Differential equation and cellular automata model

Cellular automata offered a promising modeling approach to simulate many complex systems. But researchers difficultly design suitable rules for models about real phenomena. And there is rich applied knowledge of differential equations in different fields. Researchers may model complex systems according to this knowledge from differential equations. This paper firstly survey correlative concepts about cellular automata and differential equations, and introduces general approach to design cellular automaton. According to tumor growth of Gompertz continuum differential equation, this article briefly discusses relations between cellular automata and differential equations, and builds a simple cellular automaton according to differential equations. At last this paper analyzes the results from mathematical viewpoint.