An Approach to Complexity: Numerical Computations

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Science  26 Apr 1985:
Vol. 228, Issue 4698, pp. 403-408
DOI: 10.1126/science.228.4698.403


The use of supercomputers and modern color-imaging techniques for numerical computation is beginning to fulfill von Neumann's vision that digital computers would become the most appropriate tool for solving nonlinear partial differential equations. An example of this approach, a model for the gas flow in the vicinity of a black hole, is described. From such calculations comes a realization that the multidimensional, dynamic solutions of nonlinear partial differential equations can exhibit complex behavior compared to what one normally encounters in analytic solutions. This complexity includes small-scale chaotic structure and large-scale persistently ordered structure. Computational methodology and the aesthetics that derive from it are discussed.