Here we discuss an application of HPC (not high performance computing, instead high precision computing, which is a special case of HPC) applied to dynamical systems such as the logistic map in chaos theory. defined as X(k) = 4 X(k) (1 – X(k-1)).
For all these systems, the loss of precision propagates exponentially, to the point that after 50 iterations, all generated values are completely wrong. Tons of articles have been written on this subject – none of them acknowledging the faulty numbers being used, as round-off errors propagate as fast as chaos. This is an an active research area with applications in population dynamics, physics, and engineering. It does not invalidate the published results, as most of them are theoretical in nature, and do not impact the limiting distribution as the faulty sequences behave as instances of processes that are re-seeded every 40 iterations or so due to errors, behaving the same way regardless of the seed.
The core of the discussion here is about how to write code that produces far more accurate numbers, whether in R, Python or other languages, using super precision. In short, which libraries should you use to handle such problems?
You can check out the context, Perl code, Python code, and an Excel spreadsheet that illustrates the issue, in this discussion.
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This broccoli is an example of the self-replicating processes that could benefit from HPC
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