Cellular automata often give rise to areas of single colour or uniform texture. Wolfram refers to these as 'phases', the word used by physicists for specific solid, liquid or gaseous forms of matter. Sometimes a 'seed' of a particular phase, injected into a cellular automaton, will grow and grow, like a seed crystal dropped in a crucible of molten metal. Wolfram says this is the best-yet cellular automaton model of a physical process. Fluid flow, electromagnetic fields and other physical systems are usually modelled with partial differential equations.
Quantities change smoothly with space and time.
Occasionally an exact solution can be found by manipulating the equations algebraically and plugging in numerical values at the end. More commonly, partial differential equations are solved approximately, by number-crunching techniques which would be very laborious without computers. Smooth, continuous space and time are approximated by a closely spaced mesh of points. At each point, in a typical numerical solution, physical quantities such as temperature, pressure, or velocity are represented by 32-bit numbers. A cellular automaton model would probably use the same fine mesh of points in space and time, or possibly a finer one.