I took this picture in my kitchen a few weeks ago when it was frigid outside and two hot chocolates seemed a necessity for survival. The photograph shows two coffee cups on a granite counter top. You can see the reflection of the lights off of the granite. The light patterns (i.e., caustics) that are visible inside of each cup are a result of the light interacting with the inside of the cups. Each cup has two cardioids because there are two overhead lights. Models that involve ray tracing, or approximating light with lines, produce some really interesting patterns. The collection of two light sources and cups forms an analog computer, essentially, for gaining insight on these and related "envelopes" of multiple lines crossing. The sum of places where these crossings, or intersections, occur forms the cardioid patterns. For those readers interested in sound, some microphones use cardioid patterns as a means for defining what angles are picked up by the mic.
From an automata, or machine, perspective the cups form a model of the mathematical cardioid concept, with the system input being light, and the output being the pattern you see with your eyes. You may object to my use of model here by my mentioning that the cups are models of a mathematical concept, and you would be right to object since this philosophy is a bit controversial; a subject of one of the upcoming posts. Thinking of mathematics as the ultimate target places the activity of modeling at the core of cognition.