This is the second post of my series on Cellular Automatons. In this post, I’ll show how I have designed and simulated an 8-bit Cellular Automaton using Logisim.

If you wonder what a Cellular Automaton is, go read my first post.

Elementary block

We’ll start by designing the smallest part of the Automaton: a combinational block that computes the next generation of a cell, given the cell (i1), its two neighbours (i0 and i2) and the rule (8bit). I’ll call it the elementary block:

Basically the 1 bit output is the Nth bit of Rule, where N is {i2,i1,i0}.

Cellular Automaton

This module is the 8-bit Cellular Automaton module: it computes an 8-bit input and outputs the next generation 8 bits.

It is a combinational module made of 8 elementary blocks:

Notice the wriring of the elementary blocks, especially how the block B0 takes i7,i0 and i1 as input, and block B7 takes i6,i7 and i0 as input.

Top module

In the top module we’ll put the Cellular Automaton to use. Upon start, we feed it with the first line of 8 bits (seed), then at each clock cycle we’ll compute the next generation and feed it back in into the Automaton. The current generation will be shown on a row of 8 LEDs.

The top module is made of:

• one 8-bit Cellular Automaton,
• the output is feedback to the input via a register and wired to a row of 8 LEDs,
• the mux on the input feeds the first generation (Seed) upon startup or reset

Simulation in Logisim

You can watch the simulation in Logisim on Youtube:

Files of the project

You can find the logisim project file on Github.

In the next posts of this series I’ll write about the Verilog version of my Automaton (which indeed was the first one I created). If you found this post interesting, don’t hesitate to share it and/or leave a comment.