## 3D printed bee colour spaces

Think3DPrint3D has generously donated 3D printer time and plastic filament to the unusual task of rendering the usually intangible concept of honeybee colour spaces into real, physical, matter!

The Spaces

The first two spaces we printed were chosen by me, in part because I think they are theoretically interesting, and in other part, because unlike some other colour spaces they are finite sized, 3D objects.

The first is a theoretically predicted uniform colour space (a bit like human L*a*b*) where euclidean distances between the points within it (colours) correspond to a bee’s ability to tell the difference between the colours. The shape shows to the locus of the colours of all possible lights in terms of such a perceptually uniform coordinate system (which happen to like inside a cube).

It’s a good shape.

The bottom corresponds to black, and the top corresponds to white. It is biased away from blue, towards green and UV. If you view this from above it is very similar to (more correct than) the honeybee hexagon space used in bee colour studies.

The second shape is the object colour solid for bees. This is a particular kind of colour solid that shows locus the relative proportions that the different types of cone cells get excited by all theoretically possible reflecting surfaces. Some combinations of excitations are impossible because the sensitivity of of the cone cells overlaps, like they do in humans:

Relative responses of human cone cells to light (S=blue cone, M=green cone, L=red cone)

This space also lies within a cube, but for different reasons, basically there is a maximum value that is achievable (100% reflecting surface). This shape has nice symmetry properties (it is center symmetric) and has a rounded parallelepiped shape characteristic of the object solid for all species in all conditions (though other species may require a different number of dimensions). It is displayed much like the space above, black at the bottom, white at the top.

It is also a good shape.

We also printed some tetrachromatic chromaticity spaces, which are also 3D. We had trouble with the human tetrachromat space. But an idealisation of tetrachromat chromaticity spaces (as a 3-sphericon) was quite successful … as were the other sphericons … they roll funny!

Printing

This was my first experience of 3D printing. We were using RepRaps.

The first thing you think when you see 3D printing is “I can print anything!”, but what you should be thinking is: resolution, tolerances and “can I print this without having to lay down filament in thin air”.

Printing the actual shapes was pretty straight forwards, we just made them in two halves and glued them together. We made them nice and smooth by suspending them in acetone vapor (which is a good solvent of ABS), well, in one case, by accidentally dropping the whole thing in a vat of acetone (it actually worked very well, probably because it was still attached to a bit of wire and I fished it out immediately).

The purple frames were printed out of a different material, PLA. They are made from six (different) individual parts and glued into two halves of a cube. You can take and were a bit of a pain. Because of the steps made by the layering, it was fairly hard to make them meet up and glue nicely. But a really nice thing about 3D printing is you can easily make your own tools, so I “quickly” printed a “glue jig” that I could use to put the parts in the right place.

In hindsight, it was a bit big. Given that the parts are glued together using “dead reckoning” they’ve come out really nicely.