Implied

This article is not detailed enough and needs to be expanded. Please help us by adding some more information.

Implied is a cellular automaton created by User:Aadenboy in 2026.

State space

The state space of Implied is an infinite 2D grid. Each cell is either empty, an inactive boolean, an active boolean, or a gate.

• Inactive booleans are constants and are immutable. They represent the values true and false with 1 and 0 respectively.
• Active booleans are constants, and turn into their inactive counterparts after a single tick. They are represented with ! and @ respectively.
• Gates are one of four IMPLY gates. If there are two or more booleans adjacent to it, and at least one of them is active, it will perform its respective computation and turn into the active boolean corresponding to the result.

The CA halts once there are no more active booleans.

Gates

There are four distinct gates.

Gate	Symbol	Formula
IMPLY	i	$a\lor \lnot b$ (implication)
NIMPLY	I	$\lnot a\land b$ (inverse)
CON-IMPLY	c	$\lnot a\lor b$ (converse)
CON-NIMPLY	C	$a\land \lnot b$ (contrapositive)

When a gate has three or four booleans, it operates on them in this order:

gate( gate( gate( left, right ), up ), down )

Constructions

This is still a work in progress. It may be changed in the future.

Wire

Right/left configuration:

000 111
III ccc

Up/down configuration:

i1 C0
i1 C0
i1 C0

NOT gate

Right/left configuration:

0 1
i C

Up/down configuration:

I1 c0

OR gate

Up-left OR:

 a
bi0

Up-right NOR:

 a
1Ib

AND gate

Up-left AND:

 a
bC1

Up-right NAND:

 a
0cb

Implementation

• https://github.com/aadenboy/EsolangInterpreters/blob/main/Implied/interpreter.lua