Abstract
Color-image maps are generated through computer-based simulations to study the evolution of a system of three bodies interacting under classical gravitational forces. These image maps partition the set of possible initial-system configurations into regions that exhibit similar evolutionary characteristics. This resembles the technique used to produce color images of the Mandelbrot set. A restricted case of the three-body problem, in which the initial velocities of all three bodies are zero and the bodies are all of equal mass, is examined in detail. Image maps of the time to collision (assuming a finite radius) as a function of initial configuration are presented. Symmetries of the resulting maps are analyzed for invariants by means of transformations of scale.
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Brandt, J.W., Park, A. Using color-image maps to study collisions in the three-body problem. The Visual Computer 7, 13–18 (1991). https://doi.org/10.1007/BF01994113
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DOI: https://doi.org/10.1007/BF01994113