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I'm a high school student, and I have to write a 4000-word research paper on mathematics (as part of the IB Diploma Programme). Among my potential topics were cellular automata and the Boolean satisfiability problem, but then I thought that maybe there was a connection between the two. Variables in Boolean expressions can be True or False; cells in cellular automata can be "On" or "Off". Also, the state of some variables in Boolean expressions can depend on that of other variables (e.g. the output of a Boolean function), while the state of cells in cellular automata depend on that of its neighbors.
MIT: Writing a Research Paper in Mathematics