Claytronic is a concept presented by the Carnegie Mellon University.
For now please check the wikipedia page  for a basic introduction.
From the developers introduction page
"Development ... represents a partnership between the School of Computer Sciences of Carnegie Mellon University, Intel Corporation at its Pittsburgh Laboratory and FEMTO-ST Institute."
Development attempts via current day (2017) non atomically precise technology
Unlike with the more difficult utility fog there has been and is ongoing active development.
Comparison to utility fog
The claytronics concept strongly overlaps with the concept of utility fog.
One main difference seem to be the choice for keeping complexity low and thus avoiding complicated linkage-arms. In fact the decision to put no hinges / moving components inside the "catoms" at all. The "material" (when in some kind of malleable mode) would likely behave more like an incompressible fluid. This has pros and cons:
- Unlike in the case of utility fog this design choice does not allow for emulated elasticity. (At least it seems very difficult.)
- Big changes in volume and density can still be emulated by one or many hidden voids that grow or shrink depending on the situation (letting air in or dragging up a vacuum?).
- When few voids are present the "material" then it likely could resist higher mechanical compression loads than utility fog.
For movement of the claytronic units (they have been dubbed "catoms" like the "foglets" in case of utility fog) a rolling approach seems to be preferred. The current macroscale prototypes use electromagnets. As scaling laws enforce at the microscale an electrostatic approach might become preferable.
If the lack of hard interlocking interfaces remain in a future atomically precise microscale design that is if it is still held together just through magneto- or electrostatic interaction the "materials" tensile strength may lie way below the one of the base material (possibly below the tensile strength of some utility fogs). This may raise increased concerns of rub-off and spill (the same problem as with microcomponents that are just held together by Van der Waals forces. -- See: mobility prevention guideline
Claytronics seems to be located more on the "sliding/rolling cube" end of the spectrum of Robotic mobility.
The concept of a fractal hierarchy of increasingly sized computers suspended in the "material" known from utility fog is not noted by the developers but it could be added.
There are very simple single rotation joint reconfigurable shape robots designs with base units that have a single internal rotation joint that is diagonally oriented. These have similar folding behavior to "indivisible protein like folding block chains" (a different concept) with the huge difference that all links can be disconnected at any time making arbitrary subsections foldable. Since the base units have an internal moving mechanism (as said just a simple rotative joint) designs like these do not fall under claytronics in the sense of the design goals that the claytronic developers target.
Relation to functional programming / reversible computing / immutability
Unlike information/bits physical objects like "catoms" cannot just be overwritten and vanish into intangible heat. In a sense they are like immutable data-structures. Once created one only can shift them around. (This is generally true for crystolecules and microcomponents.)
Interestingly the developers found the need to develop domain specific languages that shun imperative programming. One of these languages is called "Meld". It's A declarative logic programming language. Logic programming is relational and is a superset of pure functional programming which is functional (as the name says) which in turn relies on immutability.
As is the case with utility fog specialized mechanical metamaterials can have much higher performance.
- Claytronics project page
- Wikipedia: Claytronics
- Video: Claytronics @CMU Video (2010-06-07) features some simulations
- Video: Claytronics-Physical Dynamic Rendering (2009-12-07)
- Video: Dynamic Physical Rendering (2007-06-21) (noting switch to electrostatics)
- Likely not encompassed by the claytronics concept -- Video: Self-replicating blocks from Cornell University (2009-02-02)