## Friday, 5 February 2021

### 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.

Abbydon said...

Out of curiosity, is it possible to estimate the energy consumption (or cost of transport) of each gait to determine the most efficient speed?

Star Platypus said...

Are spidrids insect analogues or are there big ones

Sigmund Nastrazzurro said...

Abbydon,

Well, I can't at present, which is probably not much of an answer. But obviously walking faster will require more energy. With mammals, there has n=been much work down on when humans, horses, dogs, etc with from one gait to the other. Suppose you keep a walking gait and wish to move faster. at one point you get racewalking, an Olympic sport. The energy requirements of most gaits follow a curved shape, with a minimum cost at a certain speed. Running has a similar curve: it is inefficient at very low speeds an at very high speeds the cost goes up sharply. If you overlay the two you see that there is a speed at which the two lines cross; below that speed walking costs less than running, and above it running costs less. That is the point at which you 'break into a run'. The same holds for walks, trots, gallops etc.
But do various spidrid gaits have similar curves? I think they do, but perhaps only for really high speeds.

Star Platypus: from a few mm to the size of cats and smaller dogs.

Jonathan said...

How about odd-legged spidrids with 7 or 9 legs?

Keavan said...

This gives me thoughts of a chase-hunting spidrid with a centaurised front leg/lifted leg used as a spear or club.

Sigmund Nastrazzurro said...

Jonathan: I discussed spidrdids with an odd number of legs before: There is 'Odd walkers' from October 2009 and 'Odd walkers II' from June 2010.

By the way, Google offers a search function for its blogs: it is in the top left corner of the blog.

Keavan: I had soimilar thoughts: please have a look at the two posts on the 'prigoon', from October and November 2019.

Abbydon said...

It's not directly relevant to spidrids or Furaha, but I'm particularly curious about how gravity influences gaits and walking/running speed. I believe that high gravity enables faster running (i.e. greater weight produces more friction which allows greater pushing force and higher acceleration for the same mass). However, it also produces a faster walking speed as this is linked to period of a pendulum the same length as the leg. It would of course require more energy to move regardless though.

Would this lead to short legged animals that walk at Earth normal speeds but can sprint surprisingly quickly for short periods?

anthony said...

How would megafaunal "spidrids" walk? Imagine a radially-symmetrical elephant analogue that weighs 8 tons and has 8 limbs

Sigmund Nastrazzurro said...

Abbydon: Interesting question. I would have to check the books by McNeill Alexander and e the like to see whether the answer is easy to extract. Off the top of my head I can only offer some suggestions.
I doubt that 'too little friction' ever poses a serious problem, except for odd circumstances. It does not seem to pose problems even for minuscule arthropods, where the forces they exert of the terrain must be equally minuscule.
The pendulum idea is very interesting. You find it mentioned as an important feature in human walking, but human walking is decidedly odd in various aspects. I do not recall seeing a pendulum mentioned much in texts on animal walking, but may well be mistaken. I will check some sources and see if I find anything meaningful.

anthony: Furahan spidrids are exoskeletal, and that heavy exoskeleton becomes a burden at large sizes. But on other worlds you might have endoskeletal radial walkers. I would expect them to show the usual 'antigravity' tendency towards legs held straight under the body, as that reduces the effort of muscles to counteract gravity forces. Such a tendency will be needed more with higher gravity and with higher animal mass.

Dennis said...

Are there aquatic spidrids? How would they swim?

TheWingedScourge said...

I wonder how the internal anatomy of spidrids would look like. How would their digestive system work?

Unknown said...

I would wager that those last two, are surprises we will discover within The Book.

-anthony docimo

Sigmund Nastrazzurro said...

Dennis: there are now...

TheWingedScourge: I do not understand what it is you specifically wish to know. the basic process is that of any digestive system. both the mouth and the anus are at the underside of the animal, and that is where radial symmetry breaks down (evolution does not seem to care much about internal symmetry anyway).

Anthony: at present you would lose that bet, but the idea of aquatic spidrids appelas to me, so we will see...

land sea lion said...

how would eyes in predatory spidrids work. there's this thing about "predator eyes face forward" that keeps being said about humans and wolves and eagles but is probably not strictly true given that snake and killer whale eyes face to the sides, and probably gonna be harder for any predator who has no definite "forward"

just a female Kayentatherium that joined the Italian mafia said...

It would be cool to have eusocial spidrids! perhaps there could be soldier castes that like the prigoon break thw radial symmetry and weaponize one limb.

Sigmund Nastrazzurro said...

land sea lion: interesting point. Predators like the prigoon gave up radial symmetry and have eyes focused forwards, but that is not what you men. I suppose that predators that rely to a large extent on other senses than vision need not follow the 'eyes forwards' rule, so there is that. But spidrids are largely visual creatures. It may depend on the hunting strategy. Mantises and many other insects have high-resolution areas in their eyes that provide good spatial resolution over a small angle and allow distance estimation through stereoscopic vision. Spidrid eyes could have similar sopts in each eye. Another approach that appeals to me is focused attention, that you may pragmatically define here as directing increased neural activity to both stimuli and associated tasks.

just a female... I have for a long time been toying with the idea of having an eusocial species building something like a termite mound, but bigger and definitely stranger. That was just a vague idea though. I will think about whether spidrids could take up that role. until now

Unknown said...

orcas and snakes *do* have binocular vision...you don't *need* eyes facing perfectly forwards, so long as at least part of the eye has an unimpeded line of sight to things in front of it.

...that said, given the radial nature of spidrids, perhaps they only have one, two, or three eyes aiming mostly/partly/entirely at "forwards", and the rest of the eyes look around for dangers.

>Mantises and many other insects have high-resolution areas in their eyes that provide good spatial resolution over a small angle and allow distance estimation through stereoscopic vision.
That sounds familiar...is that the way it works in Furahan hexapods?

(i really like the "focused attention" idea)

-anthony docimo

anthony (not docimo) said...

Dont orcas hunt with sonar and snakes with vibration and thermo-reception? I guess having a lot of binocular range isn't really a top priority for them.

That said, jumping spiders, which pounce on their prey, are notable for having their four largest eyes face forward, while two face sideways and two face upward. Perhaps predators with multiple eyes can have similar adaptations?

Sigmund Nastrazzurro said...

Anthony (Docimo+): I did not know about binoculoar vision in snakes (I looked wuickly and found a statement that a minority of South African snakes have it: https://www.africansnakebiteinstitute.com/news/newsletters/asi-newsletter-snakes-and-sight/), but the point was, I think, that predators relying on other senses need not have a spot of high visual acuity in front.

As for spidrids, the ones with true radial symmetry have vision of equal quality in all directions, but in each eye there may still be a spot of high acuity. Eye movement is very limited, but a small movenment of the body will bring anything of interest 'into focus'.

Hexapods indeed have spots of high visual acuity. The side illustration for the marblebill shows the visual fields of its front and hind eyes, with high-acuity regions overkapping in front of the animal. I thought that that would make sense for an arboreal hunter.

Anthony (Docimo-): I agree that binocular vision, or even vision at all, may not be very important for animals relying on smell and hearing. And Furahan hexapods indeed have such eye specialisations, as I just explained for the marblebill. Wadudu do too. (Try saying that out loud a few times.)

Ted said...

wait if spidrids are exoskeletal and insect like then how are there cat sized ones

Unknown said...

they aren't as faulty as Earthly insects (also not perfectly insectlike)
-Anthony docimo

Sigmund Nastrazzurro said...

Ted and Anthony: as usual, Anthony responded first, and I agree with him. You might consider coconut crabs: exoskeletal and large. Whether they are 'insect-like' depends on how closely you look.

lava platypus said...

are there any spidrids specialized for junping like a grasshopper? which legs are modified for the task if it's such a case?

Michael C said...

I wonder if aquatic spidrids could grow bigger than their land cousins.

Gorgonzilla the cheese monster said...

What are spidrid mouthparts like? How do they feed?

Sigmund Nastrazzurro said...

lava platypus: secondary bilateral predatory spidrids like the prigoon certainly jump, and if you look for them on the blog, you can see which legs are specialised for jumping.

Michael C: that makes very good sense. I guess that aquatic spidrids largely behave like lobsters and crabs, meaning that they are relatively heavy and therefore bottom dwellers. To really swim well they would have to lose a lot of mass or add a buoyancy organ. In eother case they could easily be much larger than terrestrial spidrids.

Gorgonzilla etc.: the prigoon image gives a hint: there are hardened jaws at the end of a flexible stalk underneath, and the mouth is surrounded by limbs that can hold and lift food in a rather arthropod fashion.

Desiree said...

How many legs do spidrids have? Is it always eight or do some have more or fewer?

Sigmund Nastrazzurro said...

Desiree: always eight!

Abbydon said...

A colleague just recommended an interesting demo tool online that allows you to quickly sketch a 2D shape and then animate it in 3D. My attempts looked like balloon animals made by Dr Frankenstein but I wonder if you could draw a spidrid walking with it?

Monster Mash

Sigmund Nastrazzurro said...

Abbtdon: that is a very nice program! It should be fun ti use and useful for animals in which all bones move essentially in one plane, that of the screen. if body parts stick out towards or away from the user, you will probably get into trouble as the program does not seem to do any perspective foreshortening. By the way, that is exactly the program I encountered when I made the 2D locomotion animations on the website: no foreshortening. And spidrids will always have some legs that need foreshortening.

a five-meter high, eight-ton pig said...

Are the radially symmetrical flyers related to the spidrids or is their radial symmetry just convergent evolution

Sigmund Nastrazzurro said...

a five-meter etc: they are monophyletic, but the split occurred early in the history of their clade.

AFishWithHands said...

How do spidrids reproduce? Do they have "larval" forms?

Sigmund Nastrazzurro said...

AFishWithHands: aha; well, yes. It is perhaps odd, but I never really bothered with choices as regards procreation of Furahan animals. I made some decisions, such as that larger hexapods may change their sex according to size and group status, implying that one sex invests more in the offspring than the other. But apart from such snippets, I have not thought much about eggs, larval forms, metamorphosis and the like. Sorry.

Schitt said...

what if larval spidrids were sessile sap suckers like scale insects before metaporphosing into mobile adults

Sockmonkey said...

As I recall, regular spiders retain eight legs so they can maintain a stable stance while using 2-4 of their legs as manipulators to build webs and wrap prey.
Spidrids would have a similar advantage in that they could maintain a stable double tripod gait while using two limbs as weapons or for carrying something.

Sigmund Nastrazzurro said...

Schitt: I havenb;t gvuessed at what young spidrids do at all... Sapsucking is a possibility, but I would prefer mobile ones.

Sockmonkey: I think your reasoning is valid, and that a lrger number of legs has advabnatges, such as redundancy in case of loss, or if their is a need for legs to do something besides walking. However, I have my doubt whether it is justified to say that 'spiders retain eight legs SO they can..'. There need not be any causality here.