the direction is inherited, so each species has its own exclusive direction. It seems that the two types of slanties arose completely indepedently, so ‘clocko's’ and ‘antics’ are not at all related. The mad sickle is very agile. Please do not try to catch one: you disturb them, you are not likely to succeed, but if you should, it will pinch you very forcefully. 
Name Sicilicula insana; Sicilicula (L.): little sickle; insanus (L.): frenzied, maddening"