There are four cellular automaton(CA) models, namely cellular automata, stochastic CA model, continuous cellular automaton and dynamic CA algorithm based on time compensation^{[33] ,[34],[35]}. The following part mainly introduces the cellular automaton and continuous cellular automaton which are widely used.

The main research object of this model is the etching process and contour evolution. This model class is applied to any complex two-dimensional three-dimensional structures, and simulate various types of etching and materials to achieve high-precision and high-efficiency simulation. However, as the simulation intensity improves, the simulation efficiency will decrease^{[16]}.

CA is a dynamic system with discrete space and time. The cell is used to describe the current state of the relevant spatial location. It defines the spatial evolution rule based on the neighboring environment for each cell by defining spatial evolution rules in discrete time dimensions. It uses the cell array in the crystal grid to describe the base material, determine the connection state between adjacent cells, and determine the rules for the current cell movement ^{[36]}. The key to this model is the determination of the movement rules and etch rate. Discrete cell arrays can simulate any complex mask patterns, however since each cell in the grid can only be in one of the "removed" or "retained" state, it cannot reflect the true etch rate on different crystal faces. Therefore, this model’s simulation accuracy is relatively low.

The random CA model uses random elements to describe the true etch rate on different crystal planes and can be used to process any etch rate on the main lattice axis. However, this artificially causes the surface to be rough, making the edges and planes difficult to distinguish, and it is not convenient to directly observe the simulation results.

Continuous CA model allows the cells in the system to have non-discrete state variables, the range of values is [0, 1], and it allows for any etch rate in the direction of the main axis, avoiding artificially roughening the surface and improving analog accuracy. The cell mass M is its non-discrete state variable. It can be assumed that any state of a cell is between M=0 (etched) and M=1 (without etching), and the value of M is related to the cell’s movement trend. Based on the active cell movement rule in the non-discrete element state, the prediction of three-dimensional shape under arbitrary etchant and etch rate conditions can be realized ^{[37] ,[38]}. In the continuous cellular automaton (CCA), the occupancy rate for representing the cell state is continuous during the update iteration, which further enhances the applicability and accuracy of the CA method. The CCA model and the calculation flow are shown in the Figure 4 and Figure 5.

**Figure 4.
**CCA schematic model structure.**Figure 5.
**CCA model calculation flow chartLater on, in order to reduce the memory requirements of this algorithm, a dynamic CA algorithm based on time compensation was developed. This algorithm improves the simulation speed and lowered the memory requirement. And it can be used to simulate the entire process flow results with several sequential processing steps.