The Bifurcation Map - Made To Be Parallized


The bifurcation map is one of many examples of chaotic systems whose study seems to be nearly impossible without the extensive use of computational resources. It is described by the surprisingly simple equation,

The plot you can see above was created in the following way:
  1. Start with m=1.0.
  2. Pick an arbitrary starting value for y.
  3. Using this y calculate a new value for y.
  4. Go through this cycle 200 times to avoid transient behavior.
  5. Go through another 200 cycles but this time save the y's for the plot.
  6. Increase m by a small amount (e.g. 0.01).
  7. Go to step 2 and repeat the whole process until m=4.0.
The fact that the initial value for y is absolutely arbitrary explains why this problem is perfect for parallel processing. As the calculations for one value of m don't depend in any way on the results for a different value of m we can have different processes for different values of m run parallel and totally independent of each other (no messages!).
Again we will use the Master and Slave model for this problem.
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