The Cycle of Cyann 3: the last of the rings...

I did mention that I thought some small errors had crept into the way Bourgeon and Lacroix had depicted the shape of the terminator (that's the edge between the lit and dark halves of a planet). How do I know?

Well, the terminator is supposed to be a great circle on a globe; it just looks distorted on a flat map, but is a circle in 3D. But if we take that flat map and drape it around a globe and have a look, the terminator ought to show up as a perfect circle again. I did just that with an image taken from the book 'La clé des confins', and here it is. The flat image is shown alongside the sphere it is draped around.

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The thin latitude and longitude lines are drawn by the program I used to depict the globes (Matlab); the vaguer lines were in the original image. You can see the two equators line up nicely, so the map isn't too inaccurate. However, the terminator at the pole does not form a smooth circle, but has a distinct 'peak' there. Anyone who has tried to draw flat maps for the purpose of having them look good on a globe knows that polar areas are very difficult to get right. The map by Bourgeon and Lacroix shows some 'pinching' there.

To be fair, I also did the same trick with my own projection. Here we go:

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It does work better, but I am not making this point to gloat. The opposite, in fact: I am astonished how accurate this was all done by Bourgeon and Lacroix. Remember that the album 'Six saisons sur Ilo' appeared in 1996 or 1997. I first worked out the mathematics of the terminator shape in 1985, and in 1996 this was the best printer output I could obtain:

Not exactly impressive, is it? So, no doubt, to produce good drawings, Bourgeon had to redraw the image by hand, and I guess a small error crept in. I am curious to hear whether this explanation is correct, though, so if anyone knows how to reach the authors, please let me know.

I also promised you animations of the ring and its shadows. They're done, and as I cannot post them here, I decided to incorporate them in the Furaha website. Simply go to the site, choose the planet icon and then 'some more examples'. If that sound too complicated, go there directly by clicking here (but you will lose the context).

Cyann and Ilo's rings

The last time I introduced 'Le Cycle de Cyann', focusing on the wildlife. On browsing through 'La clé des confins' my attention was drawn to some astronomical explanations. In the second album of the series Cyann travels over the planet Ilo (there should really be a dot in the letter O, but I cannot reproduce that here). That planet is of interest as it has a very long and narrow continent winding almost like a snake over the globe. This provides an opportunity for Cyann to travel through a vast array of landscapes along with their accompanying biotopes, much to the enjoyment of the reader.

But there is another thing that struck me, and that is that Ilo has rings. I cannot say whether it is at all probable that an Earth-like planet has rings, but their presence certainly has some interesting consequences. From seeing photographs of Saturn, everyone knows that the rings cast a shadow on the planet. But that shadow will not always fall in the same area, provided the planet is tilted to a degree.

In midwinter the North pole is tilted maximally towards the sun, and so will the rings; hence they cast a large shadow on the southern hemisphere. But at the spring and autumn equinoxes the plane of the rings present to the sun edge on, so the rings cast a shadow on the planet no wider than the rings themselves. Here is one picture of Cyann, waiting for her lover on the equator, on the day of the equinox:

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She is facing the sun, and the rings behind her are lit, forming a luminescent vertical stripe in the sky. Looking in the other direction the rings form a dark stripe. Looks like an excellent setting for a romantic encounter.

The consequences of all this tilting are fairly complex. Think of how the ring shadows complicate winter: the shadow of the rings falls on the hemisphere that is tilted away from the sun, where it is winter anyway. But the shadows make the winter days even darker, but in complex ways: it is theoretically possible for the sun to come up, disappear behind the rings, come back again in midday, disappear behind the rings again, and finally to come back only to set on the horizon. All such matters are brilliantly handled in the book. Here are two pictures from 'Le clé des confins' showing how it works. One is an equinox picture, and the other is a solstice picture. If you need more explanations on why the sadows change shape, please go to the planet page on the Furaha site.

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These caught my attention as they resemble the images on the astronomy page of Furaha quite closely, in particular the way the terminator is drawn. The 2x1 ratio of the maps is a giveaway that there is some serious thought here. So I wondered whether I could copy all these ring effects, and sat down to some good old-fashioned Matlab programming. Here is how that started:

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You will see rays of the sun -the blue lines- starting from the edges of the rings. They are of course all parallel, and strike the planet (many don't of course, and these are not shown). The relative sizes of the planet and rings were taken from the book, and I estimated axial tilt to be 21 degrees. Once the x,y,z-coordinates of the rays falling on the planet are known, which only takes high school mathematics, these can be converted to latitudes and longitudes, et voilà. Project these over a rough map of the planet, redrawn from the book, and there we are:

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Nice, isn't it? It is quite close to the drawing in the book, but small changes in ring diameter and axial tilt have large consequences. I also found that ths shape of the terminator in the solstice picture in the book is not exactly right. I can only assume it is some copying error, because the rest is much too good to be guesswork. Do not underestimate the amount of thought that has gone into this. I know from experience that working out the form of the terminator can take quite a bit of effort. Bourgeon and Lacroix not only did that too, but also worked out correct ring shadows, as well as thinking up cultures, animals, etc. It's almost enough to make you desperate...

But I won't be! Instead, I think I will produce some animations of the shadows as they change in the course of a year. Later.

The Cycle of Cyann

The title should more properly be 'Le Cycle de Cyann', as this is a series of 'bandes dessinées' (the word 'comics' does not seem appropriate) by Bourgeon and Lacroix that does not seem to have been published in English. I have no idea why, but there have been arguments with the first publisher, Casterman. The series started in 1993 in a magazine called 'A Suivre' ('To be continued'). Strangely, I did not find any good websites to direct you to, not even at the two different publishers responsible for the albums: Casterman and Glénat. Amazon in the UK and the USA only have entries for French and German versions, but amazon.fr will at least show you all the album covers. The series revolves around a rather attractive headstrong young woman called Cyann. Driven by the hope to find a cure for a disease ravaging her home planet she discovers that the priest class on the planet have kept a portal system hidden from the population, that allows travel through space. The system is largely derelict, and many worlds have been out of touch for so long that they have forgotten their common ancestry, and developed their own customs, architecture, etc. The reason to mention the series here is that the authors are rather good at making up entire planets, with ecologies, etc, along with peculiarities of their human inhabitants that really seem to belong in that ecology. Cyann's home environment is humid and tropical, and the inhabitants are accordingly dressed scantily. Except that this makes sense, it allows Bourgeon to draw attractive women, something he seems unable or unwilling to forgo anyway. There are lots of plants and animals in the series, and you can tell that much attention has gone into their design. Anyone interested in the background of the series should pick up a copy of 'La Clé des Confins', that is not a story by itself, but a companion volume explaining the worlds Cyann travels on. Here I will introduce just a little sideshow from the first album (La Source et la Sonde). The two main protagonists have camped outside and are waking up. The next page starts as follows:

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We are treated to part of a food web in just a few frames: there are floating seed heads, that are of coarse ballonts (see earlier entries in this blog to learn more about ballooning animals). The balloon sac is opened by some avian to get at the seeds, while a ground-living animal has another way of getting at them: it jumps up to get at them, and its hind legs seem specifically well-developed for this purpose. But make sure you look at the background as well: there are interesting plants, there is a city with intriguing architecture, the heroine is lying on the ground, etc. And all this is just a sideshow for the main action. I think I will post some more morsels of this marvelous universe every now and then.

Why there is no 'walking with tentacles'... (4)

So the 'Walking Tentacle, Mark II' developed last time has a stack of elements able to withstand compression and still has considerable amount of freedom, with its many ball-and socket joints. In fact, I was tempted to elevate it to the level of a 'Working Solution' and to keep it in the Furaha universe. There are several things it cannot do that a completely muscular tentacle can do, and that is to lengthen or to shorten at will. It also still takes lots of muscle force just to keep it in place.

There are some interesting refinements to be considered. One thing I came up with is that the surface of the joints is now completely smooth, not obstructing movement in any way. But suppose that the surface could somehow be made to become less smooth if needed. Perhaps with small elements under the surface that can be raised to make the surface coarse-grained. If you do that on both sides of a joint's surface, the friction will become much larger, so the joint would need less muscle force to stay in place. That would be the Mark IIb...

But a much more likely development would be to reduce the number of movable elements. Simply lengthening the compressive elements inside the tentacle would solve many problems: there are fewer areas of motion, hence fewer places where muscle force is needed. The concentric muscle cylinders can go, as they are replaced by muscles spanning one or two joints.

But consider the nature of this Mark III 'Walking Tentacle' looks like: it is a series of elements made of strong material able to withstand compressive forces, and movement is effected by muscles pulling at these elements, causing them to rotate at some places only: yes, the Mark III 'Walking Tentacle' is a leg, and that's why there's no 'Walking with Tentacles': they evolved into legs...

Here it is, with just two muscles (click to enlarge)

Why there is no 'walking with tentacles'... (3)

Last time I argued that using tentacles to walk on would require wasteful amounts of energy. To withstand bending forces you would need very high pressure inside the tentacle in order to keep it stiff enough (the principle is called a muscular hydrostat by the way). The first big disadvantage that this generates is that you need a lot of power , and the second is it the high pressure puts a large strain on the circulation.

So let's do some creative evolution to work around these problems. A tentacle differs from the balloon animal in the last post in that the inside of the balloon is filled with air while the tentacle is filled with muscle cells, i.e., basically water. For walking purposes we need something well able to withstand compressive forces. The first thing I can see happening is compartmentalization. With compartments inside the tentacle, you could have high pressure in one compartment and lower in another. The next step is to have some organ inside each compartment that is built to withstand compressive forces. Evolution might start with specialised muscle cells, that no longer contract actively, but simply form an elastic blob that is fairly stiff, and less easily deformed than the cells.

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They could have a shape as shown above: a more or less cylindrical sac filled with a jelly-like substance. Perhaps its wall is non-elastic, or perhaps there are strong fibres in there, running from one side to the other. Let's call this a 'corpus gelatinosum centrale (CGC)', or, in Latin-less days, a compression blob. Whatever the solution, the blob holds its shape, and if you stack a number on top of one another they can carry weight. It will still need lots of muscles on the outside to keep the stack balanced. Three layers are shown, but that is just a rough idea. The arrangement costs less energy to keep upright, controlling it still costs lots of energy. It might just allow an animal to fumble around on shore, so perhaps this is a credible 'Walking Tentacle, Mark I'.

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Evolution will not stop there, however. The next step is shown above. The CGC's have evolved, and now fit rather well together. The top half of each is spherical and fits in a depression in the bottom part of the next one. This arrangement ensures that pressures can be safely transferred down the stack of CGC's, called the 'columna corporum gelatinosorum (CCG)'. Take care here, as you can get lost easily in anatomical jargon. The spherical joints between the blobs allow movement in all directions, so from the outside the limb still has many characteristics of tentacles. The material of the blobs has evolved as well; they no longer simply keep their shape by virtue of tension fibres inside the blobs, but the gelatinous mass is now also crisscrossed by calcareous spicules that withstand compression forces directly.

Circling the blobs the various layers are still there, but with two innovations. The first is that there are now ligaments as well as muscles that attach to one blob and connect it to the next one in the line. These are crucial in fine tuning the positions of each pair of blobs, while the outer muscle layers do the brunt of the work in moving the tentacle. The second new item is that the layer of circular fibres has atrophied, as it is hardly needed anymore: it's job was mostly to generate a high tension, but those are now to a large extent taken care of by passing the forces through materials that withstand them.

I guess I should have put these refinements in the figures, and perhaps I will, at a later date. But this concludes the 'Walking Tentacle, Mark II'.

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As for Mark III, I wonder if anyone sees where this is going; we are on the way to evolve a walking tentacle, and yet the thread is entitled ' Why there is no 'walking with tentacles'...

Why there is no 'walking with tentacles'... (2)

Well, it took a while to write a new chapter. The reason is called 'work'.

Anyway, to continue with the 'Not walking on tentacles' subject, I made some illustrations with Vue Infinite, shown below. Let's have a look at a typical tentacle.

(Click the image to enlarge it)

This particular one is almost entirely made up of muscle cells (also called muscle fibres). the fibres are the red elongated structures. I played with images of mammalian striated muscle cells to form a reasonably realistic texture. The first thing to remember is that muscle fibres can only pull; they cannot push! So, if we want to use a tentacle as a leg, pushing against the ground, we will have to devise a way to push with elements that can only pull. Normal legs, with skeletons, work because the two jobs are separated: the muscles pull on the bones and the bones do the pushing.

Back to the tentacle: it is almost entirely made of muscle cells, except for the very centre, where I have put in an artery, a vein and a nerve (these have the customary colours found in medical textbooks: the artery is round and red, the vein is rather floppy and blue, and the nerve is solid and yellow). No bone, of course; it wouldn't be a tentacle if there was one!

The muscle cells are arranged in concentric layers, and the muscle fibres are arranged in different directions in different layers. The innermost layer has its fibres running lengthwise. If they contract, the tentacle will shorten. It will also become thicker, as the total volume of the tentacle will not change; after all, the whole thing is largely water, and water is incompressible. You can also have the fibres of that layer contract on one side only; if that happens, the tentacle will bend. You do not have to have this happen along the entire length, so the bend can happen anywhere. Already our tentacle can move in various directions.

The outermost layer has its fibre running transversely. If these contract, they will squeeze everything inside. Having nowhere else to go, the tentacle will become thinner, and therefore longer. The two other layers were added to add a bit of complexity and dexterity: their fibres run diagonally, so they will tend to twist the fibre. They also have compressive as well as shortening effects. Playing with these layers and fibres should allow the tentacle to move in just about any way you can think of.

There is no particular need to have the layers arranged just so. In fact, there might be another lengthwise layer on the outside, and there are various other things you can think of. As it stands, the tentacle can pull quite well. By activating the circular fibres the tentacle will become longer; isn't that the same as pushing? Well yes, but not with any great force. What we have so far is something like the human tongue, and you can push it out of your mouth, or against your teeth. But you can't do push-ups with it.

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To understand why, look at the balloon animal shown here. Its 'legs' sacs of air, and the only reason they hold their shape is because the sac under pressure. If we do the same for the tentacle, and tighten the outermost layers of the tentacle over its entire length, the inner bits of the tentacle would be under pressure, with the same result: a structure with enough tension to hold its own shape. But you cannot put any weight on a balloon animal: the legs buckle.

With that as a given, the simplest solution is to increase the pressure tremendously, so the leg/tentacle will not buckle so easily. That seems to be the solution chosen for the 'megasquid' in 'The future is wild'.

But that is so wasteful! The tension has to be built with continuous muscle force, and that eats energy. In contrast, to stand on bones the only energy you need is to keep them from buckling at the joints, and if you balance them right, all you have to do is a balancing trick rather than a brue force approach. A second problem is that the pressure inside the tentacle would be very high, and that creates big problems for getting any blood to the muscle cells. Blood pressure in the tentacles would have to be even higher than tissue pressure to force any blood through, and that in turn puts heavy strain on the heart, or hearts, come to think of that. More energy, more engineering problems. Anything with bones would run rings around such silly squids.

I think walking on tentacles requires more than a very thick tentacle; it needs evolution to keep the costs down. More on a possible solution next time...

Just some tree designs

Real life has a habit of getting in the way of more creative endeavours, so any trusty reader will have to wait a bit for me to write some more on how not to walk on tentacles. Meanwhile here are a few trees I have been working on, which perhaps also counts as creative work. They are designed with XFrog, and rendered with Vue (links in the appropriate section of the website). As always, click on the images to enlarge them.



First, this might either be called a Thistle Tree or a Galactère. It's surprising how quickly the number of polygons rises: this version weighs in at over 1.1. million polygons, and I don't think the ratio of leaf size to tree size is good yet: the leaves should be smaller in relation to the tree, but that is the quickest way to get really high polygon counts.


Here is the same tree shot from underneath, which perhaps helps to understand how it got its names. You can get away with much rougher leaves for long distance shots, but if you want to get in close you need detail.



And just for fun a Mollum, that is rather unlikely to make it through the utterly unnatural selection process determining continued survival on the planet Furaha, also known as Nu Phoenicis IV...