Cancers are complex, adaptive ecosystems. It remains the lead cause of disease-related, pediatric death in North America. The emerging field of complexity science has redefined cancer as a computational system with intractable, algorithmic complexity. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple, chaotic attractors. Machine learning, Network science and information theory are discussed as current tools for cancer network reconstruction. The fluid dynamics of cancer-cell fate transitions and chemical pattern formation are briefly reviewed. Deep Learning architectures, delay-embedding algorithms and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complexity theory.