The results of a simple algorithm, though regular and predictable if taken one at a time, can take on great complexity if the algorithm is many times reiterated with the result of each iteration becoming a factor in the next. A classic example of such a nonlinear process is the Mandelbrot set, which can produce an infinite variety of ‘fractal’ images, all generated by a relatively simple formula run recursively on an ordinary computer.
‘Nonlinearity means that the act of playing the game has a way of changing the rules’ (Gleick 1987). If the rules of life are always changing and always undiscoverable, as Bateson said, it’s probably because life is nonlinear. Semiosis is also nonlinear, especially in the form of dialogue or conversation between two people taking turns as speaker and listener.
As we communicate in language and gesture, we interpret and understand each other dialogically. This dialogic dynamic is not a linear or additive combination of two preexisting, skull-bound minds. It emerges from and reciprocally shapes the nonlinear coupling of oneself and other in perception and action, emotion and imagination, and gesture and speech. In this way, self and other bring forth each other reciprocally through empathy.
— Thompson (2007, 402)