As I foresee, I would be working on something related to lattice Boltzmann method. Therefore, I am very serious and curious about the fundamentals behind LBM. I would be writing about the very basic idea it is based on. It is called *cellular automata* and the easiest one of that to understand is: one dimensional cellular automata.

First question? What is it? Imagine chairs assembled in a line. There are two possibility for each of these chairs: they could either be occupied or vacant i.e. if I say binary, a chair (*cell*) would be either 0 (vacant) or 1 (occupied). This is the first picture of cellular automata. So, if I say there are 10 chairs, then there could be 2^{10 }possible pictures that one might see at the beginning (initial condition).

What next? Is this it? NO! Now we define some kind of **rule** which will define the evolution of this cellular automata with time. One of the properties of CA is that the future state of a cell depends on the “immediate” past state of itself and its neighbors. For example: In the case of 10 chairs, I can define a rule that if a chair is vacant between two occupied chairs, it becomes occupied. In a mathematical sense, 101 becomes 111. It should be noticed that I am considering the effect of only one chair on *either* side of the cell under consideration and this is what we technically call **range. **This is the rule with range equals one.

Why should I know this? Is it useful? As much as I know about it, it is fundamental and mathematical in its sense. **You need to learn alphabets before making words.** So, I think of it as a alphabet in making a really big word. Specially, two dimensional automata cases with advancements are useful. These have the capability to determine the motion of fluid flow and this mathematics can be embedded in a code for simulations. This particularly is of most interest to me.

If anyone wants to read more about CA, I would recommend them this.

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