Creative exploration is central to science, art and cognitive development. However, research on creative exploration is limited by a lack of high-resolution automated paradigms. To address this, we present such an automated paradigm, the creative foraging game, in which people search for novel and valuable solutions in a large and well-defined space made of all possible shapes made of ten connected squares. Players discovered shape categories such as digits, letters, and airplanes. They exploited each category, then dropped it to explore once again, and so on. Aligned with a prediction of optimal foraging theory (OFT) prediction, during exploration phases, people moved along meandering paths that are about three times longer than the minimal paths between shapes, when exploiting a category of related shapes, they moved along the minimal paths. The moment of discovery of a new category was usually done at a nonprototypical and ambiguous shape, which can serve as an experimental proxy for creative leaps. People showed individual differences in their search patterns, along a continuum between two strategies: a mercurial quick-to-discover/quick-to-drop strategy and a thorough slow-to-discover/slow-to-drop strategy. Contrary to optimal foraging theory, players leave exploitation to explore again far before categories are depleted. This paradigm opens the way for automated high-resolution study of creative exploration.