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A Live Algorithm takes part in improvised, collaborative performance, sharing the same modes of communication and expression as its partners. The device enjoys the same constraints and freedoms as its human associates. A live algorithm would be expected to imitate, develop ideas and, at times, to contribute novelty and surprise, to experiment and take risks, and to assume leadership. Other performers experience the live algorithm as if it were a human, with a sense of validity and belief. Although designing a live algorithm with the ability to imitate and develop shared ideas is already a formidable undertaking, the additional requirement of innovation is an even harder research challenge. We suggest that it is the ability to innovate that distinguishes autonomy from automation and randomness and postulate that novelty and surprise can be explained as an emergent phenomenon. To this end, most current live algorithm research focusses on certain open dynamic systems which model some aspects of a natural system in which emergence is known to occur. Some differences between people and dynamical systems are immediately evident, however. Memory enables performers to revisit past actions and understand relationships; evaluation, followed by learning, leads to improvement; a social context provides encouragement and criticism and a cultural context imparts meaning via a web of shared experience. But dynamical systems can be augmented with memory using a counterpart to the environment-mediated stigmergetic interaction between insects. We speculate if a live algorithm culture could be also created, and if this is the missing ingredient.