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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.

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Basins of Attraction/