A spiral cache memory provides low access latency for frequently-accessed values by self-organizing to always move a requested value to a front-most storage tile of the spiral. If the spiral cache needs to eject a value to make space for a value moved to the front-most tile, space is made by ejecting a value from the cache to a backing store. A buffer along with flow control logic is used to prevent overflow of writes of ejected values to the generally slow backing store. The tiles in the spiral cache may be single storage locations or be organized as some form of cache memory such as direct-mapped or set-associative caches. Power consumption of the spiral cache can be reduced by dividing the cache into an active and inactive partition, which can be adjusted on a per-tile basis. Tile-generated or global power-down decisions can set the size of the partitions.