Monday 24 March 2014

Walking on Kepler-22b, or: How many legs are best for megamonsters? II

The documentaries 'Alien planets revealed' and 'Aliens: are we alone?' are nearly identical productions about the Kepler satellite, looking for planets around other stars. Planet hunting has been very successful: in a few years knowledge expanded from not knowing whether our own solar systems was the only one in existence  to the realisation that planets are a dime a dozen. The free app 'exoplanet' regularly updates what is known about such planets. At the time of writing it has data on 1768 confirmed exoplanets. Most are 'hot Jupiters', massive planets very close to their stars. They, and any moons orbiting them, are too hot for Earth-like life, so what everyone is really looking for are planets of an Earth-like mass circling their star in its habitable zone. This 'Goldilocks zone' is not too hot, nor too cold, but just right to have water in fluid form and therefore life as we know it.

From Exoplanet app; click to enlarge
The various techniques of detecting exoplanets all have in common that the planets most easily detected are the most massive ones close in to their star. Even so, techniques gradually get better and smaller and smaller planets can be detected. The graph above was produced by the exoplanet app, and shows the mass of planets compared to the year of discovery: if techniques keep on getting better, many planets with a mass around that of Earth will be discovered in the near future, and we may even expect much smaller planets to be discivered. I suppose that for a while each new Earth analogue will be announced everywhere, and perhaps that will generate interest in speculative exobiology as well ('Hey! We thought so all the time. Come and have a look at Furaha, Nereus, Snaiad and the others!').

'Alien planets revealed' is in part about the planet Kepler-22b, while 'Aliens: are we alone?' is about Kepler is about '701.04', or Kepler-62f, discovered later. The radius of Kepler-22b is 2.38 times that of Earth, and its mass is estimated to be 6.4 times that of Earth; for Kepler-62f the values are 1.41 times Earth for its radius and a mass of 2.8 times Earth. Both documentaries use the same image material to illustrate the consequences of a high gravity for legged locomotion, which is perhaps more apt for Kepler-22b than for Kepler-62f. Oh well, never mind...

Both might be 'ocean worlds'. Both contain a discussion of life in the seas, of which a short clip is shown above. While the text mentions the need for streamlining as something of universal value for a swimming animal, the animals are less streamlined that I would have thought. Perhaps, but I am guessing here, that is due to an unwillingness of the animator to give the animals a completely fish-like of dolphin-like shape. Even though that would make sense, the result might not look sufficiently alien anymore.

My attention was caught more by a discussion of life on land. A high surface gravity has been discussed in the blog more than once, which is not surprising as it affects so many design features of animals and plants (for instance here and here). The documentary is about walking, and high gravity can be expected to have at least four effects on the design of a walking animal.

Firstly, to minimise muscle energy expenditure you may expect pillar-like vertical legs. Any position with angled bones requires energy to keep the joints from bending. You can expect legs to become more vertical on a planet as animal mass increases, which is very visible on Earth. You would also expect animals with the same mass to have more columnar legs on a high-gravity than on a low-gravity planet; I may do the calculations one day to investigate how animal mass and gravity together should affect bone and muscle size. 

A second effect not directly found in textbooks, but which seems to make sense to me, is the 'zigzagging' of a series of leg bones: they will tend to angle forwards and backwards in alternating fashion (the principle is discussed here and here). The idea behind that is to keep all joints fairly close to a vertical line from the hip down to the foot: this decreases the leverage of the joints and again saves on muscle effort. 

A third effect is found in the number of legs. In a post entitled 'How many legs are best for megamonsters? For megamonster syou may read 'high mass animals on an Earth-sized world', but also 'medium maas animal on a high-gravity world'; the effects are very similar. I calculated the relation between the mass of an animal and the mass of all leg bones, assuming that each leg would support its fair share of the animal's mass. I was surprised to find that the least bone mass was needed if the animal had fewer legs, so theoretically one legs would be most efficient. However, that high 'efficiency' only holds true if less bone mass is the only factor to be considered. But there are other factors, and an optimal solution is biology usually represents a careful weighing of many factors. A larger number of legs would protect against falls and allows better survival chances in case of injury of a leg. In the documentaries, someone must have decided that this risk avoidance would be best served by equipping the animal with eight legs. I do not think that we know what the optimal number is, but meanwhile I have nothing against eight legs.

Finally, there are gaits to consider: there is an infinite number of ways to describe the order in which you can move eight legs in a walking cycle, but which is best? The safest solution is to move just one leg at a time, leaving the other seven on the ground. At the other side of the spectrum there are very fast gaits using just two legs: even crabs and cockroaches can run bipedally! But running can cause falling, and a fall on a high-gravity world may kill you. A safe solution is to always support the body by at least three legs, forming a tripod. So, based on safety and a guarantee that there must be three legs on the ground at any time, how many legs are needed?  It the animal has four and uses a lift-one-leg-at-a-time strategy, the puzzle can be solved. With six legs you can form the basic insect gait with two alternating tripods. That is shown above: note that the left and right legs of each pair move alternately, and each pair is exactly out of phase with the pair in front of it. The results are, going front to back, the left-right-left pairs move in unison, as do the right-left-right legs; but exactly out of phase, of course.

Are eight legs better? Well, it allows the animal to lift more legs at a time while still having three on the ground, and that can be done in various ways. Another solution is simply to expand the principle of the hexapod, and have the new pair of legs move exactly out of phase with the one in front of it. Each tripod becomes a tetrapod; a 'table' if you like. In the 'double table' scheme shown above you can lift and move each table and keep the animal perfectly stable and safe.

And here is the result of the documentary. The person doing the introduction is Lewis Dartnell, who once introduced Furaha at the Cheltenham science fair. Hi Lewis! The documentaries develop the same 'double table' gait through a genetic algorithm. That is fascinating, as it is based on a model taking many forces into consideration. The person who did those simulations, dr. Bill Sellers, has a very interesting home page on animal movement simulation. I had hoped that the genetic algorithm would have resulted in something a little more surprising than the double table that the old-fashioned logical approach predicted, but the double table does make good sense. I am playing with the idea of writing a genetic algorithm myself to see whether this is just one optimal solution, or whether there are several that are nearly just as good. Perhaps it will help to begin to answer the question 'what is the optimal number of legs for large animals taking lots of variables into consideration?.

Sunday 9 March 2014

The Creative Radiation of Cloakfish (Archives IX)

Cloakfish have not featured on this blog often (here and here); the last time was almost two years ago, so it is time to have another look, this time at their earliest evolution. Note that in the 'Archives' series of posts, 'evolution' often does not refer to the fictional biological evolution of these animals, but the evolution of the concept.

Click to enlarge; copyright Gert van Dijk
Leafing though the mouldy sketches in the damp crypts of the Museum of Furaha Biology reveals that their creative evolution started as an offshoot of Fishes. Furahan Fishes started their biological evolution not with series of paired limbs, but with an undulating membrane on either side of the body. Thinking about the movements of such membranes generated cloakfish as an offshoot. The sketch above was originally annotated in Dutch, but for this blog I overlaid them with an English translation. I hope they more or less speak for themselves. The  uppermost picture shows an undulating membrane with a central plane -a rectangle-. The second row shows the 'movement volume' of such an undulating membrane: over time, each point in this volume will be occupied by part of the membrane. In the third row I played with the idea of what would happen is this central plane would not be flat, but curved spirally itself. On the right side you can see how the membrane would undulate up and down around this central plane. The bottom row shows the movement volume of the membrane assuming such a curved central plane. The bottom right picture shows what would happen if you were to group three such volumes together, and that grouping is where Cloakfish depart from Fishes forever: we now have multiple membranes around a central axis, not one at each side of a body.

Click to enlarge; copyright Gert van Dijk
The next leaf of the sketchbook shows the evolutionary jump to a fully developed cloakfish:  the four membranes, the cloaks, surround a central rod, which I could not resist calling a 'dagger'. The body is largely a cylinder stabilised by four fins. The picture also shows an immediate variation on the theme: such a device can pull just as well as it can push. But the central plane of each membrane has reverted to a flat rectangle. I thought that undulation of the membrane around a curved surface would result in a net rotation force, so the poor animal would start rotating around its longitudinal axis. Perhaps I ought to consider the forces of that approach again, but at any rate that is how the basic cloakfish came into being.

Click to enlarge; copyright Gert van Dijk
Once there is a plan, it becomes tempting to start pulling at it to see where that leads to. The top animal here departs quite a bit from the general cloakfish, as its frontal cylinder is nowhere to be seen! It is in fact a tadpole with a cloak-and-dagger propulsion system (well, it also is not much like an earth tadpole in that it has no jaws and multiple eyes). The middle animal certainly is a generic cloakfish, although again with some twists: the front fins have rotated by 45 degrees compared to the cloak-and-dagger. The cloaks are much larger at their end than at the front or middle: this is probably as close as you can get to propulsion with a screw without continuous rotation. The bottom one has the fins and cloaks aligned, causing its four eyes to rotate as well. Whether bending the central rod as shown here would work well is dubious, is think.

Click to enlarge; copyright Gert van Dijk
Here is the result of more pushing the envelope. The left image shows a vertical cloakfish. I certainly did not spend enough attention on the cloak movement, as their shape looks rather unconvincing; then again, visualising the position of four membranes over time is not all that easy. The animal, looking suspiciously like a potted plant, could perhaps travel up and down as day makes way for night to filter plankton wherever it is most abundant. An animal with a horizontal position can do that as well, and if this animal is limited to the vertical position, that will limit its manoeuvrability severely, whereas a horizontal cloakfish could still choose to swim vertically upwards it is needs to; I like that idea. 

Click to enlarge; copyright Gert van Dijk
Of course, cloakfish can be flattened. That separates the cloaks so their movement volumes no longer all touch one another around the animal, but the membranes could still interact in pairs. How the membranes interact is explained on the main Furaha site (which is currently being redesigned). Note that this lineage has rotated its general body alignment by 45 degrees compared to the general pattern, so there no longer is a top fin, but there is a top eye. The dagger has increased in girth and now houses most of the body's internal organs; in conventional cloakfish this part of the dagger is hidden by the front cylinder.

Click to enlarge; copyright Gert van Dijk
Why not flatten the animal laterally? Here you see the result, this time with the overall rotation set to the 'top fin' mode. I doubt that such an animal, which probably has exquisite control over its cloaks, needs the four fins emanating from the front cylinder fro movement, but they do look good. The one on the right has also flattened the cylinder laterally, and is an overall exaggeration of the left one. I have this feeling that these are reef cloakfish.

Click to enlarge; copyright Gert van Dijk
Has the creative evolution of cloakfish stopped after this early burst of adaptive radiation? Not at all, but creative evolution is like biological evolution in that there may be periods of sudden intense speciation followed by slower adaptation. Dixon's recent mention of equipping his animals with a mother of pearl finish made me want to want to paint an animal with such a finish, and here is a first attempt. The result does not work well yet, but that is not surprising: painting a mother of pearl effect is difficult (if you want to see it done much better, search Google for 'Paul Quade Cambrian').

If I manage to reach that level I will certainly post the result here. Meanwhile, here is a  bioluminescent general cloakfish, another painting experiment.