User:UnmatchedBracket/2Lproof

It can be proven that 2L is Turing-complete by making a translation table from Brainfuck (a known Turing-complete language) to 2L. This document shows how to translate any Brainfuck program (minus input and output, which are not necessary for Turing-completeness) to 2L.

None of this is even vaguely optimal; there are infinitely better ways to do anything you could do by copying in these blocks. This page only serves to prove that 2L is Turing-complete.

In the flow animations below, red indicates a 0 at the data pointer and green indicates anything else.

Simply take the 2L blocks and stack them horizontally, starting with this block:

2L block	Flow
_ _ _ _ +

Brainfuck to 2L conversion table

Brainfuck command	2L block	Flow animation	Note
+	_ _ _ *
-	__________ __+__+____ ___++___+_ ______+___ _+__*__+__ _+___+____ +________+ __+____+__ ________+_
>	_______ __+____ _+___+_ ___+___ _+__+*_ +_____+ __+_+__ _____+_
<	_______ __+____ _+___+_ ___+___ _+*_+__ +_____+ __+_+__ _____+_
[	_____+___ _+_______ _+_____+_ ______+__ ____+____ ___+____+ _____++__ ___+___+_ _________ _________ __+_+____ +________ _______+_ _+_______		For sub-loops, you will need to put the bottom block down farther: __+_+____ +________ _______+_ _+_______
]	______ _+____ +___+_ __+___ ___+__ ______ ______ ______ ______ _____+ __++__ ___++_ _+____		For sub-loops, you will need to put the bottom block down farther: _____+ __++__ ___++_ _+____