"The Spirally Slanted Spidrid's Mad Dash For Safety!"

Last September I presented part of a painting showing the Mad Sickle, a species of spirally slanted spidrid ('slanties'). The comments quickly gave rise to two new ideas: the first was that the legs and body of slanties might hook up to form a nearly impregnable wall. I should probably do a painting of one. The second was that slanties might well move by cartwheeling. Imagine that as follows: a spidrid's body along with the legs sticking out in all directions forms a disk; now flip the disc onto its edge and roll it along; that's it.  Slanties might use this trick to escape very quickly down a hill.

As usual, life on earth manages to trump anything the speculative biologist can think of. To prove that, here is a short video showing a Namibian spider using exactly that same trick to escaper down a hill, narrated by Sir David Attenborough. There are also spiders that actually do a series of somersaults, head over tails, but that is another type of movement and also another story: here's a video).

Slanties have an additional trick up their sleeves: once flipped on their side, there is nothing to stop them from using the power of their legs to make this an active way of locomotion. Slanties need not be content with passively rolling downhill; they can get out of the way on horizontal terrain too. Actually, they could even roll uphill. I do not think that that would be more effective than normal walking (normal for slanties, that is!), but they could. 

Mind you, I am not saying I am the first to invent this way of locomotion for a fictive animal. I have written about Warren Fahy's 'disc ant' in the past, and there may be earlier manifestations as well.

   
So here is a quick animation of a slanted spidrid moving in this fashion. The legs flex and extend while the body rotates. I suppose it could also move on the other direction with nearly the same movement. We are looking at the dorsal side of the beast.

Here it is again, rolling in and out of view.

I doubt the animal would use this type of movement as part of its normal repertoire, because I do not think it would be able to see well, with the entire world circling around them like mad. In this respect, the movement is a bit like 'cernuation', a term to describe the movement of the 'squibbon' of The Future is Wild. To read about possible visual problems, find the posts here and here. The poor spidrid only sees the world as a blur when wheeling around in this way, and that is why it uses wheeling only as a last resort to escape from predation.

Run, rusp, run!

I keep coming back to rusps because their basic centipede shape allows me to play with gaits and movements more than I thought at the start. So far, I have only shown very large rusps, 'megarusps', having a mass equalling or surpassing that of sauropods. If you need to brush up on your crambology (yes, I invented a word to describe the knowledge of rusps), start with some earlier posts: one, two, three and four (there are more, but these will do). Of course, you can also learn about rusp gaits on the main Furaha page.  

Now, megarusps are immense, and you should not expect them to hop and jump around a place like a rabbit on speed. Instead, expect them to move ponderously and solemnly. Still, megarusps must have evolved from smaller ancestors, and that by itself suggests there could be lots of medium and small rusp species, and indeed there are. And then I wondered whether their multilegged nature might keep them from running fast?

Click to enlarge; copyright Gert van Dijk

Here is my earliest sketch of small rusps again. I have not done any full paintings of such minirusps yet, but I do envision a fruitful adaptive radiation, including arboreal and burrowing species.  I have finished two paintings showing metriorusps ('metrio-' indicates medium-sized), and to do so I had to think about their gaits and in which way these would differ from those of megarusps.

    

Digging rusp. Click to enlarge; copyright Gert van Dijk

Varkrusp. Click to enlarge; copyright Gert van Dijk

 Here are some sketches of metriorusps, that did not make it to 'evolved' status. I played with the idea of differential leg development, so I could have digging species. That design has not made it to a painting, but running and armoured rusps did make the 'evolved' status, though.     

Millipedes and centipedes on Earth can move pretty fast, but they do not really run. Can rusps run?  The answer lies in what exactly is meant by 'running'. On the one hand you can simply interpret the word as 'walking quickly', but there are more complex biological connotations too.
  Walking consists of cyclical strides, and each stride consists of two phases. In the stance phase, a leg is pushed down onto the ground and backwards, providing upwards and forwards force. In the swing phase, the leg is lifted and moves forwards so it will be ready for the next stance phase. During the lift phase the animal should not fall, and preventing that is usually accomplished by having other legs on the ground at that time. To walk more quickly there are few options: increase stride frequency and increase stride length. The latter can be done by having long legs and by swinging it over the largest distance possible, and to get that working, the time a leg is on the ground will have to be shortened.

copyright Gert van Dijk

 This is precisely what happens on Earth. Here is an old animations of mine showing a horse walking. When walking, each leg is on the ground for more than half the time, so there are likely to be multiple legs on the ground at any one time. The slower an animal moves, the more the situation resembles standing still, and for an animal standing still its centre of gravity must fall within the area described by the feet: that is static stability. The stars in the animations represent the corners of that area. The order in which the leg moves ensures that the area has the shape of a triangle under the body.

copyright Gert van Dijk

For a galloping horse, each leg only touches the ground for a short fraction of its movement cycle. The result is that the chances are low that many legs will touch the ground at any time. In fact, there may well be no legs on the ground at all at some times, so the animal is in fact making a series of jumps. At high speeds static stability gives way to dynamic stability, meaning the animal is kept from falling through inertia and a footfall at the correct time and place.

Running is regularly defined as walking with each leg touching the ground for less than half a walking cycle. On earth, all really fast animals use these principles. Having said that, it is time to go back to centipedes and rusps. Centipedes do not run: their stance phase typically lasts much longer than their swing phases. This increases the chance that there are many legs on the ground at any one time, and, seeing how many legs rusps have, this is almost a certainty. This adds up to there being no jump phases, which seems a bad idea if we want a fast rusp.

   

The answer, I thought, would lie in the gait. The animation above shows a rusp with a slow gait: each foot is on the ground more than half the time. In real life, the animation may have to be sped up for a more realistic effect, but at least the movements are well visible. To support the body well, no region of the long rusp body should be unsupported for a long time, and that is achieved by choosing specific phase differences between the legs. In this case, these seem to work reasonably well. Mind you, rusps have typical 'zigzagzig' legs (see here, here and here for what that means).

The next step, above, is to equip the rusp with a different movement cycle for its legs; the legs now swing further and touch the ground less than half the time. I kept the phase differences the same for comparison. Fortunately for this rusp, its legs do not kick one another with this setting, so the result is not at all bad. There are always legs on the ground though, and that may limit a further increase in speed.

So the gait is the next parameter to tweak. Here, the phase difference between successive legs is much less than before, so the legs on one side move almost in unison. Still, at the moment the last leg on one side leaves the ground, there is already a leg just touching the ground on the other side.            

That can easily be amended. Now the phase differences are almost gone, and there are two periods in the movement cycle when there is no foot on the ground at all. Again, you will have to imagine a proper film speed. This rusp is going so fast, its feet hardly touch the ground!  

So yes, I think there are ways to have rusps run. Actually, they might be able to change phase differences very subtly and continuously, giving them a 'continuously variable transmission', unlike Earth's large mammals, that typically have up to three gaits to choose from (walk, trot and gallop), each with a specific preferred speed.  But that will also depend on energy requirements, something I haven't studied in any detail. 

Click to enlarge; copyright Gert van Dijk

So here is the scale diagram of the runrusp, one of the metriorusps that has already been painted. To close with, it may be interesting to know that I leave hexpods for last, because I am not fully satisfied with the animation of their middle legs yet. But I must say that exploring all the nonhexapod lineages on Furaha is perhaps not a bad idea: it gives more attention to designs that are least Earth-like.  

The Trench Gobbler

For once I will show a complete painting. Well, more or less. The painting in question is part of a two page spread concerning 'Fishes VI'. The six groups of 'Fishes' are part of the hexapod family tree, with Fishes I, II, III and V as the direct ancestors of terrestrial hexapods, and Fishes IV and VI as parallel aquatic groups. Mind you, I wondered about using 'Fish' instead of 'Fishes', as 'Fish' in English can be both singular as well as plural. A singular language, English.  I found that 'Fishes' can be used to describe multiple species, so that seemed the right choice.

In Fishes VI the third, i.e. the last, pair of flippers have fused to form a horizontal fluke, very much like that of whales. The problem with making 'Fish' alien is the high probability that a torpedo-like streamlined shape is rather likely to evolve as a 'universal' feature. I chose to accept that, so 'Fishes' superficially look much like Terran animals. But they share their world with cloakfish, kwals and aquatic wadudu, so there are definitely some odd shapes to be found too. And Fishes VI are not all that 'earthy': after all, they have four jaws, four eyes, their respiratory system is completely separate from the digestive tract, etc.

The painting combines several themes. I will split it in four panels that show various species of Fishes VI in 'powers of 10', meaning each species is 10 times as large as the previous one, starting at 4.5 cm. Each panel will also show the species eating, so food webs can be illustrated as well.

Click to enlarge; copyright Gert van Dijk

This is the Trench Gobbler; I haven't thought of a binomen yet. This painting forms the second panel of the four. The Gobbler is a typical deep sea species. In this biotope, the only light is that produced by lifeforms, and these are scattered far and wide. This is in fact a very barren ecosystem, which is due to the fact that it is almost entirely based on a slow and sparse trickle of organic material from above. Before anyone asks, I do not know whether there are hydrothermal vents. Animals need to conserve energy here. The water is largely still, and there is no need to swim fast habitually. Hence, there are no fast swimmers here, so there is no overriding advantage in streamlining. If the rare opportunity to catch some fresh food presents itself, it must be jumped upon, because there may not be a second chance anytime soon. These two influences together have resulted in very odd shapes, just as on Earth. The Trench Gobbler has elongated lateral jaws to grab anything possibly edible. In this image, it is attacking a tentacled creature, probably some larval Cthulhuoid. The larva has just emitted a cloud of bioluminescent ink to try to escape, a trick that seems to be working.

Click to enlarge; copyright Gert van Dijk

And here is a detail, for once at full resolution. It is fun to paint such structures, in particular the somewhat glassy structures of the teeth and fins.      

(PS: There is something wrong with my access to the main Furaha website, so I cannot update the loading screen for a while. To check for new posts you should check here directly)

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"

Flying animals or true 'weight lifting'

In response to a question on the Speculative Evolution website I thought it might be useful to write a short post on animal flight, with an eye on other worlds besides Earth. It will turn out that the logic is very similar to that of leg design. That subject, focussing on bone thickness, was discussed in two earlier posts, here and here. There is some math involved, but nothing more complicated than understanding powers and roots.

This post will only deal with the most basic aspect of flight, which is staying aloft. Let's start by considering an animal that is in stable flight. This means that is neither losing nor gaining height, with some kind of propulsion we will ignore (the same reasoning will also hold when the animal stably glides downwards, so lift is a bit less than weight). When the animal says aloft without sinking two forces must be equal in size: gravity pulls the animal down and lift pulls it up. We need to take a closer look at each. First, weight; it is the force induced on a body by gravity:

   weight = gravity constant (g) * body mass (m),

Click to enlarge; copyright Gert van Dijk

The image above shows several views of a general avian of the genus 'Avidisneius'. We will deal with the size of the animal's body; the wing will come later. For that we need to understand that its mass equals the product of its density and its volume. We will not alter density at all but will play with the volume. Volume is determined by its length, height and width. If this sounds as if the animal is shaped like a rectangular brick, that is essentially correct. But a more complex shape than a brick does not alter the principle that its volume depends on the product of its length, width and height; there will just be various constant factors thrown in, that we ignore. All three are measurements of length that we can label as 'L'. Volume thus equals L* L* L, or L to the third power: L^3. Weight was g*m, and we now replace 'm' with L^3:

    weight =  g * density * L^3.

Now we can go on to lift. Textbooks will tell you that it depends on a fairly simply equation:

  lift = rho * area * v^2.

Rho is the density of air.  'Area' is the wing area as seen from above, and 'v^2' is the square of the velocity of the animal with respect to the air. What this tells us is that there are three ways to get more lift. Obviously we cannot change the first, atmospheric density, but the equation tells us that an atmosphere with double the density doubles lift. Halve that density and you get half the lift, which is bad news for animals trying to fly on planets such as Mars. We can and will play with wing area: double the wing area and you obtain double the lift. The real winner here is velocity: doubling velocity gives four times the lift, because the formula contains velocity squared.

Of course, a wing can also be described by length and width and height. We will not use 'L' here but 'W' to specify that we are dealing with the wing. The mass of the wing will be W^3, but its area is proportional to W^2. So the equation for lift becomes:

  lift = rho * W^2 * v^2.

Click to enlarge; copyright Gert van Dijk

The two equations for weight and lift are all we need, for now. Let's take 'Avidisneius' and either double or treble its size as in the image above. To get the new forms, we replace 'L' in the weight equation with '2L' or '3L'. The volume becomes (2L)^3 or (3L)^3, giving us 8*L^3 and 27*L^3. The mass and weight change linearly with volume, so weight will increase by a factor of 8 or 27.

Unfortunately, this 'simple scaling' disturbs the balance between weight and lift. Why? Remember that lift depends on area, and hence on W^2. So if we double or treble W just as we did for L, we get new wing areas of (2W)^2 and (3W)^2, or 4*W^2 and 9*W^2. These wings, even though they are larger, are too small to hold the larger weight up. It's because of that infernal third power for weight versus the square for lift. (As an aside, the usual expression for 'scaling every dimension by the same amount' is 'geometrically similar'.)
              

Click to enlarge; copyright Gert van Dijk

Alas, the wings will have to be made even bigger. The image above shows the results, first for the previous 'simple' scaling and for a 'corrected' scaling attempt. We have seen that doubling body size (L=2) will make weight increase 8 times. What we therefore need is a new wing with 8 times the area. Similarly, if we make the body three times larger (L=3) then the new wing area must be 27 times the original one. We can find out how much we need to change the wing dimension 'W': area was the square of W, so to find the new 'W' we take the square root of 8 and of 27: the numbers are 2.82 and 5.20 respectively. So, if the body dimension (L) is to be 2 times bigger, the wing dimension (W) has to become 2.82 times bigger, and if the body becomes 3 times larger, the wing has to become 5.2 times larger.
 
Is everything solved now? Alas again... The additional increase in wing generates just the right amount of lift to compensate for the larger body. But the wing itself will also become heavier. Remember that volume corresponds to length to the third power? If our new wing dimension W is 2.82 times the original, the new wing mass will be 2.82^3 larger than the original, or 22.43 as much! This is not funny anymore. For the animal that became 3 times larger, the wing dimension W had to become 5.2 instead of 3, meaning the new wing volume is 140 times the original one, even though the body became only 27 times heavier. The 'corrected' scaling definitely falls short...

There is no escape from these cubic effects. Here is another way to look at its devastating effects. Suppose that the mass of the wing was originally about 20% of the mass of the animal. For an original Avidisneius of 500g in total, the wing would have a mass of 100g and all the rest has a mass of 400g. Let's take the animal we made three times larger using the 'corrected' scaling: the new mass of the body will be 27*400g, or 10,800g. The wing mass of 100g becomes 140*100g, or 14,000g. So our original 0.5 kg beastie now weighs 24.8 kg, and a staggering 56% of it is now wing. That's good if you like wing meat, and the animal should be easy to catch: can its heart and lungs even keep up with these massive wings? Mind you, in reality the bones and muscles themselves also need to increase by additional amounts, as their strengths depend on diameters (for examples see the posts mentioned above or my discussion of the giants in Game of Thrones here). 

The lesson is that, if you increase a flying animal's size, the wing dimension must increase more than the body. This actually happens in nature: larger birds have relatively larger wings. But there is no escape from the merciless differences caused by weight depending on cubic effects and lift, while bone and muscle strength depend on cross-sectional areas. At some size, the only weight that the wing can lift is that of the wing itself! But long before that point is reached, the construct will no longer be a viable animal. It is difficult to say where the 'Limit of Flight Plausibility' lies. On Earth now, kori bustards are arguably the largest flying birds. They weigh up to 18 kg, with a 275 cm wingspan. But extinct birds may have weighed 40 kg or even 72 kg. Did pterosaurs really weigh up to 250 kg? There is room for speculation here (which convinces me that Furaha needs some gargantuan beasts in the sky). However, please do not just geometrically enlarge a sparrow and present it as a 250 kg avian: approaching the Limit calls for profound changes in anatomy and flight efficiency.      

Other planets

The lessons for other planets are not very complicated: if you increase gravity by a certain amount, you increase weight by the same amount. If you transplant an Earth-like flying animal to a heavy world, you should make certain that lift increases by the same amount. Enlarging the wings will do that, but, because of the heavier wing, you should trim off a considerable amount of weight wherever you can. You could also make your animal fly faster, but do not think that that solves everything: your animal must be able to fly at low speeds to start and stop. You could evolve the propulsion system in such a way that it provides additional lift.

A high atmospheric density is a luxury, in contrast: if you double density, you can get away with half the wing area, which means that 'W' need only be 0.7 of what it would be on Earth. The soupier the air is, the more you can dream of avians with short stubby wings, resembling flying penguins.
  
But could you have something as large as a 'Game of Thrones' dragon flying around on a planet with an apparently Earth-like gravity and atmosphere? Of course not. Don't be silly. Dragons fly through magic. Birds don't.          
   

Mr Masato's CGI creatures

Well before I cut down on blogging altogether, I had stopped writing about other people's projects regarding life on other planets. I did so more often when I first started blogging in April 2008, but then it was difficult to find anything about speculative biology. The 'speculative evolution' website that now caters for such needs probably started at more or less the same time (it says that I became its 42nd member on July 21, 2008). But in the following years the field grew, so I thought everyone would be able to find interesting work for themselves.

I will make an exception now, as I miss blogging. The main reason I chose to present the work of Mr Masato here is that it seems to have gone unnoticed, perhaps because it is shown on a Japanese website only, as far as I know.

His work can be found here. Oddly, that page will not take you to his speculative biology images; that is found here, or, without further clicking, here. You will find 30 images there, showing a love of strong colours, a fondness of cuteness that may be particularly Japanese, and a wide variety of forms, some odd, some less so. Mr Masato told me that there is no underlying story and that the images may well be from different planets.   

Speculative biology of the 'alien world' type is not his major interest. That is dinosaur work, as the other pages on his site show (I liked the page on Gallery 4 where he places CGI dinosaurs in Japanese street scenes). Mr Masata is one those artists who rely heavily on computer-generated images to produce his art. That approach has many advantages, such as that it is easy to take another view of a scene from a different angle, or change the lighting, etc. Once all such decisions are made, you set the programme to 'render', have some coffee, and there's the image. For some of the best work done along such lines, I recommend the book 'Dinosaur Art' (there will be a second volume too). But it is very difficult to get photorealistic CGI work to look convincing, oddly enough. Often there is something unnatural or even sterile about the placing of plants; the surface of water looks like it is made of jelly or of glass, rocks look like sponges, etc. Among the few people who can really pull it off is Marc Boulay, whose work I discussed more than once in this blog (for instance here and here). I personally do use CGI techniques, but only as scaffolding for a painting. Here is an example.

Click to enlarge; copyright Masato Hattori

Anyway, on to Mr Masato's work. I picked out three paintings. The first one is this odd head sticking out above the surface of the water. Well, I assume it is a head and not the entire animal. The hair is well done, in particular for CGI work, and the image as a whole is nicely mysterious. Notice the lack of background. In essence it's just the beast, but that scarce approach works well here.

Click to enlarge; copyright Masato Hattori

These 'armoured marmots' are rather cute, with their spectacular headdress. In my own creatures I often reduce the extravagance of such elements after the first sketch, but having looked at these daring shapes I should probably do the opposite once in a while. The rocks are interesting here; I think I can identify the texture from Vue Infinite that was used to make them. 

Click to enlarge; copyright Masato Hattori

I like this one because it is so full. It can be chore filling up a scene in a programme such as Vue Infinite, even though it has an 'ecosystem' features to help with that. There variety of plants helps top create a convincing scene. The tetrapod has very interesting rainbow colours, suggesting iridescence. The young animal again adds a cute element to the scene. The tusks worry me a bit: they look very slender, so they could break easily. With such a long neck the animal would have little need for them. The animal approaching the tetrapod seems to behave like a crocodile, slowly making its way towards its potential prey. The bony head with all those bumps reminded me of an uintathere. The best feature of this image are the wildly coloured blue flying thingies. Are they just there by coincidence, or do they have some relation with the 'uintacroc'? I like images that tell a story.
 

Upgrade your planet: add rings!

This is the first on two or three posts on adding rings to Furaha, or any other fictional planet. The reason to add any is simple: rings add drama! Ron Miller, an excellent artist specialising in astronomical illustration, provided fascinating examples of how dramatic rings can look by transplanting Saturn's rings to Earth. He has shown and discussed the results a few years ago on this io9 page (the comments are also interesting).
 

Click to enlarge; copyright Ron Miller (used with permission)

Here is one of his examples, showing a view from Guatemala. Impressive, isn't it? Somehow I only started wondering whether rings would look just as good on Furaha a short while ago. I certainly studied rings before, in the context of the planet Ilo, as can be seen from this post and this one.

Click to enlarge; copyright Gert van Dijk

The animation above shows the planet Ilo and was taken from the main Furaha site (under the 'astronomy/seasons' tab. It shows how the shape of the areas lit by the sun changes over a year; the curved horizontal band is the ring shadow.

Adding rings to a view as expertly as Mr Miller did is not a simple matter of drawing some curves in the sky. Once you start thinking about the problem, you will realise that their aspect depends on how large they are, but also on where you are on the planet, on the direction your 'camera' is pointing in, and finally on the 'lens' you are using, by which I mean the visual angle. And as if that is not enough, the lighting of the rings differs for every hour and day of the year. Some places on the surface will be in the shadow of the rings, and at other times the planet will cast a huge shadow on the otherwise sunlit rings.    

So I started exploring these matters. I am not certain I will actually add rings to Furaha, but it is fun to explore. In this post I will start with basic ring astronomy (mind you, the only astronomy I can deal with is of a very basic variety). Planetary rings consist of many pieces of ice or rock, from boulders to dust particles, all circling a planet in its equatorial plane, and only there. There can be no rings directly overhead on the poles. In Earth's solar system, rings usually do not form one continuous band from the inner to the outer radius, but are divided into several distinct ringlets with gaps in between. These are apparently the effect of moons that sweep clean parts of the rings through their own gravitational effects. While there must be strict Newtonian rules underlying where these ringlets and gaps are placed, the large variety of ring shapes in our own solar system suggests that there is wiggle room here, allowing some creativity on the wordbuilder's side. Just compare the rings of the gas planets, for which this Wikipedia article is a good start.

click to enlarge; copyright:  http://astronomy.nju.edu.cn

The image above can be found at this website; it compares the various ring systems and stresses another important feature: rings are always situated inside a planet's Roche limit, or 'tide limit'. The word 'tide' here has nothing to do with seas, but concerns 'tidal forces' acting on a piece of ice or rock coming close to a large mass (a planet or sun). The gravitational forces act differently on the parts of an object closest and farthest away from the planet. These tidal forces will break up an object if it is within a certain distance of the planet, and that distance is the Roche limit. The breaking of the object, say an asteroid, goes on until the remnants are small enough to stay whole. If you start this process with a large enough object, the resulting pieces may collide with one another, breaking off more pieces, adding to the fun. The Wikipedia page on Roche's limit shows very clearly what happens to a heavenly body when it crosses the limit, and also contains a formula to calculate how far out from a planet the limit lies (this is the formula for 'fluid' objects).

distance= 2.44 * radiusP * (densityPlanet /densityAsteroid)^1/3

The distance is in km, and is governed by the planet's radius (radiusP, in km) and on a fraction, involving the density of the planet divided by that of an asteroid coming near the planet. If you wish to express the Roche limit in units of the planetary radius, you can just leave RadiusP out. If the asteroid has the same density as the planet, the fraction is one, and then the formula simply reads: 'The Roche limit is at 2.44 planetary radii'. But asteroids are probably less dense than a terrestrial planet, making the fraction greater than 1, so the Roche limit will be further out. I found estimates for various types of asteroids ranging from 2 to 5 gram per cubic centimeter, and the density of Furaha is 5.9 gram per cubic cm (the Furaha planetary system was kindly worked out by Martyn Fogg). So we can take the Roche limit for Furaha up to 3.5 radii.

Click to enlarge; copyright Gert van Dijk

Here is a ring of which the outer margin is exactly 3.5 planetary radii away from the centre of the planet. The planet is shown at the point in its orbit where the northern pole points directly towards the sun (the summer solstice). The glowing orange arrow show the direction of sunlight, and the thin lines show the plane of the orbit (and the direction perpedicular to it). The rings are 50% transparanet. You can see the shadow of the planet on the rings, and you can just also see the shadow of the rings on the planet.

That ring seems overly large, so I will set for a safer maximum value for the outer radius of the ring at 2.5 radii out from the centre of Furaha. But what should the value for the inner radius be? That is less clear; the outer parts of the atmosphere would form an effective limit, but I do not think I want the rings to come that close: bits and pieces might rain down continuously, and if these are large enough they will mess up the biosphere. So let's start with a fairly narrow ring with an inner radius of 1.8 to 2.0 radii.

click to enlarge; copyright Gert van Dijk

So here we are; that looks better. I also adjusted the transparency of the rings: this one is 67% transparent. How much light should the the rings let through? If the density of rocks in the rings is high and the rings are thick, not much light will come through. The reason this matters is because the rings casts shadows on the daylight side of the planet. They do so on the Northern or Southern hemisphere depending on the time of year.

click to enlarge; copyright Gert van Dijk

Here is a simple scheme explaining that. Furaha's axis is tilted by 18.3 degrees, and so are the rings. When it is summer in the Northern hemisphere (at the left), the North pole is tilted towards the sun, and the shadow of the rings falls on the Southern hemisphere. When it is winter in the Northern hemisphere (at the right) the ring shadow darkens the Northern hemisphere. I do not want these shadows to be big and black, because that will have large and unpredictable effects on the climate, the weather and the life forms (well, I certainly cannot predict them, and that is the actual limiting factor). So I prefer narrow transparent rings: I still get drama without too many unknown problems. I will assume that a small asteroid, breaking up and filling a large area, would result in largely transparent rings. In fact, it is the other way around: the rings are about two thirds transparent, because the asteroid forming the rings contained exactly the right amount of matter to make it so.

The final matter is the composition of the rings; they can theoretically be made of ice or of rocks. I doubt ice would last long this close to the sun, so the rings are made of rock. Earth's moon consists of  very dark rock, and yet its appears bright enough in the night sky to have inspired generations of poets; that seems a suitable unit of measurement for drama. Let's therefore assume that the putative Furaha ring system is made of dark rock.

So far we have the main features of the ring system in place, based on science, as it should be, but with a fair amount of handwavium. I am not certain about whether I should give up on Furaha's two tiny moons. Ideally, I should calculate appropriate gaps in the rings, but admit that at present I do not have the knowledge to do so. Any readers who can do so are friendly invited to comment on the matter!

Click to enlarge; copyright Gert van Dijk

This image shows Furaha with some fancy rings, for even more drama. The inner one is nearly completely transparent.  Another step in deciding whether or not I should add rings to Furaha may be to calculate the effects of this particular ring system on the lighting of the planetary surface. But, having done so once for Ilo, I already have a fairly good idea of what the effects for Furaha will be.

click to enlarge; copyright Gert van Dijk

This is another image of the same fancy rings, now from a lower point of view that lets you see the Southern hemisphere with the ring shadows. These shadows do not look too bad. Now that we have reasonable options to design rings, it is time to take the next step: what do the rings look like from any point on the surface of the planet, for any point in time of the year? That will require another post...                          

Kwals 2: from universal back to local

Since the last post I have busily worked on some two-page spreads, one of which shows an advanced kwal. Each spread probably takes about 25 hours of work: there is an animal to design, one 6000 x 4200 painting to do, text to write, a silhouette to design and paint, a map to be made, and often an additional illustration to do. If I ever produce a book again, I will write it as normal people do, not paint it...

Anyway, designing the kwals proved less than easy. In the previous post I designed kwals with central valves to let in water on the upstroke, but when I sat down to design species built on that concept, I was became less and less satisfied with it. It seemed biologically possible, possibly plausible, but not painterly pleasant. So here is what happened next.

Click to enlarge; copyright Gert van Dijk

This is a quick sketch of a 'gatkwal'. It is still very much like Earth's jellyfish, with its single bell at the top of the body, with tentacles dangling below it, in part from the edge of the bell, and in part from the central body below the bell. The major departure here is the hole in the bell, meant to let water stream through on the upstroke. Obviously, the water has to stream right through, meaning the body must not block the hole. So there are spokes connecting the bell to the body underneath. Of course, this comes about embryologically as a hollow cylinder with secondary fenestrations in its sides. Same thing, really. Here there are six spokes, meaning that the gatkwal has six-sided symmetry, representing a doubling compared to the prototypical three-sided radial kwal design (we'll get to that).
   When the bell contracts, it sends down a rotating torus of water, as happens with Earth's jellyfish (see the previous post).

Click to enlarge; copyright Gert van Dijk

While I was thinking about the three radial 'pie slices' that make up a kwal, I started pulling on the edges of the bell, which then together no longer formed a nice circular edge, but a three-lobed shape. Take that idea and separate the lobes more and more until they are fully separate. We now have a kwal with three bells instead of one. The first stages of these trikwals are not shown here, but the finished painting is about one such, the 'tribune' ('Tribunus vacans'). The musculature of the bells had to evolve: rather than only having circular muscles to squeeze the bell together, there is now a more complex arrangement to control movement in the 'longitudinal radial' as well as 'transverse radial' directions. And those in turn necessitated rods of less compressible material (the 'chordae') embedded in the jelly to give the muscles something to work against. With all these changes, kwals became less like jellyfish with every step. This is ironic, as they started as supposedly 'universal' shapes. By now that are probably quite specifically Furahan. Just as well, I guess.
  Anyway, here is the 'klapkwal', in which the three bells have evolved some more: each bell has two halves that fold together as they are lifted up, but open as they are driven down. It is here shown during an upstroke. It looks a bit like a plant, but that is because the context is missing: you have to imagine it drifting through the ocean.

Click to enlarge; copyright Gert van Dijk

Here is another advanced kwal, which is as yet nameless. Its bells have evolved to beat slowly through the water. In this case they are supple on the upstroke but less so on the downstroke, which is shown here. Mind you, this is probably as far as the design can go: it is tempting to speculate how far kwal evolution can move towards quicker or more efficient propulsion. The problem is that the rest of the design may not allow this. The biggest obstacle is probably the way kwals feed, which is by dangling tentacles in the water and waiting until something edible blunders into them. The elaborate tentacles offer considerable resistance to movement. This is not a real problem at low speeds, but does form a major hindrance at high speeds. To move quickly, kwals would have to acquire a different feeding mechanism. The conversion would have to happen in small steps, as this is how evolution works: it is like rebuilding your house a bit at a time, while you keep living in it. But designing a whole new feeding mechanism is more like tearing down the house before you can rebuild another one. Unfortunately, that leaves you with nowhere to live.
  So these 'rowing bells' may be the most advanced feature kwals will ever possess. Still, give them another 100 million years or so, and let’s see what happens.    

Adding 'universal background animals': kwals

The Book is over half done and is changing as it develops. I started by repainting existing oil paintings digitally, and by now most paintings with a pleasing design have been done. At first the paintings were merely cleaned up and details were added, but in the latest cases not a single pixel from the original painting survived: they were completely recreated from start. More importantly, the content changed: writing more elaborate texts forced many story elements and biological principles to be firmly defined for the first time. The painting 'arrival at Furaha' is a good example of this process (first post here, last one here): painting an internal  spaceship scene forced me to turn my previously rather vague ideas how they might work and in-world design aesthetics into written concepts and painted shapes that will guide things coming later.

The next big step will be finally defining hexapod legs: I will have to decide once and for all whether each of the three pairs of legs will start with zigzag pattern or with a zagzig pattern as well. It is the middle pair that causes headaches: its design should not simply mimic that of either the first or the third pair, so how do I make it work? My thoughts on that subject are slowly coalescing.

But meanwhile another thought came up. So far, the animals in the paintings are fairly big and conspicuous; but how about the 'small fry', all those little creatures that together make up much more of the animal biomass than big animals do? Shouldn't I give them some attention? But what of their shapes? Must they all have truly alien shapes, or should they simply look like they were taken from a textbook of Earth invertebrates? Currently, I think the latter probably applies, based on two considerations. The first is the enormous variety of invertebrate shapes on Earth; it is hard to come up with an original design when evolution produced many oddities that would be dismissed as impossible if they were presented as fictional animals. The second consideration is that some principles will apply universally; streamlining must be a universal solution for moving through a fluid at any speed.

The challenge, of course, is to push their design boundaries a bit. They may not always be possible: 'worms' are probably universal. I mean small boneless elongated burrowing animals with a round or flattened cross section. So The Book shall contain at least one spread on 'wurms', and I doubt that I can come up with designs that do not already exist on Earth. A second group to merit attention are arthropod analogues: insects, spiders and the like. I already designed some of those: spidrids and tetropters. But the concept of a small bilateral exoskeletal segmented animal seems so good that it is hard to avoid. I will name the Furahan reprentatives of this design the name 'wadudu'; this is one of the remnant Swahili words left by the spacefarers of the good ship 'Ngonjera'.

Click to enlarge; from http://fox.rwu.edu/jellies/

Earth's oceans are full of jellyfish for the last 500 million years. They are radial bell-shaped organisms without complex nervous systems that move in a simple cycle: the bell contracts, water is pumped  downwards and by reaction the animal moves upwards. Then the bell relaxes , becomes broader and lets in water again. This has always seemed a bit odd to me: when the bell relaxes, it flattens but also broadens, which must hinder its upward movement. Also, water has to flow upwards into the bell from below, which must because an equal but opposite reaction pulling the animal down a bit. That was my unconsidered opinion, but recent studies showed that jellyfish swimming is much more sophisticated that I thought. Some swim as I described, by jetting water downwards. Those tend to be bullet-0shaped. The flatter ones drive down a toroidal vortex of rotating water, and that actually pushes water back up underneath the bell, pushing the jellyfish up when the bell is relaxed. Here is a very nice website explaining these matters.

And the video above shows the toroidal vortices that provide propulsion even in the relaxed phase. The paper to which the video belongs was published in PNAS and is freely available.
 
I wondered whether there was room for creativity here. What if some water can flow downwards right through the jellyfish while it is moving passively in the relaxation phase? Making a hole in the bell will of course impair its propulsive upwards force when the bell contracts, so the hole should be open during the relaxed phase to prevent the animal being sucked down, but closed when it contracts? Valves should do the trick, shaped perhaps like those in the mammalian heart. The ones in the aorta are a useful example: they open when the ventricle pushes blood out, and close to prevent blood flowing back into the relaxed ventricle from the aorta. I decided to play with that idea a bit, and give Furahan jellyfish analogues a twist.

Click to enlarge; copyright Gert van Dijk

Here is such an animal in a rough sketch. The first image shows that there are three valves. Instead of one central bunch of tentacles, as in Earth jellyfish, there are three outlined here. I may make the body less perfectly circular to reflect this triune design. 

Click to enlarge; copyright Gert van Dijk

This cutaway shows a section just off centre of the animal, a bit near the camera. The cut goes through the two nearest valves and as you can see they are closed. This is what their position would be during the propulsion phase, when the bell contracts so pressure is high underneath the bell.   

Click to enlarge; copyright Gert van Dijk

And here is an open phase, with the valves apart from one another. I should have drawn the rest of the bell in a more relaxed shape, but thought this would be enough to convey the idea. 

So there we are: Furahan jellyfish analogues. I do not wish to simply call them 'jellyfish', so they needed a name that would in the Furahan story setting. In Furahan lore, settlers came mostly from a Western European background with a smattering of people from other parts of the world (the down-to-Earth reason for that is that I am only comfortable with a few Germanic and Romance languages). I looked up the word for jellyfish in various languages (here is a site to check some all at once for yourselves).  Many languages use variants of Medusa (the Greek monster woman whose hair takes the shape of snakes and whose regard turns you to stone). I like the Brazilian name 'agua-viva', or living water; very poetic. But I will go with the German and Dutch variants of 'Qualle' and 'kwal', words that evoke a soft flabby and unpleasant nature. I considered an anglicised version in the form of 'quall'. To be certain I checked, and found that 'quall' already has a meaning as yet completely unknown to me. Hm. I had better avoid that connotation. So, 'kwal' it will be, unless someone comes up with a better suggestion. Actually, the 'a' in the Gemran and Dutch versions sounds like the 'a' in 'father' or in British 'bath', but for Furahan purposes a pronunciation like an 'o' is the likelier one.