Nanofunge

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Nanofunge, like Nopfunge, is a fungeoid. It's a 2D esoteric programming language base on 3 commands which is a "subset" of Befunge. The goal of it is to discover the minimum number of commands to make a direction-only language Turing-complete.

Language Overview

Nanofunge, like Nopfunge, is made out of a two-dimensional playfield which can have any size. The infinite repeating part's size is said at the start. For example,

5 5 3 3
   C
 C C<
CCC C
C<<C<
C   C

expands to

   C  C  C  C  C  C  C  C  C 
 C C< C< C< C< C< C< C< C< C<...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...
CCC CC CC CC CC CC CC CC CC C...
C<<C<<C<<C<<C<<C<<C<<C<<C<<C<...
C   C  C  C  C  C  C  C  C  C...

Instructions

Nanofunge has 3 instructions:

Caption text
Command Description
(Space) NOP
< set direction to left
C turn clockwise

Program halts on 2 consecutive ineffective <'s (< when direction is already left)

Computational Class

Turing-complete, because it can be substituted from Nopfunge. Nopfunge space and < are trivial. halt:(4 empty lines before)



 C<<<    
         
  <<<<<< 
C       C
CC     CC

right:

CC  CC   
C    C   
C   C<   
   C  C  
  CC<C   
CC<  CC  
    CC   
  C  C   
        

up:(2 empty lines before)


CC C CCCC
C   CC  C
  CC< <C 
C C      
CC     C 
 CC   CC 
        

down:(1 empty line before)

 C    C  
 C  CC CC
   C C< C
  CC< <C 
 CCCC  C 
   C CCC 
         
         

This proves that Nanofunge IS Turing-complete.