Amorphous computing in the presence of stochastic disturbances

Amorphous computing is a non-standard computing paradigm that relies on massively parallel execution of computer code by a large number of small, spatially distributed, weakly interacting processing units. Over the last decade or so, amorphous computing has attracted a great deal of interest both as an alternative model of computing and as an inspiration to understand developmental biology. A number of algorithms have been developed that can take advantage of the massive parallelism of this computing paradigm to solve specific problems. One of the interesting properties of amorphous computers is that they are robust with respect to the loss of individual processing units, in the sense that a removal of some of them should not impact on the computation as a whole. However, much less understood is to what extent amorphous computers are robust with respect to minor disturbances to the individual processing units, such as random motion or occasional faulty computation short of total component failure. In this article we address this question. As an example problem we choose an algorithm to calculate a straight line between two points. Using this example, we find that amorphous computers are not in general robust with respect to Brownian motion and noise, but we find strategies that restore reliable computation even in their presence. We will argue that these strategies are generally applicable and not specific to the particular AC we consider, or even specific to electronic computers.