In a two-player subtraction game, the players remove stones from a pile, until one player is stuck, so the other wins. Subtraction sets with one or two allowable move sizes have been understood since the 1970's, but a precise characterization of the game with three allowable move sizes x,y,z remains unknown. We used 37 years of computation, and more than 6 TB of data, in a massive data-driven approach to a full characterization of these periodicity. In the three-dimensional space that characterizes the game, we have recently developed a full characterization that holds, except for a neighborhood near the plane x+y=z. During the past six months, we uncovered the complex structure near the plane x+y=z as well. We will use a three-dimensional visualization to display the fractal nature of the underlying principles of this game. We next endeavor to introduce a methodology for pinpointing the structure of the game at any point (without traditional recursive brute-force computations), which will yield additional insights into the structure. This material is supported by NSF grant 1246818 and by the NSF-sponsored REUF program of the American Institute of Mathematics.