In nanotechnology , exponential assembly is a form of self-replication in which tiny devices called nanorobots repeatedly construct copies of themselves. Four conditions must be met for exponential assembly to take place in an orderly manner.
The first condition is that each nanorobot must construct at least two copies of itself during its operational life. These copies must be exact in every detail, including the ability to reproduce. The more copies each unit can produce, the more rapidly the population will grow.
The second condition is that there must exist sufficient energy and ingredients so the process can continue for the specified length of time, or until a specified population of nanorobots is reached. Because the population grows exponentially, the number of units will increase rapidly. For example, if a population begins with one nanorobot, and if each unit creates three copies of itself, then the population will grow by powers of three. Suppose replication takes place on a daily basis and each nanorobot ends its useful life as soon as it has reproduced. Then after two days the population will be 3 2 = 9 units, after three days it will be 3 3 = 27 units, after four days it will be 3 4 = 81 units, and, in general, after n days the population will be 3 n units.
The third condition for exponential assembly is that the environment be controlled so the replication process can proceed efficiently. Excessive turbulence, temperature extremes, intense radiation, or other adverse circumstances might prevent the proper functioning of the nanorobots and cause the process to falter or fail before it is supposed to terminate.
The fourth condition is that the process be programmed to end at a certain point, or be modified so that the population cannot exceed a certain maximum number of units. Otherwise, the nanorobots will eventually crowd each other out of their world, and the process will come to a catastrophic halt.