We report on a project that could be characterized as a mining and discovery expedition among the data fields that reside within, and are expressed with, the Dynamic Stochastic Synthesis (GENDYN) algorithm as realized in The New GENDYN Program1. The New GENDYN Program is a faithful implementation of Iannis Xenakis’ sound synthesis algorithm (as realized in his work GENDY3, 1991), that also provides a framework within which extensive research into the world of rigorous algorithmic composition is possible. The GENDYN algorithm can generate an entire work of computable sonic art from a baseline of “nothing”, i.e. with no a-priori defined sonic source material: all sound is the emergent result of the definition of initial conditions among the multitude of parameters within the algorithm, and as then executed by the probability distributions incorporated therein: a musical work is created by execution of a computational process obeying an algorithmic procedure. We report on work that has extended the GENDYN algorithm by implementing large-scale and massively parallel techniques, illuminating and demonstrating capabilities such as dynamic stochastic granular synthesis, stochastic melody (pitch distribution), and stochastic harmonic (vertical) structures. We focus our analytics on a custom user interface created with the Matlab algorithmic development environment that integrates with the New GENDYN Program, achieving a level of organizational control among the synthesis parameters within the GENDYN. We identify the relationships between the defined parameters of the algorithm’s initial conditions and their ultimate influence on the characteristics of the resulting sound such as timbre, event duration, density, and pitch. We also investigate the problem of representing the multi-faceted dimensions of the stochastic synthesis: organizing the extensive and expansive quantities of numerical data generated by the GENDYN algorithm; systematizing the relationships across the initial conditions and the structural functions they serve within the computed compositional sonic work. Examples of computed etudes are presented as well as demonstrations of the aforementioned relationships between GENDYN initial conditions and resulting synthesized works. We propose areas of research for future investigation.