- Over the past year we have discussed examples of cellular automaton
modeling in fields of applied science such as ecology,
microbiology, marine biology, and
chemistry. This week's soup depicts a classic
experiment from the most frequent area of CA applications: physics. We show
the familiar refraction pattern as a traveling wave (the blue stripe) crosses a 'lens'
(the red ball) with higher refractive index than its surroundings, causing slower propagation
through an 'ether' of lattice gas particles.
- Particle motion and interaction is modeled by means of the previously
discussed HPP Gas. Wave 'solitons' within the
lens simply advance at half the speed, diffusing on alternate updates. Our graphic, generated
by CAM8, shows the resulting configuration after the wave has traveled almost half way across
the lens (from left to right). Originally a demo for the earlier CAM6
mixmaster, details of the source code may be found on pp.182-3 of Toffoli and Margolus'
Cellular Automata Machines (MIT Press, 1987). They describe the effect as follows:
- The part of the wave that enters the lens first is slowed down first; this
bends the wave-front and makes the wave converge. Since we are using a
circular lens the converging rays show spherical aberration :
instead of a sharply defined focal point they produce a caustic -
the pattern one sees when light is reflected on the inside of a cup filled
- Notice that there is also a weak reflected wave. This is not an
artifact of the model; in a reversible medium, theory predicts reflections
whenever there is a sharp discontinuity in the index of refraction, i.e.,
in the speed of propagation of information. If information arrives
faster than it can proceed onward, some of it must be reflected since none
can be lost.