The objective of this work is to investigate the emergent properties of the gaits of the simulated snake-like robot, Snakebot. The gaits are automatically designed through Genetic Programming (GP) to be robust, general, adaptive, and the fastest possible sidewinding, locomotion. Considering the notion of emergent intelligence as the ability of Snakebot to achieve its goals (of moving fast) without the need to be explicitly taught how to do so, we present empirical results demonstrating the emergence of sidewinding locomotion from relatively simple motion patterns of morphological segments of Snakebot. We discuss the emergent properties of the evolved robust high velocity sidewinding locomotion gaits of Snakebot when situated in challenging environments. Then we elaborate on the ability of Snakebot to adapt to partial damage by gradually improving its velocity characteristics, and the emergent properties of obtained adaptive gaits. Verifying the practical implications of the analogy between the emergent properties of the robust and the adaptive sidewinding gaits, this work could be viewed as a step towards building real Snakebots, which are able to perform robustly in challenging environments.