Cellular Laws of Form

April 2022

The paper demonstrates how to simulate visually and intuitively the dynamics of Spencer-Browns Laws of Form using a cellular automaton. First conceived as a tool to visually simulate the Laws of Form, the attempt unfolds certain philosophical implications that could be relevant to the discourse of the form within the form. Among other things, it will be shown how one can intuitively simulate a full adder and parts of the reentry in this cellular automaton. Full adder equations in LoF

For the project, rules were derived for a cellular automaton from which the axioms of Spencer-Brown's system can emerge. A simulator was then developed for demonstration purposes. Konrad Zuse proposed in his paper »calculating space« what might be the internal structure of the universe, namely a cellular automaton (a discrete mathematical model). In the same year 1969, Spencer-Brown independently proposed, through his Laws of Form, a system that has the distinguished observer as its underlying and self-generating structure (see the LoF simulator). Full adder equations in LoF

Interestingly, the necessary rules for the automaton are far more complex than Spencer-Brown's postulated axioms. The implications should be clear.