|Click to enlarge; copyright Thomastapir|
The Moebius fish consists of a body sitting like a node in a complexly folded ribbon. The ribbon folds in upon itself, resulting in a complex movement. Please read Thomastapir's own descrition on his DeviantArt page, using the link above. I wish there was an animation though, as I would dearly like to see which part goes where. Luckily, the German firm Festo has produced a flying inversion device, wit a perhaps similar movement. Festo is a technology firm that often plays with biologically inspired designs, such as helium-filled balloons moving like jellyfish or manta rays. Their most recent devices include a robot flying like a dragonfly.
Festo's inversion device is shown above. This too is a helium filled balloon, shown to turn inside out in the air. It is remarkable difficult to understand what you are actually looking at. I will come back to such complex inversion shapes in a later post; the basic design consists of a series of tetrahedra (a tetrahedron is a four-sided object, with a triangle for each side). In the Festo 'inversion cube', the tetrahedra are connected to one another to form a ring. When I first saw the Festo film I immediately wondered whether that intriguing movement could be used for animal locomotion; thomastapir had already designed his Moebius fish by then though!
The whole concept of inversion shapes is interesting enough to consider how it works in a bit more detail. I will not tackle the complex shapes in this post, but will starts with the easiest version I could think of. I will call them 'fish', using that word in the time-honoured but zoologically incorrect fashion meaning 'animals regardless of descent, nature or shape, with as the only shared characteristic that they live in water'. The Festo animal is in fact a ballont, and there is no strong argument against such creatures floating in air rather then water on other planets; having them swirl around in water is so much simpler however that that is where I will put them.
The basic shape is a ring that inverts itself, so after a bit of programming here is a very simple version: a ring that continually inverts itself. I do not think that this flat shape lends itself well as a Bauplan for an animal, but give it a bit of thickness and there is room for muscles, say for starters circular muscles running lengthwise along the two rims. If one of the two ring-shaped muscles contracts, that rim will contract and will tend to move inwards. Alternate the movement and you might get something like the 'ring fish' above.
It doubt that the animal has much to gain from the movement though: when the outer part of the ring moves downwards, that part will provide an downwards thrust, but at the same time the inner part moves upwards, providing an upwards thrust. The outer part has a larger area than the inner part, so perhaps there is a net downwards thrust, but the movement cannot be particularly effective. I wonder whether this also holds for the Festo thingy: the video is not too clear about it actually moving through the air, although it obviously moves in the air.
Let's give the 'ring fish' a bit more body. Its shape is now a torus with a triangular cross section. It is intriguing to see the movement. Again, the animal can be equipped with muscles running lengthwise around its body in the corners of the triangle. By contracting and relaxing them in the right order the fish could turn itself in and out continually as shown here. Perhaps shorter muscles running at right angles between the three ridges might help in contracting the successive ridges, to result in the inversion movement. But will it move through the water?
To achieve that we need a trick. Equipping the surface with something that provides traction, such as fins, would do the trick. Here, I added simple lines to the inversion fish. If the animal is microscopic the lines may stand for hairs, and at that scale hairs do provide propulsion. Lots of microscopic animals on Earth use hairs ('cilia') for that purpose. Note that the cilia do not always simply stick out from the surface, but move depending on the phase of the movement. The cilia are swung back during the upstroke so they do not provide much of a downwards force then, but they stick out during the downstroke, providing an upwards force. I assume that the animal could reverse its thrust to sim down, and if it turns on ist sde it can move horizontally. I animated just one ring of cilia, but there could easily be lots more, providing continuous force. For larger animals, change the lines into shapes with a bit of surface area, and there you are: the 'hedgehog inversion fish'.
This design is not without its problems, unfortunately. The biggest problem is probably that it is none too obvious why they move in the way; this is rather a big problem, but I will largely ignore it -for now- . Their bodies are distorted greatly during movement: just have a look at the rectangular outlines on the body, and compare a rectangle on the inner aspect of the torus with one on the outside: to turn one into the other much stretching and squashing is needed. Some animals can do that, of course, such as octopuses, but all this distortion must limit the design severely. One way to avoid that would be to add a node to the torus that does not change shape, to house things such as a brain etc. Thomastapir's Moebius fish has such a body, and if I understand the design correctly, the body does not rotate. But if I were to equip the torus designs above with a body by just gluing it to the torus, that body would still rotate along with the torus, so any eyes there would have to cope with a continuously rotating world view. The squashing and stretching can be solved completely by doing away with the torus and substituting a series of tetrahedra, as in the Festo device, but that is something for another post.