Gaming machine and method having persistent continuum feature

A method of operating a game through a game cabinet in which is housed at least one electronic display and a player interface with buttons, the method performed by one or more electronic controllers executing program code held in tangible non-transitory computer readable memory coupled to the one or more electronic controllers, the method comprising:

• displaying conduct of a game and a player point total, and updating the player point total as points are won in the game;
• displaying a gaming continuum having an advancement level in a first display area;
• responsive to a first player activation input activating a round of the game, randomly determining to either partially advance the advancement level of the gaming continuum or totally advance the advancement level of the gaming continuum;
• causing the gaming continuum to enter a decay state after each round of the game, the decay state including displaying the advancement level of the gaming continuum decreasing at a decay rate over time toward an initial state until it reaches the initial state or a subsequent activation input occurs;
• and
• starting a subsequent game round with the advancement level of the gaming continuum at a different level than that provided at a conclusion of a prior game round.