Since 1986 and K. Eric Drexler´s classic The Engines of Creation (EOC) the meme of selfassembling machines has been a source of imagination and horrifying ideas:
This is Drexler himself (EOC):
"Genetic evolution has limited life to a system based on DNA, RNA, and ribosomes, but memetic evolution will bring life-like machines based on nanocomputers and assemblers. Assemblers will be able to build all that ribosomes can, and more; assembler-based replicators will therefore be able to do all that life can, and more. From an evolutionary point of view, this poses an obvious threat to otters, people, cacti, and ferns - to the rich fabric of the biosphere and all that we prize. (...)
Replicators can be more potent than nuclear weapons: to devastate Earth with bombs would require masses of exotic hardware and rare isotopes, but to destroy all life with replicators would require only a single speck made of ordinary elements."
For those of you who have been reading Drexler merely as science fiction, the following article written by Zyvex LLC Research Scientist Robert A. Freitas Jr. may be illuminating:
"...the possible dangers posed by future technologies such as artificial intelligence, genetic engineering and molecular nanotechnology have made it clear that an intensive theoretical analysis of the major classes of environmental risks of molecular nanotechnology (MNT) is warranted. No systematic assessment of the risks and limitations of MNT-based technologies has yet been attempted."
Freitas uses the term "global ecophagy" for the risk that self-replicating nanorobots capable of functioning autonomously in the natural environment could quickly convert that natural environment (e.g., "biomass") into replicas of themselves (e.g., "nanomass") on a global basis..."
"The maximum rate of global ecophagy by biovorous self-replicating nanorobots is fundamentally restricted by the replicative strategy employed; by the maximum dispersal velocity of mobile replicators; by operational energy and chemical element requirements; by the homeostatic resistance of biological ecologies to ecophagy; by ecophagic thermal pollution limits (ETPL); and most importantly by our determination and readiness to stop them."
After a thorough analysis Fritas ends up with the conclusion: "The smallest plausible biovorous nanoreplicator has a molecular weight of ~1 gigadalton and a minimum replication time of perhaps ~100 seconds, in theory permitting global ecophagy to be completed in as few as ~104 seconds.
In short, the paper calculates that the maximum speed that self-replicating nanobots could eat the Earth is 2.78 hours. (This was calculated by Jurvetson, here.
Read it your self at Foresight.org!