Allow me to repost this idea once again
http://en.wikipedia.org/wiki/Logistic_map
just pick the value of r that is in the chaotic region.
Implement reals as long double that is 80-bit (10-bytes) on the Intel/AMD CPUs. Not all the C++ compilers really support long double, but the logistic map function is so trivial that you can include in-line assembly which will be in the order of 10 lines.
2) This is a variant of the above that embraces the enemy instead of fighting it. Implement (1) with reals as cl_double which is supported in OpenCL by NVidia cards but not by AMD cards. Then short AMD stock and go long NVDA for additiona gains.
Again, good luck!
I'm thinking about throwing 80-bit FPU at something like Mandelbrot or Julia sets to get a cool looking block hashes