We propose a graphics processor unit (GPU)-accelerated method for real-time computing and rendering cellular automata (CA) that is applied to hexagonal grids. Based on our previous work –which introduced first and second dimensional cases– this paper presents a model for hexagonal grid algorithms. Proposed method is novel and it encodes and transmits large CA key-codes to the graphics card and consequently, this technique allows to visualize the CA information flow in real-time to easily identify emerging behaviors even for large data sets. To show the efficiency of our model we first present a set of characteristic hexagonal behaviors, and then describe computational statistics for central processing unit (CPU) and GPU on a set of different hardware and operating system (OS) configurations. We show that our model is flexible and very efficient as it permits to compute CA close to a thousand times faster than classical CPU methods. Additionally, free access is provided to our downloadable software for hexagonal grid CA simulations.