Interactive Self-Replicating, Self-Incrementing and Self-Decrementing Loops

Self-replicating loops presented to date are usually worlds unto themselves, inaccessible to observer once the replication process is launched. In this paper we present a self-replicating loop which allows for user interaction. Specifically, the user can control the loop’s replication as well as the size of the replica. After presenting the design of this novel loop, we delineate its physical implementation in our electronic wall for bio-inspired applications, the BioWall. Introduction: Interactive Self-Replication All self-replicating loops presented to date (Langton 1984; Byl 1989; Reggia 1993) are usually worlds unto themselves: once the initial loop configuration is embedded within the cellular automaton (CA) universe (at time-step 0), no further user interaction occurs, and the CA chugs along in total oblivion of the observing user. In previous works we have described the design of self-replicating loops which could be activated by the user (Stauffer 2001; 2002). The user was able to control the loop’s replication and induce its destruction. In this paper we present another interactive self-replicating loop which give birth to a daughter loop whose size is identical, incremented by one or decremented by one. The next section explains the corresponding self-replication, self-incrementation and self-decrementation processes. Section III discusses the hardware implementation of the loop in our electronic wall for bio-inspired applications, the BioWall. Finally, we present concluding remarks in Section IV. Loop Design and Operation Contrary to previous loops, which self-replicate continually, the novel one presented below is idle unless externally activated. This n×n loop, with n ≥ 3, is therefore an interactive self-replicator. Defined in a two-dimensional, five-neighbor cellular space, with seven basic states per cell (Figure 1), our minimal 3 × 3 loop is made up of eight cells. As long as no external input is provided, the loop is inert, continually undergoing an eight-time-step cycle (Figure 2). 0: empty component 1: building component 2: east-moving growth signal 3: north-moving growth signal 4: west-moving growth signal 5: south-moving growth signal 6: left-turn signal 7: east-branching signal (rep), east data-decrement and cut-off signal (inc) 8: east-branching and cut-off signal (rep), east data-increment and cut-off signal (dec) 9: north-branching signal (rep), north data-decrement and cut-off signal (inc) 10: north-branching and cut-off signal (rep), north data-increment and cut-off signal (dec) 11: west-branching signal (rep), west data-decrement and cut-off signal (inc) 12: west-branching and cut-off signal (rep), west data-increment and cut-off signal (dec) 13: south-branching signal (rep), south data-decrement and cut-off signal (inc) 14: south-branching and cut-off signal (rep), south data-increment and cut-off signal (dec) 15: cut-off signal (rep), A: replication-activate variable (rep,inc,dec) I: data-increment variable (inc) D: data-decrement variable (dec) Figure 1: The seven basic cellular states 0 to 6 used for the idle loop and the nine additional states 8 to 15 involved in the self-replication (rep), self-incrementation (inc) or self-decrementation (dec) processes when the control variables A, I or D are activated. In order to launch the self-replication process, the selfincrementation process or the self-decrementation process, the user activates the idle loop by providing an external input on one of its eight cells (in Section activation occurs by physically touching the BioWall). This external input presets respectively one out of three control variables: the replication-activate variable A, the data-increment variable I or the data-decrement variable D of the cell. Presetting the replication-activate variable (A = 1) leads to the appearance of a shadowed state 6 which corresponds to an activated left-turn signal at time-step 0 (Figure 3). The activated loop is then ready to selfreplicate and the process is performed in 48 time-steps. 2 in Artificial Life VIII, Standish, Abbass, Bedau (eds) (MIT Press) 2002. pp 53–56 1 1 6 2 0 1 2 3 1 1 1 1 3 1 6 3 1 1 1 4 3 1 1 6 1 1 1 4 6 1 1 1 4 1 1