Saturday, 4 May 2013

Inversion fish I

In November 2012 I wrote about thomastapir's 'Xenohox Gazelle', an extremely original concept for alien animal locomotion. In that post I also mentioned that I might write about another of his inventions, the equally creative and original  'Moebius fish'.

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?


A natural development is to add more details, turning the torus into a smooth-skinned shape. The one above has a pentagonal cross section. The muscle arrangement would still work to make it turn inside out, but as the sides become smoother it becomes ever more clear that the inside-out movement, the 'inversion', is by itself not a sound propulsion device.


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.


Bewildermunster said...

That is quite fascinating, I'd love to see something like that 'swim' IRL, although from that video I can somewhat imagine it!

Jan said...

Thank for the new post. What if different parts of the ring do not move at the same time? I am trying to imagine something like terrestrial moebius worm.

Sigmund Nastrazzurro said...

Bewildermunster: so would I... the wish to really see such things is what drove me to start programming them.

Jan: 'what if different parts of the ring do not move at the same time'.Now that is a suggestion that overheats my visualition facilities. Do you mean that at one cross section the rotation is slower than at an adjacent cross section? If so, that would produce a shearing force, so the difference in motion cannot be sustained, but it would affect movement. Is that what you meant?

Christmas Snow said...

I drew a concept which is a four-jointed model using google sketchup:

or access it through Sketchup using the title "propulsion by turning inside-out".

Back then I used a model describing a soft-bodied jelly-fish-like creature. The new design must feature a skeleton and it replaced the old one.

The model you posted on your page solves the problem of "organ differentiation", as it seems to feature a mouth, gill opening or both (if this is a plankton feeder).

Jan said...

SN: You are right. When I take rubber band, I can roll it only by rolling opposite parts in opposite directions. So I am asking myself how to make moebius worm move in only one direction. Maybe some sort of asymmetry?

Jan said...

Or if the worm do not form perfect circle... Well, I give up.

Nicky said...

I'm guessing the brain and other organs would have to be ring shaped.

Evan Black said...

I've wanted to comment on this post since it was published, but have only now gathered together the materials I wanted to share. What I have to say is far too complex to post here, so here is a link to what I have to say.

Sigmund Nastrazzurro said...

Christmas Snow: that is a fascinating design. Have you drawn an animal with such a design yet?

Jan: the analogy with a rubber band is a very useful one. I was actually using strips of paper to get a feel for the subject, but Evan has already done something more elaborate and much more refined.

Evan: that is amazing! I had intended to have a closer look in a future post at the Moebius Fish: the ribbon overlapped itself, so I realised the ínversion rings (kaleidocycles) were not a good model for its design. Well, I don't need to study it anymore...
I am very curious to hear what thomastapir will have to say.

Evan Black said...

Jan, I actually used a rubber band and a ribbon in my early stages to help me understand how this thing could plausibly move.

And I didn't mean to supplant the efforts of anyone else in exploring the Moebius Fish. I just wanted to add my two cents to the discussion. Somebody with better skills and resource could no doubt produce something much prettier than what I did.

As far as the "inversion fish" explored in this post, it has many similarities with the Sugerea on Nereus (like I mentioned in my blog post). For those creatures, take the torus shape and stretch it out to form a worm-like body, with a long tube going along its center. Sugerea can surely swim using this method, but they also crawl and dig with it as well.

Christmas Snow said...

SN: No, I haven't drawn such creature yet and for one good reason – the issue of organ differentiation: Can this organism be more evolved than a jellyfish, for instance? Where to locate gills, feeding organs and the eyes, is it around the joints or along the segments? Is the nervous system centralized and has a brain?
It is interesting to discuss the evolutionary options of rigid (segmented) Vs. soft (Jellyfish-like) organisms, in terms of propulsion power and organ differentiation. A soft-bodied version may become differentiated (distinctive front and back side) if we use the rubber-band model:
This is a "screw-drive" model. The band keeps twisting inside-out in one direction. The front and the back side will then accommodate some organs such as gills, mouth and so-on. The convoluted parts form two screws (helices) with opposite handedness that constantly turn in opposite directions and propel the animal forward. Inevitably, to avoid shear, the front end and back end flip in opposite directions.

Sigmund Nastrazzurro said...

Evan Black: the Suerea are indeed very similar to the 'inverting torus'. When you sais that turning that into a species of Sugerea involved stretching the torus, I first misconstued that, thinking you would end up with something resemble the inner tire of a bicycle; but of course you meant stretching it another way, so the hole in the torus becomes a tunnel.

Christmas Snow: I was/am also worried whether you can turn such inversion animals into something more complicated than jellyfish. Jellyfish were in fact what I aimed for, northing more complex. Then again, if you design something with a nonrotating node in it, then you have room for more complex speciation. The Moebius Fish has that, and so can your 'screwdriver'.

Jan said...

My imagination just is not enough. The simpliest model of the inversion fish I can think of is something like square which would flap its corners like wings. Unfortunately I can not draw a picture, but if the corners were A - B - C - D, it would be at first pointing the corners A and C forward, then moves them backward, so that it would be corners B and D that were pointing forward, them move B and D backwards and so on. It would have to change its shape for optimal drag of course. Please, excuse my poor explanation skills. Would it be working?