On Polymorphic Logical Gates in Subexcitable Chemical Medium

In a subexcitable light-sensitive Belousov–Zhabotinsky (BZ) chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragments can conserve their shape and velocity vectors for extended time periods. The size and life span of a fragment depend on the illumination level of the medium. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. In computer simulations based on the Oregonator model, we demonstrate that the outcomes of inter-fragment collisions can be controlled by varying the illumination level applied to the medium. We interpret these wave-fragments as values of Boolean variables and design collision-based polymorphic logical gates. The gate implements operation XNOR for low illumination, and it acts as NOR gate for high illumination. As a NOR gate is a universal gate, then we are able to demonstrate that a simulated light sensitive BZ medium exhibits computational universality.

[1]  Kenneth Showalter,et al.  Signal transmission in chemical systems: propagation of chemical waves through capillary tubes , 1994 .

[2]  J Gorecki,et al.  Sensing the distance to a source of periodic oscillations in a nonlinear chemical medium with the output information coded in frequency of excitation pulses. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Norman Margolus,et al.  Physics-Like Models of Computation , 2002, Collision-Based Computing.

[4]  E. D. Weinberger,et al.  Chemical implementation of finite-state machines. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Jerzy Gorecki,et al.  Information Processing with Chemical Excitations - from Instant Machines to an Artificial Chemical Brain , 2006, Int. J. Unconv. Comput..

[6]  Andrew Adamatzky,et al.  Collision-based computing in Belousov–Zhabotinsky medium , 2004 .

[7]  Andrew Adamatzky,et al.  Binary collisions between wave-fragments in a sub-excitable Belousov–Zhabotinsky medium , 2007 .

[8]  Adrian Stoica,et al.  On Polymorphic Circuits and Their Design Using Evolutionary Algorithms , 2002 .

[9]  F. W. Schneider,et al.  LOGICAL GATES USING A NONLINEAR CHEMICAL REACTION , 1994 .

[10]  J Gorecka,et al.  Multiargument logical operations performed with excitable chemical medium. , 2006, The Journal of chemical physics.

[11]  Kenichi Yoshikawa,et al.  Information operations with multiple pulses on an excitable field , 2003 .

[12]  Kenneth Showalter,et al.  Logic gates in excitable media , 1995 .

[13]  Valentina Beato,et al.  Pulse propagation in a model for the photosensitive Belousov-Zhabotinsky reaction with external noise , 2003, SPIE International Symposium on Fluctuations and Noise.

[14]  Jerzy Gorecki,et al.  On Chemical Methods of Direction and Distance Sensing , 2009, Int. J. Unconv. Comput..

[15]  Andrew Adamatzky,et al.  Experimental validation of binary collisions between wave fragments in the photosensitive Belousov–Zhabotinsky reaction , 2009 .

[16]  K. Showalter,et al.  Wave propagation in subexcitable media with periodically modulated excitability. , 2001, Physical review letters.

[17]  Andrew Adamatzky,et al.  Simple Collision-Based Chemical Logic Gates with Adaptive Computing , 2009, Int. J. Nanotechnol. Mol. Comput..

[18]  E. Berlekamp,et al.  Winning Ways for Your Mathematical Plays , 1983 .

[19]  Andrew Adamatzky,et al.  On computing in fine-grained compartmentalised Belousov-Zhabotinsky medium , 2010, 1006.1900.

[20]  A Hjelmfelt,et al.  Pattern Recognition in Coupled Chemical Kinetic Systems , 1993, Science.

[21]  Kenichi Yoshikawa,et al.  On Chemical Reactors That Can Count , 2003 .

[22]  Jerzy Gorecki,et al.  Basic Information Processing Operations with Pulses of Excitation in a Reaction-Diffusion System , 2009, Int. J. Unconv. Comput..

[23]  Jerzy Gorecki,et al.  On the Simplest Chemical Signal Diodes Constructed with an Excitable Medium , 2009, Int. J. Unconv. Comput..

[24]  A Hjelmfelt,et al.  Chemical implementation of neural networks and Turing machines. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Jerzy Gorecki,et al.  Logical Functions of a Cross Junction of Excitable Chemical Media , 2001 .

[26]  Andrew Adamatzky Collision-Based Computing , 2002, Springer London.

[27]  John Ross,et al.  Implementation of logic functions and computations by chemical kinetics , 1995 .

[28]  Jerzy Gorecki,et al.  Information processing with structured excitable medium , 2009, Natural Computing.

[29]  Andrew Adamatzky,et al.  Slime mould logical gates: exploring ballistic approach , 2010, 1005.2301.

[30]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[31]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[32]  Andrew Adamatzky,et al.  Implementation of glider guns in the light-sensitive Belousov-Zhabotinsky medium. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  J Gorecki,et al.  T-shaped coincidence detector as a band filter of chemical signal frequency. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  A. Hjelmfelt,et al.  Mass-coupled chemical systems with computational properties , 1993 .