Open-endedness is (should be) a primary topic in ALife. Tim Taylor proposed three stages of open-endedness, paraphrasing: exploratory, doorways, and dimensions. Roughly speaking, the first stage is the ability to explore the range of a particular genotype/behavior within a known, often expected, range. E.g., brownian walk in a 2d plane. Taylor's second stage is the ability to open doors-- that is, explore regions that are not trivially available via incremental search. Take an Atari game that uses keys to open doors as a pretty literal example: finding and holding a key suddenly enables gradual search to explore a whole new area. Taylor's third stage is opening up new dimensions. I suppose this is intended in a flat-land style-- directions of exploration become available that were previously unimagined. Are stages two and three just matter of degree or perspective?