Chapter 8: Implications for Everyday Systems

Section 2: The Growth of Crystals


The boiling of a liquid such as water involves a kind of growth inhibition that is in some ways analogous to that seen in dendritic crystal growth. When a particular piece of liquid boils—forming a bubble of gas—a certain latent heat is consumed, reducing the local temperature, and inhibiting further boiling. In the pictures below the liquid is divided into cells, with each cell having a temperature from 0 to 1, corresponding exactly to a continuous cellular automaton of the kind discussed on page 155. At each step, the temperature of every cell is given by the average of its temperature and the temperatures of its neighbors, representing the process of heat diffusion, with a constant amount added to represent external heating. If the temperature of any cell exceeds 1, then only the fractional part is kept, as in the systems on page 158, representing the consumption of latent heat in the boiling process. The pictures below illustrate the kind of seemingly random pattern of bubble formation that can be heard in the noise produced by boiling water.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]