This paper presents a general-purpose simulation approach integrating a set of technological developments and algorithmic methods in cellular automata (CA) domain. The approach provides a general-purpose computing on graphics processor units (GPGPU) implementation for computing and multiple rendering of any direct-neighbor three-dimensional (3D) CA. The major contributions of this paper are: the CA processing and the visualization of large 3D matrices computed in real time; the proposal of an original method to encode and transmit large CA functions to the graphics processor units in real time; and clarification of the notion of top-down and bottom-up approaches to CA that non-CA experts often confuse. Additionally a practical technique to simplify the finding of CA functions is implemented using a 3D symmetric configuration on an interactive user interface with simultaneous inside and surface visualizations. The interactive user interface allows for testing the system with different project ideas and serves as a test bed for performance evaluation. To illustrate the flexibility of the proposed method, visual outputs from diverse areas are demonstrated. Computational performance data are also provided to demonstrate the method’s efficiency. Results indicate that when large matrices are processed, computations using GPU are two to three hundred times faster than the identical algorithms using CPU.