Implementing Gompertz model with a one-dimensional cellular automaton

The paper focuses on modeling tumor growth with cellular automata. A one-dimensional cellular automaton is proposed for implementing the Gompertz: model to formulate tumor growth dynamics, which is called Gompertz CA. First, a discrete Gompertz model is derived from the standard Gompertz model. Then, stochastically evolutionary rules for the Gompertz CA are developed based on the discrete Gompertz model. The Gompertz CA is therefore randomized by the stochastically evolutionary rules so that it can be represented with a stochastic process or a stochastic difference equation.