Illustrating symmetry

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

Click to enlarge; copyright Gert van Dijk

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

Click to enlarge; copyright Gert van Dijk

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

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

Click to enlarge; copyright Gert van Dijk

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

Click to enlarge; copyright Gert van Dijk

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

Brachiation versus cernuation, as well as mono- and tribrachial brachiation

I have tried to make the title of this post as obtuse as I could; I hope everyone appreciates that...

In my recent post on the marblebill, a Furahan brachiating predator, I discussed several restrictions that a brachiating lifestyle puts on an animal's body plan. Among others, those were a need for other limbs beside the swinging ones, so the animals would also be able to walk as well as climb vertical surfaces. There is of course no need to completely separate such purposes among limbs. After all, gibbons use their arms for climbing and walking as well.

I also wrote that I knew of only one other brachiating type of animal in speculative evolution, and that this was the squibbon in 'The Future is Wild'. It turns out that that statement was wrong on at least two counts. Firstly, in Dougal Dixon's 'After Man' there is a striger, a tree dwelling feline carnivore. Although its description does not stipulate brachiation, the accompanying picture certainly suggests it. There are bound to be other brachiators too somewhere in the growing field of speculative evolution. Secondly, the squibbon does not brachiate at all! It somersaults, meaning its body is upside-down at some stages in its locomotion, which is a fundamental difference with brachiation, in which the body stays upright. I should have checked that before I wrote it.

Clip from 'The Future is Wild' DVD

To illustrate the difference I have cut a short clip from 'The Future is wild' to show the squibbon's way of propulsion through the trees (easily available through Amazon etc). I know of no Earth animal that does this, so this is really a very ingenious design. Often when you try to think of a novel animal locomotion, evolution has been there and done it already. It is a pity that the designers did not give this locomotion mode a nice name. I now propose 'cernuation', derived from the verb cernuare, meaning to 'fall headfirst / dive / turn a somersault'. Cernuation does pose a problem than brachiation does not: the visual field rotates 360 degrees in each jump, which must make the job of working out where to jump at high speeds even more difficult than it already is. The placement of the squibbon's eyes near the horizontal axis around which it cernuates proves that a lot of thought has gone into this animal. Being on the axis the visual field will still rotate 360 degrees with each movement, but will not shift as much as when it would be somewhere else (there may be room for creativity here though).

The remainder of this post will deal with the number of limbs involved in brachiation. The marblebill uses just two arms for brachiation, just like gibbons and other brachiating primates. This being a blog about speculative biology, the question rises whether it can be done with other numbers of arms.

How about just one? Theoretically this is possible: the animal has to leap from one handhold to the next. There would be no way to go slowly though, as you can with two arms. Slow-moving brachiators can afford to let one arm go while the other has a firm grip. In effect, one-armed brachiation is very much the same as hopping on one leg: each hop is a jump and requires lots of energy. It would be dangerous as well.

Two arms has been dealt with, so three is next. Actually, there are three-limbed brachiators on Earth: there are brachiating monkeys using their tail as well as their hands. When I discussed walking with an odd number of limbs, I could not find any animal that did so with three legs. Tripod walking poses the problem of phase: do two legs move together while the third moves on its own, or is the cycle divided in three equal parts? In the monkey case, the starting point is bilateral symmetry: two limbs are paired and the tail is not, which suggests that an equal division of the cycle is not feasible. The other possible solution is not the case either: that would be that the two arms swing together while the tail holds a branch and vice versa. So how does it work? Essentially the monkeys alternate their arms in the usual brachiating way. The tail helps along by being placed in time with the hand, and right next to it, in fact. Moving the tail in this way may act as a safety mechanism, but has an effect on body sway as well.

Click to enlarge;

Turnquist et al; Pendular motion in the brachiation of captive Lagothrix and Ateles.

Am J Primatol 1999; 48: 263-281

The image above requires some study. If the tail is placed next to the hand, does it do so for both hands? That is indeed possible, and the tail then moves twice as often as each hand does. The authors of the paper describe the movement as 'choppy'. I suppose that this may be only known locomotion in which one limb moves at twice the frequency as other limbs do. I know of one speculative animal that does this, but was not aware of anything of the sort occurring on Earth! This is not the only solution though: some monkeys use their tail in the same frequency as their hands, to the effect that the tail only helps one hand, either the left or the right one. Odd, isn't it?

Is brachiation with more arms possible? Theoretically you could do it with four arms, and the pattern then becomes an upside-down tetrapod gait. Nothing new there.

Can you brachiate with radial symmetry? Yes; an intriguing way would be to let each successive arm take the weight. Envisage a spoked wheel and roll it: the successive spokes point to the ground one after another. Of course, this causes the body the rotate once more, and gain the body's axis of rotation is horizontal, at right angles to the direction of movement, so this is cernuation once more.

There are no cernuators on Furaha, or at least not yet. I do not think that spidrid anatomy lends itself well to moving into the trees. One or two species sometimes roll downhill on their sides to make a getaway, but that is as close as they get. I wonder about other places...

Cathedral Tree screensaver

1280 x 1024; click to enlarge

1280x800; click to enlarge

1024 x 768; click to enlarge

I have been looking into a new and more self-evident menu for the website. I have also been trying to found out more about stomatopod vision, so it is perhaps no wonder there was little time for an extensive post. But I thought I could give you something new: a Furaha screen saver. The scene is that of an open forest dominated by cathedral trees. It is early morning, and the shadows are still long.

Click on the image, which should open a larger version. Right-clicking on that should allow you to copy it and set it up as a screensaver.

The three resolutions (1024 x 768, 1280 x 800 and 1280 x 1024) are the ones most readers use; together they serve over 50% of readers. The remainder almost all use higher resolutions. The original image is at 1920x1200, so I can produce a larger one if anyone wants me to. By the way, issue 32 of Cosmos Magazine should be out in Australia now, and it has another scene of the same forest in it. I will write more about it when my copy arrives.

G is for Greenworld ( Greenworld III)

Click to enlarge

It's been only a few days since my last post here, and I normally try to post at intervals of one week or a week and a half. The present post is an extra: it is short, did not require any research, and is a kind of Easter egg. The occasion is Greenworld again. Dougal Dixon sent me an email about my earlier post on his new book, Greenworld. As that book is in Japanese, I had to guess a bit at what was happening here and there. Dougal wrote an email about my guesses; rather than just adding it as a comment, I decided to give the book some additional attention. That's why you will find the other half of the children's alphabet above. The 'G' of 'G is for Greenworld' can be found in the provious post. There is 'D for Dixon' though. So here is his email: "Dear Gert, I would just like to express my appreciation of what you are doing for GREENWORLD on your blog. As to your speculations, you are quite right in the interpretations of what you have seen. The TAME YOUR OWN STRIDA poster is indeed an advertisement for a service that allows the customer to train this animal and use it as we would use a horse. In the book it is followed by another poster that implies that the industry has moved on and that now all the training is done by the kraal itself, and the customer does not need to bother himself with the dirt and inconvenience. The subtext here is that the colonists are still using the living resources of the planet but, but bit by bit, are moving away from any connection or empathy with those resources. (And there is a suggestion that one of the partners has ducked out of the business in protest at the way things were going.) And this item is South African in background - there is a whole multicultural spread throughout the book representing the cosmopolitan nature of the settlement. The ARTEMIS poster is a bit of fantasy, showing an idealized relationship between settler and animal life. The reality of taming one of these beasts involves hobbles, muzzles, blinkers, whips, goads, force-feeding and all the rest. The illustration labelled "17" is meant to be part of a series of "survival guides", this one being how to trap a rogue spitter - one that is not part of anyone's herd. The lure is based on sexual attraction. These guides tend to emphasize over-exploitation and waste. I have just thought - I should be putting all this on your blog site. Please feel free to do so if you wish. Dougal"