A bush robot is a hypothetical form of robot formed simply of repeatedly branching limbs. One trunk divides into three, three into nine, nine into 27... and so on, potentially down to nanotech scales.
This type of robot has appeared in science fiction novels in various forms for decades, but it was formally explored for NASA by Hans Moravec, so it is often called a Moravec bush, and sometimes -- not often -- referred to by NASA's official term: "fractal branching ultra-dexterous robots".
This form of robot is specifically designed to provide maximum dexterity; a robot would have highly articulated arms that could grasp and oppose at almost any angle, and the terminal buches quickly begin to look like prickly grasping pads rather than individual fingers. At least, hypothetically; no working model has yet been constructed. Moravec went so far as to print out a crude, non-working, model of a tridactyl bot with 9 layers -- with 19,683 terminal digits. His 3D printer repeatedly gave out when attempting a 10 layer bot (59,049 terminal digits), but visually they would look essentially identical.
Moravec estimated that it would be around 2050 before this form became practical for development, even at the limited level of his simulations. Theoretically, a finely designed and calibrated bush robot could divide to the point that it would be able to manipulate individual cells, proteins, molecules, or even atoms. In his words:
"Bush robots may provide a uniform, top down, incremental bridge to nanotechnology. Macroscopic machines with a few levels of branching could be built today, and could exhibit human-like dexterity. As microtechnology advances, the number of branching levels could be increased with ever finer sub-fingers. An ultimate nanoscale bush robot might begin with a stem a meter in length and a few centimeters in diameter, able to move with a one second timescale. At 30 levels of branching, one might find a billion fingers each a micron long, able to move at a megahertz. At 50 levels, there could be 1015 fingers, each a nanometer long, and in principle able to move at gigahertz rates, if not constrained by exotic physical effects."
While bush robots have a number of advantages, it is possible that they are simply not specialized enough to compete with more targeted technology. Molecular assemblers -- also hypothetical outside of naturally evolved organisms -- are rarely visualized as bush robots, although mechanical structures of this sort may be useful as part of a nanofactory's assembly line.