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"The Mandelbrot set is a fractal that has become popular far outside of
mathematics both for its aesthetic appeal and its complicated structure,
arising from a simple definition...
Mathematically, the Mandelbrot set M is defined as the connectedness locus of the family
of complex quadratic polynomials...
The Mandelbrot set can also be defined as the set of parameters c for which the set {0, | fc(0) | , | fc(fc(0)) | , | fc(fc(fc(0))) | ,...}- has a finite upper bound. This definition lends itself immediately to the production of computer generated renderings,.."
from
Wikipedia article
One of our class assignments was to generate an image from the
Mandelbrot set within a range, in parallel, on a local computer
cluster using
MPI.
Here's Mine.
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"The classical N-body problem simulates the evolution of a system of N bodies, where the force exerted on each body arises due to its interaction with all the other bodies in the system. N-body algorithms have numerous applications in areas such as astrophysics, molecular dynamics and plasma physics. The simulation proceeds over timesteps, each time computing the net force on every body and thereby updating its position and other attributes. If all pairwise forces are computed directly, this requires O(N2) operations at each timestep. Hierarchical tree-based methods have been developed to reduce the complexity. There have been several papers that have looked at parallel implementations of these tree-based methods.."
from
"Parallel N-Body Simulations"
Here
is an unsophisticated demonstration of n-bodies flying around,
using inefficient algorithms
and cheap scripting languages, but amusing nonetheless.
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