Implied

Implied

Paradigm(s)	cellular automaton
Designed by	User:Aadenboy
Appeared in	2026
Dimensions	two-dimensional
Computational class	Unknown
Major implementations	[1]

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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	$a\lor \lnot b;a\Rightarrow b$ (implication)
NIMPLY	I	$\lnot a\land b;a\nRightarrow b$ (inverse)
CON-IMPLY	c	$\lnot a\lor b;b\Rightarrow a$ (converse)
CON-NIMPLY	C	$a\land \lnot b;b\nRightarrow a$ (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 III ccc ccc
    000     111

Up/down configuration:

i1 1i C0 0C
i1 1i C0 0C
i1 1i C0 0C

NOT gate

Right/left configuration:

0   1
i i C C
  0   1

Up/down configuration:

I1 1I c0 0c

OR gate

Left OR:

 a
bi0 bi0
     a

Right NOR:

 a
1Ib 1Ib
     a

AND gate

Left AND:

 a
bC1 bC1
     a

Right NAND:

 a
0cb 0cb
     a

Implementation

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