 Instantaneous description of a Turing machine

An instantaneous description records the current control state, head position, and tape contents. For a tape blank outside a finite window, a word $huqvh$ records the symbols $u$ to the left of the head and $v$ from the scanned cell rightward, with unrecorded cells blank. If $v$ is empty, the head scans an implicit blank. Extra outer blanks can represent the same infinite tape. The instruction of a Turing machine determines its successor description.