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Basins of attraction

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Basins of attraction

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To plot a basin of attraction for given governing equations: x^3-y = 0 ; y^3-x = 0

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While solving a system of equations using any numerical method, the point to which the method converges is strongly dependent on the initial guess. The set of points that converge to a given root is called the basin of attraction of that root. It would be interesting to visualize the basins of attraction by coloring each starting point with a different color depending on which root it converges to. The different basins will thus be given different colors. The basins of attraction obtained will look like fractals.

MATLAB release MATLAB 7.10 (R2010a)
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