Morphologists study the structure of space. Depending on who you are working with, this structure may be related to physics as with crystals or elementary particles. Or it could be simply an exploration of all the possibilities.
Of the latter, the earliest historically are those that worked with polyhedra; how faceted ball-like structures can fill space in a repeatable way. Haresh Lalvani — mentioned in another note here — is the most interesting of these in my opinion.
But what if the repeating structures are something else? A fascinating approach looks at so-called minimal surfaces. These are easily envisioned as the shape a soap film will take on a bent coat hanger. Werner Fischer has a paper (alas, with no diagrams) that reviews his work on classifying the types of these periodic minimal surfaces via their symmetries.
We have in the same volume the rather important companion paper on then new discoveries with periodic minimal surfaces by Elke Koch, also without images.
The Relationship to Kutachi
We have three areas this can help with.
One is our need to represent large sets of information and their relationships. We can do this with graphs, but if we make the graphs regularly structured, then we can leverage symmetries among them as shortcuts. This helps computation over large sets because knowledge is partially abstracted onto well behaved form. At the same time, we get the benefit as humans that it make envisioning large sets more intuitive, again because we map complex knowledge onto easy to comprehend form.
A second is that we will have a notion of fluid moving through a medium that affects it. The form of the flow should tell us something. But we should also be able to zoom into the flow and examine individual particles, each particle being a fact. We could display these as droplets moving together, but as they have forces that tie them together, it is better to envision them not as balls with elastic springs, but as nodes in a minimal surface array. The minimal surfaces then represent the surface tensile attraction among them.
The third takes advantage of both of these. We will have the need to show individual facts by themselves in text or near-text form. We’ll relate facts by lines drawn between them. These lines should visually indicate the forces associated with the relationship in governing situations. It would be good if the form of these lines was drawn from the inferred minimal surfaces we have in this case behind the scenes.
Links
On 3-Periodic Minimal Surfaces I. Symmetry and Derivation. Elke Koch. [Symmetry of Structure] 1989.
Burt papers
The Kutachi essay on Fluid Flows. (not online yet)
The Kutachi essay on Lines with Increasing Gravity. (not online yet)
The Kutachi essay on Quantum Clouds. (not online yet)