1. A game of chance for a gaming machine controlled by a processor in response to a wager, comprising: a basic game including a plurality of possible randomly-selected basic game outcomes, the plurality of possible basic game outcomes including a start-bonus outcome; and a maze-based bonus game triggered by the start-bonus outcome and indicated on a visual display, the bonus game including a bonus-generating indicator movable along a plurality of different intersecting paths containing a plurality of consumable elements, the bonus-generating indicator generating an award based on a randomly-selected bonus game outcome as the bonus-generating indicator visually consumes the elements.