julia_set_openmp


julia_set_openmp, a C code which produces an image of a Julia set, using OpenMP to carry out the computation in parallel.

Suppose we have a function f(z) defined for any complex number z. Suppose that we repeatedly carry out the iteration z <== f(z). It's natural to assume that the sequence of z values will blow up in magnitude; however it's possible that for some starting values z, the sequence will stay small. We call such points the Julia set for f().

A simple class of test functions has the form f(z)=z^2+c, and some interesting values of the complex number c include 0.4+0.6i, 0.285+0.01i, and 0.7269+0.1889i. For our experiment, we will use c=-0.8+0.156i$. We will only look at points in the rectangle [-1.5,+1.5]x[-1.5,+1.5]. We will pick a 1000x1000 grid in this rectangle, and for each z{i,j} we will iterate 200 times. If the norm of the iterates stays below 1,000, we will consider that it is a member of the Julia set. So our result will essentially be a 1000x1000 array of 0's (not in the set) and 1's (in the set).

Every candidate point can be checked independently. Therefore, determining the stucture of a Julia set is a good candidate for a parallel computation.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

julia_set_openmp is available in a C version.

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julia_set_openmp_test

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SUPERLU_OPENMP, C codes which illustrate the use of the SUPERLU_OPENMP library, a version of SUPERLU compiled with the OpenMP parallel programming interface, for the fast direct solution of large sparse systems of linear equations.

ZIGGURAT_OPENMP, a C code which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

Reference:

  1. Heinz-Otto Peitgen, Hartmut Juergens, Dietmar Saupe,
    Chaos and Fractals - New Frontiers in Science,
    Springer, 1992,
    ISBN: 0-387-20229-3,
    LC: Q172.5.C45.P45.

Source Code:


Last revised on 01 August 2020.