Cellular Automata (CA) are computational models used in computer science, mathematics, physics, complexity science, and theoretical biology. They consist of a grid of cells, which can be in any number of finite states (like "alive" or "dead" or a range of intermediate values). The grid can be in any number of dimensions but, here, we are using a 3-dimensional grid (i.e., a 3D volume).
Standard CA Process
Grid Setup: The CA consists of a grid where each cell has a state. In 3D cellular automata, this grid is three-dimensional, like a cube made up of smaller cubes.
Initial State: The simulation starts with an initial configuration, where cells are assigned initial states. This could be random, based on certain rules, or a specific pattern set by the user.
Rules: The heart of CA is the set of rules that determine how the state of a cell will change. These rules typically depend on the current state of a cell and the states of its neighbors. For example, a rule might be "a cell turns on if exactly two of its neighbors are on, otherwise it turns off".
Time Steps: The simulation proceeds in discrete time steps. At each step, the rules are applied to all cells simultaneously, creating a new generation of cell states. This is key – the state of all cells is updated based on the previous state, not based on the changing state during the current time step.
3D Cellular Automata metaball structure generated from the Python script
"Meta" CA
In this application, the term "meta" has dual significance.
The structure within this 3D CA is composed of "metaballs". In a graphical context like Blender, metaballs are organic-looking, non-tessellated surfaces. They represent a way to create fluid, amorphous shapes that appear to merge and blend smoothly when they are close to each other. Here, these metaballs serve as an alternative visual representation of the cells within the automaton, differing significantly from the traditional, more explicitly grid-like representations of cells in conventional CAs.
Beyond the visual aspect, the term "meta" reflects the complexity of the rules governing the CA's evolution. Unlike traditional CAs, where the state of a cell is determined primarily by the immediate states of its neighboring cells, 3D Meta CA incorporates additional 'meta' parameters.
Time Series and Nonlinearity
Crucially, 3D Meta CA also explores the concept of time in a non-traditional manner. Unlike standard CAs where the future state of the system is solely a function of its past and present states, this project considers the influence of potential future states on the current visualization.
The same structure converted to a mesh
Lighting test
Placed in a scene using Unreal 5
Interior