IF YOU think the complex microchips that drive modern computers are models of deterministic precision, think again. Their behaviour is inherently unpredictable and chaotic, a property one normally associates with the weather.

Intel’s widely used Pentium 4 microprocessor has 42 million transistors and the newer Itanium 2 has no fewer than 410 million. “Their performance can be highly variable and difficult to predict,” says Hugues Berry of the National Research Institute for Information and Automation in Orsay, France.

Berry, Daniel Perez and Olivier Temam say that chaos theory can explain the unpredictable behaviour. The team ran a standard program repeatedly on a simulator which engineers routinely use to design and test microprocessors, and found that the time taken to complete the task varied greatly from one run to the next.

But within the irregularity, the team detected a pattern, the mathematical signature of “deterministic chaos”, a property that governs other chaotic systems such as weather. Such systems are extremely sensitive – a small change at one point can lead to wide fluctuations at a later time. For complex microprocessors, this means that the precise course of a computation, including how long it takes, is sensitive to the processor’s state when the computation began.

read more here:
http://www.arxiv.org/nlin.AO/0506030